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ReviewMarch 9, 2016

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and Experiment
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Cite this: Chem. Rev. 2016, 116, 9, 4937–4982

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https://doi.org/10.1021/acs.chemrev.5b00507

Published March 9, 2016

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Abstract

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Natural anthocyanin pigments/dyes and phenolic copigments/co-dyes form noncovalent complexes, which stabilize and modulate (in particular blue, violet, and red) colors in flowers, berries, and food products derived from them (including wines, jams, purees, and syrups). This noncovalent association and their electronic and optical implications constitute the copigmentation phenomenon. Over the past decade, experimental and theoretical studies have enabled a molecular understanding of copigmentation. This review revisits this phenomenon to provide a comprehensive description of the nature of binding (the dispersion and electrostatic components of π–π stacking, the hydrophobic effect, and possible hydrogen-bonding between pigment and copigment) and of spectral modifications occurring in copigmentation complexes, in which charge transfer plays an important role. Particular attention is paid to applications of copigmentation in food chemistry.

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SPECIAL ISSUE

This article is part of the Noncovalent Interactions special issue.

1 Introduction

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Copigmentation is a fascinating natural process based on noncovalent (supramolecular) complexation. It has been shown to be the main mechanism by which certain colors, particularly blue, violet, and red, are stabilized and modulated in flowers, (1) vegetables, and fruit (in particular, berries), as well as food products derived from them (in particular, wine, (2) but also jams, purees, and syrups). The term “copigmentation” is commonly reserved for anthocyanins, a large class of phenolic derivatives spread over the plant kingdom. Because of their extended π-conjugated systems, they absorb in the visible range and can readily form supramolecular assemblies with other pigments and cofactors (so-called, in this case, copigments), mainly phenolic acids and flavonoids (Scheme 1). Other pigments/dyes are also known to form supramolecular assemblies, for example, carotenoid aggregates. (3) However, this aggregation is usually not termed “copigmentation” because this process is primarily driven by self-association governed by dispersion interactions. (4)

Scheme 1. Prototypical Copigmentation Complexes^a

The definition of copigmentation has been refined over time, and recently by complementing experimental investigations with accurate computational studies. The atomistic understanding of copigmentation is inevitable to better understand, on the one hand, the diversity of color in nature, (5) but on the other hand, the process of color stabilization. Indeed, there has been growing interest for the latter issue in the food industry, which aims at using and controlling copigmentation by addition of copigments in food products to enhance the color palette, in direct relation with consumers’ perception. Here, modern food engineering requires a precise (computer-aided) control of the noncovalent supramolecular pigment-copigment assemblies.

This review links experimental and theoretical chemistry approaches to a coherent interdisciplinary understanding of copigmentation, which has been enabled by the recent developments in computational methodology. We aim at providing a comprehensive picture of the current knowledge in copigmentation, mainly concerning driving forces and structure-affinity relationships between pigments and copigments. With reference to several examples (including blue flowers, wine, and other food products), sections 2 and 3 describe the families of pigments and copigments that are most likely to exhibit copigmentation. Section 4 describes the experimental tools to study copigmentation, mainly based on UV–vis absorption spectroscopy, NMR (nuclear magnetic resonance), CD (circular dichroism), and X-ray crystallography. Stability of inter- and intramolecular copigmentation complexes is discussed in sections 5 and 6, respectively, based on experimental data. Section 7 then details all possible driving forces that are involved in the copigmentation process. Section 8 introduces molecular mechanics (MM) and molecular dynamics (MD) methods that can be used to sample the conformational space of supramolecular pigment-copigment assemblies. The use of MD-based methods to estimate enthalpies and Gibbs energies of association is also discussed. Section 9 describes the quantum mechanics (QM)-based methods that can be used to accurately describe the noncovalent interactions involved in copigmentation. Section 10 rationalizes the UV–vis spectral shifts upon copigmentation based on time-dependent density functional theory (TD-DFT) calculations and excited state description, allowing elucidation of the electronic origin through Molecular Orbital (MO) analysis. Finally, a summary and outlook are given in Section 11.

2 Pigments and Copigments

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2.1 Pigments

Anthocyanins are intriguing natural compounds that are responsible for the color of many plants. Their study was pioneered by the German chemist R. Willstätter, who conducted extensive investigations into their properties, as reported in his “Untersuchungen über die Anthocyane” monograph. (6) Anthocyanins were subsequently shown to be a subclass of the flavonoids present in numerous flowers, leaves, fruit, and vegetables as well as beverages made from fruit, notably red wine but also some fruit juices and even some pink ciders. Anthocyanins are commonly referred to as pigments (i.e., a coloring agent plants). It should be remarked however that different to the use in biology, “pigment” in strict terms is used for nonsoluble colorants, whereas soluble colorants are named “dyes”. Although anthocyanin-based crystals have been observed in plants, (7) these compounds are mainly water-soluble and exist in solution, in the vacuoles of plant cells.

2.1.1 (Proto)typical Pigments

As of the time of writing, almost 1000 plant-derived anthocyanins have been identified. An exhaustive list of these pigments is beyond the scope of this review; partial lists can be found in various books and other review papers. (8, 9)

Twenty-three anthocyanidins that mainly differ in terms of their B-ring hydroxyl and methoxyl substitution patterns have been identified in fruit and vegetables. (8) Six of these 23 compounds are particularly abundant, namely cyanidin, delphinidin, malvidin, pelargonidin, peonidin, and petunidin (see Figure 1). Most anthocyanins are 3-O-glycosides. Approximately 50% of the known anthocyanins feature the cyanidin moiety. Compared to those derived from fruit and vegetables, anthocyanins from flowers tend to have a higher degree of glycosylation and acylation. The most common sugar moiety is d-glucose, but anthocyanidins are also often conjugated to l-rhamnose, d-xylose, d-galactose, arabinose, and fructose as well as rutinose (6-O-α-l-rhamnosyl-d-glucose), sophorose (2-O-β-d-xylosyl-d-glucose), gentiobiose (6-O-β-d-glucosyl-d-glucose), sambubiose (2-O-β-d-xylosyl-d-glucose), xylosylrutinose, and glycosylrutinose.

Figure 1. Chemical structures of anthocyanidins (R₃ = OH) and anthocyanins (R₃ = glucose).

Most detailed studies on anthocyanins are found for red wine driven by the need for understanding and control of wine color. The main anthocyanins in red wine are the 3-O-monoglucosides of five major anthocyanidins [i.e., cyanidin-3-O-glucoside (kuromanin), delphinidin-3-O-glucoside (myrtillin), peonidin-3-O-glucoside (peonin), petunidin-3-O-glucoside (petunin), and malvidin-3-O-glucoside (oenin), see Figure 1]. The last of these compounds is by far the most abundant. (9)

Many anthocyanins are acylated (generally at the C6-OH group of a glucose moiety), with either an aliphatic acid (e.g., acetic, malic, malonic, oxalic, or succinic acid) or a phenolic acid (e.g., p-hydroxybenzoic, caffeic, p-coumaric, ferulic, or sinapic acid). There are hundreds of known anthocyanins bearing multiple acyl groups linked to linear or branched oligosaccharides bound to the A-, B-, and/or C-rings of the anthocyanidin nucleus. (10)

As demonstrated over the past decades, wine is a very complex system of dissolved and suspended pigments in which many chemical reactions involving anthocyanins occur including electrophilic aromatic substitutions on the electron-rich A-ring (hemiketal form) of the flavylium cation and nucleophilic addition to the electrophilic pyrylium ring (C-ring). (11, 12) Consequently, a large variety of anthocyanin derivatives is formed during wine preparation and aging, including flavanol-anthocyanin adducts (with or without CH₃–CH bridges originating from ethanal formed by EtOH oxidation), anthocyanin dimers and related polymers, pyranoanthocyanins (e.g., vitisins A and B, oxovitisins), pyranoanthocyanin-phenols, pyranoanthocyanin-flavanols, the more recently discovered vinylpyranoanthocyanin-flavanol portisin, which is bluish at acidic pH (Figure 2), and pyranoanthocyanin dimers. (11, 13-17) Most of these pigments form as the wine is stored and aged in bottles or barrels. All pyranoanthocyanins are colored as well as more than 50% of their ethyl-linked derivatives. These new pigments are known to (i) induce color shifts from red to orange or purple/blue; (18, 19) (ii) enhance color intensity (i.e., to exert hyperchromic effects on the visible absorption band); and (iii) enhance resistance to water and sulfite addition and subsequent bleaching. They have extended π-conjugated systems and/or a comparatively high propensity for self-association, which allows colored forms to remain stable at higher pH values independently of any copigmentation effect.

Figure 2. Chemical structures of pyranoanthocyanins (flavylium cation form).

2.1.2 Chemistry of Anthocyanins

Anthocyanins are O-glycosides of anthocyanidins (i.e., 3,4′,5,7-tetrahydroxyflavylium ions with additional OH and/or OMe groups at the C3′ and/or C5′ positions) (Figure 1). When considering their structures, anthocyanins are depicted in their flavylium cation (AH⁺) form. However, extensive studies on their chemistry (20, 21) have demonstrated that they can exist in various colored and colorless forms; the form that predominates under any given set of conditions is largely determined by pH. This chemistry is somewhat beyond the scope of this review, and it is assumed that the reader is broadly familiar with the contents of some recent reviews of this field (see for example refs 22 and 23). However, to understand copigmentation and its consequences for the expression of natural colors, it is necessary to clearly recall the structural transformations that anthocyanins can undergo in aqueous solution. Therefore, these transformations are briefly summarized below (see also Figure 3).

Figure 3. Structural transformations of anthocyanins in acidic to neutral solution. Proton loss from C5-OH omitted for simplicity.

The AH⁺ form only predominates at very low pH values; experimentalists usually work below pH = 2 to ensure its exclusive presence in solution. In the pH range of interest in plants and plant products (pH = 3–8), anthocyanins are diacids with two successive pK_a values of about 4 and 7. Thus, AH⁺ loses a proton under mildly acidic conditions and is converted into a mixture of neutral quinone methide tautomers, which are known as bases, formed after the deprotonation of one of the three most acidic phenolic OH groups (C7-OH, C4′–OH, or C5-OH, respectively). These quinonoid bases (A) lose a second proton around neutrality to form the anionic quinonoid bases (A^–). Above pH = 2, the flavylium cation of common (nonacylated) anthocyanins also becomes prone to water addition (hydration) at C2 to form a mixture of colorless hemiketal epimers (B or AOH) that exist in a fast cycle-chain equilibrium with a cis-chalcone tautomer (C_cis), itself in slow equilibrium with the trans-chalcone (C_trans). The thermodynamic constants of these three equilibria are designated K_h (hydration), K_t (hemiketal-chalcone tautomerization) and K_i (cis–trans chalcone isomerization), respectively. The overall hydration equilibrium connecting AH⁺ and the other forms at equilibrium, is given by the overall thermodynamic constant K_h^′:

(1)

The anthocyanidin core is a fully delocalized π-conjugated system, which is why these compounds can absorb visible light. However, the color is strongly affected by pH and hydration (see Figure 3). Namely, AH⁺ is usually red, the different forms of A are purple, and the A^– anions are blue. Proton transfers cause (i) bathochromic (red) shifts of the lowest-energy visible absorption band, (ii) band broadening, and (iii) decreases in absorbance that are known as hypochromic effects. (24) In addition, B is colorless while both the C_cis and C_trans isomers are yellowish. Thus, based solely on their structural and electronic features, anthocyanins can exhibit many hues in solution. Depending on the conditions, their absorption may be UV-only (making them colorless) or may extend over the entire visible spectrum.

With natural anthocyanins, K_t and K_i are lower than 1, and chalcones only make a minor (<20%) contribution to the global pool of colorless forms. The pK_h^′ value, which is a relevant indicator of color stability, normally falls in the range from 2 to 3. Thus, considering the competitive fates of AH⁺ (i.e., proton loss vs water addition), it can be stated that hydration is thermodynamically favored. However, it is much slower than proton loss. In other words, in the reversible competitive fates of AH⁺, the hemiketal (the most abundant colorless form) is the thermodynamic product while the tautomeric quinonoid bases are the kinetic products. Thus, at the pH values found in beverages or living plant cells, the concentration of strongly colored anthocyanin forms should in principle be low at equilibrium. However, the half-life of these colored forms is strongly pH-dependent and typically ranges from a few seconds at pH = 3 to several minutes at pH = 5–6. This is mainly because the proportion of electrophilic AH⁺ in solution (which is the only colored form capable of undergoing water addition) declines as the pH is raised. The competition between the different forms can be illustrated with reference to the 3′,4′-dihydroxy-7-O-β-d-glucopyranosyloxyflavylium cation, a simple anthocyanin analog with no C3 substituent (Figure 1). In this case, C_trans accumulates and is the only significant colorless form present at equilibrium, as shown in Figure 4. (25)

Figure 4. Structural transformations of the 3′,4′-dihydroxy-7-O-β-d-glucopyranosyloxyflavylium ion. (A) Fast formation of the quinonoid base. Spectral measurements immediately after addition of pigment to buffer, pH = 2.0 → pH = 6.0. (B) Slow accumulation of *trans*-chalcone (C_trans). Spectral measurements on solutions equilibrated overnight, pH = 2.0 → pH = 4.0. Adapted with permission from ref 25. Copyright 2013 Elsevier Ltd.

2.2 Copigmentation

The pH effects and chemical variation (specifically, structural transformations, and different patterns of functionalization, mostly in the B-ring) alone cannot satisfactorily explain the great diversity of anthocyanin-derived hues observed in plants. This diversity is largely attributable to a process termed “copigmentation”. Copigmentation can be defined as (i) the formation (in the presence or absence of metal ions) of noncovalent complexes involving an anthocyanin or anthocyanin-derived pigment (e.g., a pyranoanthocyanin or anthocyanin-flavanol adduct) on the one hand and a copigment on the other (Scheme 1) and (ii) the subsequent changes in optical properties of the pigment.

2.2.1 Types of Copigments

There are over ten-thousand compounds that could potentially serve as copigments. While an exhaustive list will not be provided, they can be classified into a number of distinct categories, thus giving an idea of the large number of plausible pigment-copigment pairs.

In general, copigments should have (i) sufficiently extended π-conjugated systems, which are supposed to favor π–π stacking interactions (see sections 5 and 7 for more details) and (ii) hydrogen bond donor/acceptor groups such as OH and C═O groups. The major natural copigments that have been identified are hydrolyzable tannins, flavonoids, and phenolic acids. Flavonoid copigments include flavonols, flavones, flavanols, and even dihydroflavonols (Figure 5). Due to extension of their π-conjugation over their entire tricyclic core structure (rings A, B, and C), flavones and flavonols (e.g., quercetin, kaempferol, isoquercitrin, (26) and rutin) appear to be the most efficient copigments (i.e., those that provide the strongest bathochromic and hyperchromic effects) and which have the highest Gibbs energies of association (see next sections for more details on binding energies and structure-affinity relationships).

Figure 5. Chemical structures of series of copigments.

Various hydroxycinnamic acids (HCA) and derivatives such as caffeic, p-coumaric, ferulic, sinapic, chlorogenic, and caftaric acids (Figure 5) are commonly described as relatively efficient copigments, with potencies comparable to those of flavanols and dihydroflavonols; (27) benzoic acids are generally less efficient copigments than HCAs. (28-32) HCAs are usually more efficient if they are linked to the pigment via acylation of a glycosyl group in a way that offers sufficient conformational flexibility for the pigment and copigment to be in close contact and form noncovalent intramolecular interactions (see section 6 for more details).

Anthocyanins themselves can also be regarded as copigments because self-association can be seen as a special case of copigmentation in which the two partners are colored if they both exist in the AH⁺, A, or A^– forms. Although it is generally less efficient than copigmentation (at least with common nonacylated anthocyanins), self-association has been widely observed (see section 5). Some nonphenolic copigments have also been described, including alkaloids, amino acids, organic acids, nucleotides, and polysaccharides, (9) but their efficiency is typically much lower than that of polyphenols; it is still unclear whether such compounds can significantly contribute to color expression by anthocyanins.

2.2.2 Key Historical Milestones

The copigmentation phenomenon was first discussed in 1916 by R. Willstätter and E. H. Zollinger, (33) who noticed that the hue of the grape pigment oenin (malvidin 3-O-glucoside) could be changed by the addition of tannin or gallic acid. This was initially believed to be a rare phenomenon specific to oenin. R. Robinson subsequently investigated these findings in more detail and defined a copigment as a “substance in solution which intensifies and modifies the colour”; the terms “co-pigment” and “co-pigmentation” have later been replaced by “copigment” and “copigmentation”, respectively. As a particular advanced concept, he discussed the modulation of anthocyanins’ optical properties (bluing effects) in terms of intra- and intermolecular interactions. (34) Much later, S. Asen, R. N. Stewart, and K. H. Norris described bathochromic shifts in pigment-copigment pairs. (7, 35) These authors stressed the crucial influence of the copigment concentration. (36) Copigmentation was thus described as a concentration-dependent process that is also sensitive to pH, temperature, and solvent. (37) The authors concluded that “the phenomenon of copigmentation offers a more logical explanation of the infinite variation in red to blue flower colors that exists in a pH range where anthocyanins alone are virtually colorless” and proposed for the first time that anthocyanins (e.g., aureusin from Yellow Rocket snapdragons) may be able to self-associate, which can also induce shifts in visible absorption bands. (38)

A few years later, T. Hoshino and T. Goto made a key contribution to the understanding of anthocyanin copigmentation (Scheme 2A) and self-association (Scheme 2B) by using CD experiments to demonstrate anthocyanin self-association. (39-44) This was made possible by the sensitivity of CD to the chirality of supramolecular assemblies. Their results confirmed that anthocyanin quinonoid bases can self-associate in water but not in DMSO. (39, 42) The forces driving self-association were identified as “hydrophobic interactions among the aromatic nuclei stacked parallel to each other”. The authors considered vertical stacking driven by π–π interactions more likely than horizontal stacking driven by hydrogen bonding. (42) Interestingly, stacking between the neutral forms led to spectral shifts whose magnitude was comparable to those induced by the stacking of adjacent base pairs within DNA; the corresponding association constants were even larger than those observed for nucleic acids in solution. (45)

Scheme 2. π–π Stacking Interactions in Anthocyanins and Their Complexes^a

During roughly the same period, R. Brouillard proposed an advanced method for investigating the thermodynamics of copigmentation, which provided fundamental insights into the mechanisms of association between pigment and copigment. In particular, Brouillard et al. emphasized the importance of considering all of the equilibrating species when estimating the copigmentation binding constant. (46) This is important because copigmentation shifts the proton transfer and hydration equilibria (potentially suppressing the hydration reaction when AH⁺ is part of the copigmentation complex), thus limiting the formation of colorless compounds. This phenomenon is known as color stabilization. Brouillard et al. confirmed that the main driving force of pigment-copigment binding is the hydrophobic effect. Intramolecular copigmentation was later observed in acylated anthocyanins; (47, 48) in such cases, the pigment and copigment are covalently linked by a glycosyl spacer, allowing the two partners to come into close contact and form noncovalent interactions (Scheme 1). These authors also showed that copigmentation is dramatically weakened by the presence of organic cosolvents.

3 Pigment···Copigment Complexes in Nature

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Virtually all plant organs that biosynthesize anthocyanins and flavonoids or phenolic acids could potentially provide pigment···copigment complexes (Schemes 1A and 2A), although in some cases they have only been hypothesized. Many binary systems (forming intermolecular copigmentation complexes, see Schemes 1A and 2A) have been studied by mixing a pigment and a copigment directly in solution, which is supposed to mimic plant and food environments. In two representative recent examples, oenin was mixed with five hydroxybenzoic acids (49) and with increasing concentrations of catechin, epicatechin, epigallocatechin, epigallocatechin gallate, procyanidin B3, and prodelphinidin B3. (50) Such studies performed in solution under various conditions (i.e., at different pH values and concentrations, in different solvents) have provided information on structure–efficiency relationships, as discussed in section 5.1. Many (poly)acylated anthocyanins have been reported, and such pigments may be involved in complex molecular assemblies that exhibit self-association and/or intra- or intermolecular copigmentation (Schemes 1B and 2). (1)

In addition to simple studies in solution, many pigment···copigment systems have been investigated directly in plant and food matrices. Copigmentation has been studied intensively in blue flowers, which have attracted particular interest for many decades; there have been a number of reviews covering this field, including a recent one by Yoshida et al. (1) Over the past decade, numerous works have also examined copigmentation in wine, and in all food matrices in which copigmentation is likely to occur (see sections 3.2 and 3.3). The next three sections discuss copigmentation in these three representative environments.

3.1 Copigmentation in Blue Flowers

In ancient Greek, “antho” means flower and “cyanin” comes from cyan (blue); indeed, anthocyanin coloration is closely linked to blue and violet flowers such as hydrangea (hortensia), pansy, tulip, and morning glory. However, in mildly acidic to neutral conditions, blue flowers would hardly be blue without copigmentation; instead, they would be yellow or even colorless. The development of blue coloration has been studied intensively over the last 50 years or so.

As explained in the review by K. Yoshida, M. Mori, and T. Kondo, (1) the role of metal ions in copigmentation was initially ignored. This is partly because there are many known nonmetallic pigment···copigment assemblies in blue and violet flowers, such as gentiodelphin (from the blue Gentiana makinoi), heavenly blue anthocyanin (HBA from Ipomoea tricolor cv. HeavenlyBlue) and ternatin (from Cliteria ternatea). These systems feature anthocyanins that bear (poly)acylated branched chains on both A- and B-rings, the C-ring, and the B-ring, respectively (Figure 6). In aqueous solution, these chains adopt conformations that allow aromatic acyl moieties to stack on both sides of the anthocyanidin chromophore (Scheme 2C), thereby stabilizing the blue quinonoid form. Other polyacylated anthocyanins have different stabilizing copigmentation mechanisms. In tecophilin (from Tecophilaea cyanocrocus) and cyanodelphin, which both bear branched polyacylated chains on their A-rings (Figure 7), intra- and intermolecular stacking may occur simultaneously (Scheme 2E). Similar arrangements were proposed for phacelianin, alatanin, and petanin, all of which have linear (poly)acylated chains on the C-ring, and also for two other pigments, one from Matthiola incana with branched polyacylation on the C-ring and another that is linked to a flavonoid moiety (Figure 8). Fossen et al. also reported a covalently linked anthocyanin-flavone C-glycoside copigmentation system (Figure 9A) that was isolated from the leaves of Oxalis triangularis. (51) Two other pigments were found in Allium “Blue Perfume” (Figure 9B), which exhibited intramolecular copigmentation (i.e., they featured an anthocyanin core linked to a flavonoid via an acylglycoside moiety with sufficient conformational flexibility so that the chromophore and the flavonoid could come into close contact). (52) There is only indirect evidence of intramolecular stacking between pigment and copigment in these polyacylated anthocyanins, mainly derived from UV–vis absorption spectroscopy, CD, and NMR. Unfortunately, X-ray crystallography cannot be used to study these systems due to the difficulty of growing crystals of such labile molecular assemblies.

Figure 6. Chemical structures of three nonmetallic pigment···copigment assemblies.

Figure 7. Chemical structures of two polyacylated anthocyanins.

Figure 8. Chemical structures of polyacylated anthocyanins.

Figure 9. Anthocyanin-flavone C- or O-glycoside pigments with a malonate bridge from leaves of (A) *Oxalis triangularis* and (B) Allium “Blue Perfume”.

Copigmentation also occurs within metalloanthocyanin supramolecular complexes in petal cell vacuoles (Scheme 2F). (1) Copigments simply stack within metal–anthocyanin complexes (i.e., there is no binding between metal ion and copigment) or are connected to the anthocyanin via metal binding (a special case of intramolecular copigmentation). The structure of commelinin, the blue crystalline pigment of Commelina communis, (53) was elucidated for the first time in 1992. The structural description of this complex was based on the metal complex theory for blue color development, which was originally proposed by Shibata et al. (54) and brought to wider awareness by Yoshida et al. (1) It was shown to exist as a fascinating helical aggregate (see Figure 10 and section 5.4. for more details).

Figure 10. Structure of commelinin. Blue: malonylawobanin (MA), yellow and orange: flavocommelin (FC), red: Mg²⁺(A). A side view of a left-handed stacking of two MA units that coordinate to different Mg ions. (B) A side view of a copigmentation of MA and FC in a right-handed stacking arrangement. (C) A side view of a left-handed stacking of two FC units. (D) A side view of commelinin. (E) A skew view of a copigmentation between MA and FC. (F) A skew view of the self-association of two FC units. Adapted with permission from ref 1. Copyright 2009 The Royal Society of Chemistry.

Many other metalloanthocyanin complexes have since been isolated and characterized, featuring various pigments (in various charge states), copigments, and metal ions. For example, the blue color of Ceanothus papillosus petals results from the intermolecular copigmentation of a polyacylated anthocyanin pigment (Figure 11) in its quinonoid base form with kaempferol 3-O-glycoside (Scheme 2, stackings A and F). (55) Protocyanin is the blue pigment of cornflower petals (Centaurea cyanus); crystallographic analysis suggests that it has a supramolecular structure of well-defined stoichiometry with stacking between a flavone derived from apigenin (6 equiv) and a cyanidin derivative (6 equiv), with two different coordinated metal ions (Fe³⁺ and Mg²⁺) that stabilize the quinonoid base (Figure 12). Some other stoichiometric metal-pigment-copigment complexes are presented in Table 1.

Figure 11. Chemical structure of the anthocyanin derived from *Ceanothus papillosus* petals.

Figure 12. (A) Structure of protocyanins from *Centaurea cyanus* (cornflower). (B) X-ray diffraction crystal structure, showing the two metal ions Fe³⁺ and Mg²⁺ in the center of the supramolecular assembly. Adapted with permission from ref 1. Copyright 2009 The Royal Society of Chemistry.

Table 1. Metal-Complex Pigments

common name	anthocyanin	copigments	metal	stoichiometry/pHv (vacuolar pH)	λ_max (nm)	source	ref
stoichiometric metal-pigment-copigment complexes
commelinin	delphin 3-(6-p-coumaroylglucoside)-5-(6-malonylglucoside)	6-glucoside 4′-O-glucosylapigenin	Mg²⁺	6 A: 6F: 2M	646	Commelina communis	56
protocyanin	cyanidin-3-O-(6-O-succinylglucoside)-5-O-glucoside	apigenin-7-O-glucuronide-4′-O-(6-O malonylglucoside)	Mg²⁺; Fe³⁺	6–8 A: 6–8F: 2M	676	Centaurea cyanus (corn flower)	57
protodelphin	delphin 3-(6-p-coumaroylglucoside)-5-(6-malonylglucoside)	7,4′-O-diglucosylapigenin	Mg²⁺	6 A: 6F: 2M	–	Salvia patens	58
cyanosalvianin	delphin 3-(6-p-coumaroylglucoside)-5-(6-acetylmalonylglucoside)	7,4′-O-diglucosylapigenin	Mg²⁺	6 A: 6F: 2M	–	Salvia uliginosa	59
nemophilin	petunin 3-(6-p-coumaroylglucoside)-5-(6-malonylglucoside)	7-O-glucoside 4′-(6-malonylglucosyl)apigenin	Mg²⁺; Fe³⁺		712	Nemophila menziesii	1
		7,4′-O-diglucosylapigenin
nonstoichiometric metal-pigment-copigment complexes
	delphinidin-3-glucoside	caffeoyl and coumaroyl derivatives of quinic acid	Al³⁺, 4,5 equiv	pHv = 3.6 ± 0.3	586	Hydrangea macrophylla (blue color)	60,61
	delphinidin-3-glucoside	caffeoyl and coumaroyl derivatives of quinic acid	Al³⁺, 1,2 equiv	pHv = 3.3 ± 0.2	539	Hydrangea macrophylla (red color)	60,61
	cyanidin-7-O-glucoside-3-O-(2-O-glucosyl)-glucoside	kaempferol derivatives	Mg²⁺; Fe³⁺	pHv = 4.8	646 and 606	Meconopsis grandis	62,63
	malvidin 3-O-glucoside-5-O-(6-O-acetylglucoside)	3-glucoside and 3-sophoroside of kaempferol and myricetin	–	pHv > 5.5		Geranium	64
	malvidin 3-O-(4-O-p-coumaroyl-rhamnosyl-6-O-glucoside)-5-O-glucoside	isovitexin (apigenin-6-C-glucoside)	–			Iris ensata	65
	Petunidin, delphinidin

3.2 Copigmentation in Wine

During winemaking and aging (in barrel or bottle), the initial red-purple color originating from the grapes is modified. Wine is by far the most studied beverage in which copigmentation has been repeatedly confirmed. It has been suggested that some of the reported copigments may originate from oak barrels in which the wine was stored, but this suggestion must be treated with some caution because the corresponding color modifications have not been comprehensively documented. (2) Regardless, grape contains significant amounts of flavonoids (flavonols and flavanols), phenolic acids, and mainly their derivatives such as caftaric acid largely found in wine. All these compounds favor the occurrence of copigmentation at all stages of winemaking. During storage, the levels of anthocyanins decline rapidly but those of copigments (e.g., the total quantity of flavonols) do not decrease over a month timescale. (66) This suggests that copigmentation in the beverage competes with other chemical reactions involving anthocyanins. Because it stabilizes the anthocyanins’ coloration, copigmentation has a strong influence on the perceived color of wine; it has been shown to be responsible for 30–50% of the coloration in young red wines. (2, 9, 67, 68) Anthocyanin copigmentation and self-association in wine can be demonstrated by gradually diluting young red wines at a constant pH, so as to at least partially dissociate the pigment···copigment and pigment···pigment complexes. Because of this dissociation, Beer’s law is not obeyed upon dilution, and a nonlinear color loss is observed. (2)

To estimate the extent of copigmentation in wine, the pigment and copigment contents of the different grape fractions (i.e., skin, pulp, and seeds) and different wine varieties must be carefully determined. (69) In wines, the total anthocyanin content varies from 150 mg/L (ca. 305 μM in oenin equivalents) to 800 mg/L (ca. 1620 μM) in some Pinot noir and Merlot wines, respectively. Most red wines contain ca. 300–500 mg/L of the most abundant anthocyanin (oenin) and thus have more than ten times the amount needed (ca. 35 μM, i.e., 17 mg/L) to enable sensitive detection of copigmentation in the visible range. (2)

Red wines contain many copigments. For example, in a study examining 34 hybrid grape varieties (22 red and 12 white), (70) 24 flavonol glycosides were identified, including derivatives of quercetin, myricetin, kaempferol, isorhamnetin, laricitrin, and syringetin. Other weaker copigments can be even more abundant in wine; for example, one publication reported a total concentration of phenolic acids and flavanols of 150 mg/L (800 μM in caffeic acid equivalents), compared to a total concentration of 30 mg/L (100 μM in quercetin equivalents) for myricetin, kaempferol, and quercetin. (2) Dihydroflavonols may also occur in wine and function as copigments, (27) although they are usually less abundant than other phenolic copigments. Overall, the copigment/anthocyanin molar ratios in wine are likely to be somewhere within the (rather wide) range of 0.05–2.

Many parameters influence the occurrence of copigmentation in wine, of which by far the most important are the concentrations of pigments and copigments. Rosé wines have much lower anthocyanin concentrations (20–50 mg/L) than reds (9, 71) and, therefore, do not exhibit copigmentation producing the blue to purple tones. Surprisingly, certain phenolic compounds have been shown to produce color loss (hypochromism associated with anticopigmentation) rather than the expected hyperchromic effect due to copigmentation. (69) However, such anticopigmentation has only been reported once; further investigations will be required to verify its occurrence and clarify the underlying mechanisms.

Interestingly, it has been suggested that a ternary copigmentation complex consisting of an anthocyanin and two different flavonoids (oenin··· (+)-catechin··· quercetin-3-β-d-glucoside) may be formed in wine when all three species are present at high concentrations. (72) This may cause synergistic color-enhancing effects, depending on the pH, temperature, and presence of sulfites. A thorough characterization of the role of each partner would increase our understanding of color stabilization by ternary complex formation.

The relative contributions of self-association and copigmentation to wine coloration are a matter of intense debate. On the basis of CD analyses, R. Boulton concluded that self-association is not very relevant in young red wines. (2) Conversely, Gonzalez-Manzano et al. concluded that self-association accounted for 8% to 60% of the absorbance increases observed in wine-like solutions at 520 nm as the pigment concentration was increased from 50 to 600 mg/L. (2, 73, 74) Acylated anthocyanins are more prone to self-association than their nonacylated analogs. (75) With these pigments, intramolecular copigmentation and self-association may be tightly related and difficult to distinguish. (1) However, acylated anthocyanins are only minor pigments in wine.

Because grapes differ in their pigment and copigment contents, copigmentation in wines will obviously be sensitive to the grape varieties from which they are made. For example, Herras Roger et al. recently estimated that copigmentation is responsible for 31%, 22%, 22%, 16%, 15%, 14%, 11%, and 9% of the coloration of Ruby cabernet, Listan negro, Syrah, Merlot, Tintilla, Baboso, Negraoll, and Vijariego young red wines, respectively. (76) In another study, Tempranillo and Graciano monovarietal wines were compared to blended or “coupage” wines, which are made by grape blending (comaceration) and wine blending (covinification). Such winemaking techniques are intended to create wines with colors that are stable over time. (77) Forty-six pigments were identified in this study (including common anthocyanidin glucosides, their acylated analogs, and pyranoanthocyanins) as well as 12 flavonols (myricetin, quercetin, kaemferol, isorhamnetin, and their glycosides) and 12 phenolic acids (4 hydroxybenzoic acids and 8 HCA). Of the two monovarietal wines, the Graciano appeared darker and more intensely colored than the Tempranillo. Moreover, grape blending produced more bluish hues than wine blending. The authors concluded that copigmentation was enhanced in the early stage of winemaking. Moreover, copigmentation was enhanced in wines whose production involved pre- and postfermentative addition of rutin, caffeic acid, p-coumaric acid, and isoflavonoids. (78-82) Copigmentation also influences the extraction of anthocyanins from grapes into wine during winemaking; the efficiency of extraction was shown to depend on the concentrations of pigments and of certain copigments such as procyanidins from grape seeds. (2, 83, 84)

Other factors may influence the amount of pigments and copigments in wines, such as the soil on which the grapes are grown, the climatic conditions, the applied winemaking technique, and the degree of aging. For example, the copigmentation level in Cabernet sauvignon decreased from 42% to 0%, over the nine months immediately after the end of alcoholic fermentation, whereas its content in anthocyanin derivatives (including polymeric pigments), which are apparently much less prone to copigmentation, increased sharply.

Metal ions may also contribute to wine coloration if the wine has an appreciable content of anthocyanins with a catechol B-ring (e.g., cyanidin, petunidin, or delphinidin). High concentrations of copper are likely in certain grapes due to the use of copper-containing fungicides. However, metal-anthocyanin binding is poorly documented in wine and certainly has little impact on wine color.

Wine is a complex system that evolves as it ages, leading to the formation of diverse anthocyanin-derived pigments such as pyranoanthocyanins, which may also exhibit copigmentation. While anthocyanin copigmentation has been relatively well studied, the same is not true for copigmentation involving pyranoanthocyanins. Whereas anthocyanins and other flavylium derivatives like catechin-(4 → 8)-oenin express their maximal color intensity under acidic conditions, it was demonstrated that pyranoanthocyanin-flavanol pigments absorb visible light more strongly at wine pH (around 3.6), under which conditions their absorption is up to 30–50% stronger than at pH = 1.0. Such hyperchromic effects may indicate the occurrence of intramolecular copigmentation and/or self-association in pyranoanthocyanin-flavanols, which would produce higher molar absorption coefficients. (9) These results become even more interesting and surprising when one considers that pyranoanthocyanins, unlike anthocyanins, generally do not undergo water addition and therefore can only participate in proton transfer reactions as the pH increases. (85-87) On the other hand, the addition of (+)-catechin to a mildly acidic solution of the oenin-vinylguaiacol pyranoanthocyanin caused a large increase in visible absorption (even greater than that observed for oenin), illustrating the potential contribution of pyranoanthocyanins in the manipulation of wine color. (86)

In some cases, copigmentation is just the first step in a process of chemical change that anthocyanins undergo in aging wines and may be followed by the formation of covalent linkages between the components of the copigmentation complex. (88) For example, catechin-methylmethine-anthocyanins in wines are formed by the reaction between anthocyanins (pigment), catechin derivatives (copigment), and acetaldehyde (which is the source of the methylmethine bridge and functions as a covalent linker) produced by ethanol oxidation. This reaction is probably favored by the proximity of the reactants within the copigmentation complex.

3.3 Copigmentation in Food and Beverages

While there have been many studies on copigmentation in flowers and (to a lesser extent) in red wine, there have been far fewer on copigmentation in fruit, vegetables, and beverages other than wine. Nevertheless, copigmentation is likely to occur and stabilize coloration in fruit products (juices, purees, jams, and syrups). Early studies showed that metal ions stabilize the colors of products made from berries, such as strawberry puree, (89) cranberry juice cocktail, (90) and crowberry juice. (91) The blue color of blueberries (vaccinium sp.) has been linked to aluminum-anthocyanin complexes. (92) However, adequate pigment and copigment profiling or copigmentation measurements have not yet been conducted on fruit and vegetables.

One way of stabilizing color during food processing and storage is to add specific copigments; this technique has been studied especially intensively in the context of berry juices. (2, 67, 93) For example, phenolic acids have been shown to enhance color stability in some berry juices (strawberry, raspberry, lingonberry, cranberry, and orange juices) during storage. (93, 94) Moreover, chlorogenic acid enhanced the color intensity of strawberry and chokeberry juices. Some authors have observed that the presence of flavone C-glycosides induced significant hyperchromic effects and enhanced anthocyanin stability in products rich in cyanidin glycosides, particularly açaı́ fruit beverages. (95) Flavonol glycosides such as rutin have repeatedly been identified as copigments that stabilize the color of fruit juices including blood orange and plum juices during storage. (94, 96) In addition, the purplish-red color of jambolan anthocyanins is reportedly enhanced and stabilized by copigmentation with sinapic acid, caffeic acid, and rosemary polyphenolic extract. (97) The red color of pomegranate juice, which is due to cyanidin and delphinidin glycosides, was also stabilized by the addition of 2 equiv of phenolic copigments, although the addition of higher concentrations had negative effects, most probably due to the formation of aggregates. (98) Vitexin, orientin, and other flavonoid C-glycosides from pigeon pea leaves enhanced color stability in blueberry juices by intermolecular copigmentation, with pigeon pea leaf extract being the most effective. (99) It has been suggested that self-association is more important in berry coloration than in young red wines. (100) Finally, the ability of copigments (ferulic acid, caffeic acid, p-coumaric acid, rutin, and hesperidin) to limit bleaching in purple sweet potatoes has been tested, although none exhibited strong effects. (82)

4 Experimental Techniques to Analyze Copigmentation

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A full understanding of copigmentation requires a thorough analysis of the noncovalent interactions responsible for specific spectral variations. In wine chemistry for example, a comprehensive description of the supramolecular interactions involved in copigmentation would be advantageous at all stages of winemaking, from the selection of grape varieties in the vineyard to the characterization of an old wine in the glass. (2, 85, 101) Copigmentation and the associated interactions influence the wine’s colorimetric ratios, including the color/colorless, red/blue, and red/orange ratios, and can thus affect consumers’ perceptions of the product. These ratios are affected by grape variety, winemaking procedure (e.g., the protocol applied during maceration), as well as environmental and agricultural conditions. In the food industry, characterizing the contribution of copigmentation to the overall color requires the complete panel of available experimental techniques.

Copigmentation is an observable, so most of the color variation it produces is discernible by simple visual inspection, and many details of its functioning can be understood simply by using conventional UV–vis absorption spectroscopy. Although this technique is by far the most popular in this case, copigmentation complex characterization is amenable to other techniques widely used to characterize noncovalent assemblies, mainly NMR and CD spectroscopies. It is worth noting however that even the simplest (nonacylated) anthocyanins are typically available only in limited amounts, either by time-consuming extraction protocols or by multistep chemical synthesis or from a few commercial sources. Moreover, except in highly acidic (non-natural) conditions, aqueous solutions of anthocyanins are actually a mixture of several colored and colorless forms (vide supra), all characterized by their peculiar thermodynamics. These are probably the reasons why many nowadays standard and powerful techniques used in supramolecular chemistry, such as isothermal titration calorimetry (ITC), have been little applied to copigmentation so far. Even investigations of copigmentation by NMR are generally limited to the sole flavylium ion (highly acidic solution).

4.1 UV–vis Absorption

The most characteristic manifestation of copigmentation is the combination of color intensification and spectral shifts observed when a copigment is added to a mildly acidic solution of an anthocyanin. Monitoring by UV–vis absorption spectroscopy makes it possible to evaluate these phenomena in terms of hyperchromic effects and bathochromic shifts. (29, 31, 46, 49, 102-106) This is why UV–vis spectroscopy is by far the most widely used tool for studying copigmentation, also because rather low pigment concentrations (<0.1 mM) can be used, which is a valuable asset in this field. As an example of the spectacular spectral changes that can be observed, malvidin 3,5-di-O-β-d-glucoside (malvin) forms a highly stable copigmentation complex with 7-O-sulfoquercetin that triggers a bathochromic shift of nearly 40 nm in the flavylium visible band (λ_MAX = 525 nm for malvin), which is best evidenced at pH = 1. This bathochromic shift corresponds to a color change from red to purple. Moreover, a large hyperchromic effect of ca. 1 order of magnitude is also observed at pH = 3.5, reflecting the partial conversion of the free (colorless) hemiketal [largely dominant at pH = 3.5, pK′_h(malvin) ≈ 2] back to the (red) flavylium cation (Figure 13). (107) Raising the temperature markedly attenuates this color gain, which is consistent with a partial dissociation of the copigmentation complex and suggests that the binding of the two components is exothermic.

Figure 13. Copigmentation of malvin (malvidin 3,5-di-*O-β*-d-glucoside) by 7-O-sulfoquercetin. Reprinted with permission from ref 107. Copyright 2001 John Wiley & Sons.

This section focuses particularly on the dependence of the visible absorbance on temperature, pH, and copigment concentration. Assuming a 1:1 stoichiometry for the copigmentation complexes and no binding between the copigment and the colorless forms, the visible absorbance changes can be analyzed so as to estimate the pigment–copigment binding constants and the corresponding enthalpy and entropy. (102, 106, 108-111)

Briefly, the relative hyperchromic effect observed in copigmentation can be derived from simple solution chemistry combining Beer’s law, the law of pigment conservation, and the expressions of the thermodynamic constants. (102) It can thus be written as

(2)where A and A₀ are the absorbance values at the same wavelength in the presence and absence of copigment, respectively, and [CP] is the copigment concentration. Parameters α and β are the following combination of a spectroscopic term K_S (involving molar absorption coefficients) and a second term K_C that only depends on proton concentration and thermodynamic constants: α = K_C/(K_S– K_C), β = 1/(K_S– K_C).

(3)

(4)where K_a and K_h′ are the acidity constant and overall hydration constant of the flavylium ion, respectively; K_AHCP+ and K_ACP are the pigment–copigment binding constants for the flavylium ion and quinonoid bases, respectively; r_A = ε_A/ε_AH⁺; r_AHCP⁺ = ε_AHCP⁺/ε_AH⁺; and r_ACP = ε_ACP/ε_A.

At low pH (<2), the flavylium cation and its complex are the sole species in solution and eq 2 is converted into the classical Benesi–Hildebrand relationship. (112) We must also note that at low pH, the hydration equilibrium is no longer established and no colorless forms are available for conversion into colored forms upon copigment addition. Hence, the hyperchromic effect is not observed and copigmentation only produces bathochromic effects, which may be very weak. (108)

Eq 2 can be used for the fitting of the pH dependence of the hyperchromic effect for fixed pigment and copigment concentrations. (102) For investigations of the dependence on temperature or copigment concentration, eq 2 can also be simplified by selecting a pH where either the flavylium ion (pH < pK_a – 1) or the quinonoid bases (pH > pK_a + 1) are present. (106, 108-111) With anthocyanins that are especially sensitive to water addition such as 3,5-O-β-diglucosides (pK′_h ≈ 2), the conditions pH < pK_a – 1 and pH > pK′_h + 1 can be met, thus permitting additional simplification: (46)

(5)

A similar relationship can hold for quinonoid bases in mildly acidic conditions (pH 5–6): (113)

(6)

Enthalpy and entropy changes of copigmentation are typically deduced by determining binding constants at different temperatures and constructing a linear Van’t Hoff plot (assuming ΔH⁰ and ΔS⁰ are temperature-independent over the selected temperature range):

(7)

The simple situations described above (eqs 5 and 6) are particularly interesting as the hyperchromic effect is directly related to the copigmentation binding constants, without interference of the thermodynamics of proton transfer and water addition. This advantage can be exploited for the construction of structure-affinity relationships. (113) Thus, a direct plot showing the temperature dependence of the hyperchromic effect (for a fixed concentration of copigment in large excess) is possible, as follows:

(8)

For a fixed CP concentration, the slope and intercept of ln(A – A₀/A₀) as a function of 1/T thus provide estimation of ΔH⁰ and ΔS⁰, respectively. The spectroscopic parameters r_AHCP+ and r_ACP can be determined beforehand by comparing the spectra of the pigment alone and pigment plus copigment in large excess, both in the absence of colorless forms. The values of r_AHCP+ and r_ACP can be determined in highly acidic solution and immediately after pigment addition in a pH = 5–6 solution, respectively, because hydration is either absent or slow under such conditions. Alternatively, the hyperchromic effect can be recorded at the isosbestic points of both the pigment and copigmentation complex, which are defined by r_AHCP⁺ = 1 (i.e., ε_AHCP⁺ = ε_AH+) and r_ACP = 1 (i.e., ε_ACP = ε_A), respectively.

Hyperchromic effects can be observed when a pool of colorless forms initially exists and are converted back to colored forms upon selective binding with copigment. Thus, it is clear that a pigment with a high K_h^′ value (K_h^′ = [H⁺] [B′]/[AH⁺], where B′ is the global pool of colorless forms B, C_cis, and C_trans) (i.e., when the anthocyanin is especially prone to water addition) will usually produce a stronger hyperchromic effect. A simulation of the hyperchromic effect as a function of pH (Figure 14) also confirms that the color gain is maximal when it takes place from a mildly acidic almost colorless control solution (with no copigment).

Figure 14. pH dependence of the copigmentation hyperchromic shift. Spectroscopic monitoring at λ_MAX of free flavylium. Simulations from eq 2 using the following parameters: CP concentration = 10 mM, pK′_h = 2.5, pK_a = 4.0, r_AHCP+ = 0.8, r_ACP = 0.9, r_A = 0.7. Hydroxycinnamic acids (red line): K_AHCP+ = 3 × 10² M^–1, K_ACP = 2 × 10² M^–1. Flavones and flavonols (green line): K_AHCP+ = 3 × 10³ M^–1, K_ACP = 10³ M^–1.

Many experimental studies have evidenced that bathochromic shifts require copigment-to-pigment charge transfer (CT). (105, 108, 114) On the basis of the explicit correlation between the free enthalpy of copigmentation and the difference between the copigment’s ionization potential and the pigment’s electron affinity, it was proposed that CT state formation contributes significantly to the driving force of copigmentation. (105) However, even relatively potent copigments such as vinylcatechin dimers can bind anthocyanins but induce no significant bathochromic shifts. (108) Stable copigmentation complexes may form with only marginal spectral changes if colorless forms are minor and CT negligible. This is the case for the 3-deoxyanthocyanidins (relatively abundant in red sorghum), which are known to be much more resistant to hydration than common anthocyanins. (115) Even when it has little visible impact on color, copigmentation may be quite important in limiting the accumulation of colorless forms and the subsequent (irreversible) degradation of pigments (see section 6.2).

By comparing the spectral changes at pH = 1 (pure flavylium and bathochromic shifts only) and at higher pH values (mixtures of colored and colorless forms), it is possible to outline the normally minor contributions of the colorless forms to copigment binding. (109, 116) This contribution turned out to be very significant in the particular case of copigmentation by the purine caffeine, which was also observed to form 1:2 pigment-copigment complexes. (109, 116, 117) It may also be noted that the copigment-induced decrease in the apparent rate constant for water addition to the flavylium ion provides another method for estimating pigment-copigment binding constants. (113) Moreover, copigmentation can be interpreted by considering that the copigment increases the apparent pK_h^′ value (noted pK_h^′CP) (i.e., it extends the pH range over which the colored forms prevail) (Figure 15). (74, 118)

Figure 15. Distribution diagram of anthocyanin forms in the presence of a copigment. Parameters: pK′_h = 2.5, pK_a = 4.0, pigment and copigment concentrations = 10 and 30 mM, respectively. (A) Hydroxycinnamic acid, K_AHCP = 3 × 10², K_ACP = 2 × 10² M^–1, pK′_h^CP (pH of a 1:1 mixture of colored and colorless forms) ≈ 3.5. (B) Flavone or flavonol, K_AHCP = 3 × 10² M⁻¹, K_AHCP = 3 × 10³ M^–1, pK′_h^CP ≈ 5.2.

The preceding sections discussed the quantification and analysis of colors expressed by anthocyanins and their complexes in terms of the maximum absorption wavelength λ_MAX and increases in visible absorbance. However, color perception also depends on a number of factors that are inherent to the colorant, as well as its concentration, illumination, and interactions with the human eye. All of these factors should be well understood to analyze and/or modulate a specific visual impression of, for example, a wine. For a given pigment-copigment pair, the inherent optical properties are entirely contained in the details of the absorption spectrum, plotted in terms of the molar absorption coefficient, in a given solvent (e.g., water). Light scattering can be neglected if the number of associated chromophores is (very) small with respect to that of solvent molecules, as is usually the case in copigmentation. It is worth noting here that increasing concentrations give rise to hyperchromic effects but may also lead to the formation of larger aggregates and precipitation, which can dramatically modify optical behavior. For solid state samples, the description becomes much more complex, taking into account the specific chromophore assembly, which changes the colorant’s optical properties via (long-range) intermolecular interactions, the size of the assembly, and the resulting reflectance and absorbance; for further details see, for example, refs 119 and 120.

Color perception can be robustly evaluated within the CIELAB (for ’Commission International de l’Eclairage’ and L*,a*,b*) model based on the color-opponent theory using hue or chromatic tonality (e.g., the amount of red vs green a*, the amount of yellow vs blue b*), saturation C* (i.e., vivid or bright vs dull color perception), and lightness L* (i.e., dark or light color perception) for standard illuminant D65 to mimic “average daylight”. (121) For applications in the food industry, it is now mandatory to evaluate copigmentation using a combination of λ_MAX spectral shifts and total color difference ΔE* measurements, which help refine the color perception assigned to copigmentation. As a general trend, copigmentation produces darker colors (lower L*), bluing effects [higher Δh_ab, where h_ab = tan^–1(b*/a*) is the hue angle] and increased saturation (higher C*). (72, 122) The bluing effect of pigment···copigment association historically evidenced by R. Robinson was reevaluated by the conduction of colorimetric measurements of copigmentation between cyanidin 3,5-O-diglucoside and the flavonol rutin (quercetin 3-O-rhamnoglucoside). (121, 123) The solutions containing the copigment provided a much more complex hue palette than would be expected for a simple bluing effect, with the eye perception of copigmentation strongly depending on the pH and the concentration of both pigment and copigment. ΔE* values usually increase in the presence of copigments (e.g., when adding quercetagetin to anthocyanin solutions). (124) This was also shown with purple sweet potato anthocyanins (82) and grape juice, in which chlorogenic acid increased ΔE* by almost 2 units. (125) The addition of rosemary polyphenols to jambolan (Syzygium cumini) fruit anthocyanins also yielded a more vivid purplish-red color with a decrease of lightness L* and an increase of chroma C*. (97) A decrease of L* and b* was also observed with the oenin-isoquercitrin pair. (26)

The concentration effect was confirmed and supported by colorimetric measurements. Molar ratio up to 1:7 (malvidin 3-O-glucoside···epicatechin) provided the lowest L* and b* values but the highest a* values, meaning that this was the ratio at which the pigment-copigment pair exhibited the darkest and most vivid bluish color. (122) The modulation of the colorimetric parameters was used to evaluate the efficiency of copigments in anthocyanin-flavanol-flavonol ternary systems. (72) Quercetin 3-O-β-d-glucoside was shown to be more efficient than (+)-catechin at stabilizing color changes (in particular lightness) expressed by malvidin 3-O-glucoside. However, the synergism and antagonism within these ternary systems have not yet been elucidated.

Relative contributions to ΔE* can be assessed by means of CIELAB measurements. Concentration-dependent decreases in L* and increases in saturation can be evaluated in wine models. (27) These effects are associated with hyperchromic effects and bathochromic shifts, which remain noticeable two months after preparation. Chromatic changes typical of copigmentation (still visible two months after storage) were related to red-purple shifts. After two months, a gradual displacement toward red-orange colors was observed, suggesting the formation of new pigments. Colorimetric measurements pointing to copigmentation have also been conducted in various wines. (77)

4.2 Other Analytical Tools

¹H NMR provides direct evidence that copigmentation proceeds via (vertical) π–π stacking interactions between phenolic nuclei. In the NMR spectra of copigmentation complexes, the aromatic proton signals of both pigment and copigment molecules are shielded (in comparison to those of the free molecules), suggesting that each phenol undergoes the ring current of the other’s π-electrons. (42, 107, 126) The magnitude of these chemical shift modifications is comparable to those observed for stacked nucleotides in solution. (127) Moreover, each proton of the two partners is differently shielded, which provides information about their relative positioning in the complex. For example, the shielding of H2′ (B-ring) was greater than that for the other H atoms of the anthocyanins, providing the first evidence that anthocyanin stacking does not involve perfectly superimposed noncovalent interaction and confirming the importance of the B-ring. The B-ring’s importance was further demonstrated by considering substituent effects. (44) In strongly acidic solution of an initially pure flavylium cation, plots of the pigment protons’ diamagnetic shifts as a function of copigment concentration can be quantitatively analyzed to determine pigment-copigment binding constants. The method can also be used for the determination of self-association constants, using either a simple monomer-dimer model or the so-called isodesmic model, which assumes higher oligomers (i.e., the successive formation of n-mers with identical stepwise binding constants). (128, 129)

The NOE (Nuclear Overhauser Effect) has also been used to evaluate noncovalent interactions in copigmentation, by measuring the transfer of nuclear spin polarization through space (rather than through covalent bonds). NOE experiments confirmed the occurrence of anthocyanin self-association. For instance, upon irradiation of malvin’s anomeric protons, negative NOEs (decreases in the signal intensities of H4 and H6) were observed at room temperature (but not at 60 °C), which were attributed to a lowering of the pigment’s tumbling motion caused by self-association. (44) NOESY experiments on malvidin 3-O-β-D-(6-O-p-coumaroyl)glucoside at different concentrations have shown that the coumaroyl group is oriented toward the anthocyanin chromophore. Cross-peaks between the H6 proton of the anthocyanidin moiety and the Hα proton of the aromatic acyl group were detected, indicating that the chromophore and acyl group were associated with one-another in solution. (75)

The sugar residues of anthocyanins are chiral, so their self-association can result in chiral stacking, making CD a very powerful and sensitive tool for its study. In particular, CD is very convenient for discriminating between intramolecular copigmentation (which produces a flat CD spectrum in the visible region) and noncovalent dimerization of acylated anthocyanins with chiral stacking of the chromophores, for which a strong exciton-type Cotton effect is observed in the visible region. (1) The sign of the Cotton effect can be used to distinguish between assemblies with right-handed or left-handed screw axes in both metal-free aggregates and metalloanthocyanin complexes. (1, 43, 45, 100) Exciton-type CD is allowed only if the transition dipole moments of both partners are not parallel or antiparallel. For example, due to electrostatic repulsion in A^–:A^–, the angle is higher than in A:A and so the CD magnitude is higher too. (45)

Despite their strong UV–vis absorption, anthocyanins are only very weakly fluorescent because of the many competing fates of their excited states. Consequently, fluorescence spectroscopy has only rarely been used to reveal and quantify copigmentation. For instance, in a strongly acidic solution, rutin was shown to quench the weak fluorescence of the flavylium ion of malvin at 600 nm (excitation at 540 nm). The binding constant between these two partners was estimated from their quenching curve (K_AHCP+ ≈ 2.6 × 10³ M^–1, in good agreement with the value determined by UV–vis spectroscopy). (130)

A relevant way of determining the supramolecular arrangement of copigmentation and self-association complexes is through X-ray crystallographic analysis. However, to date the only such complexes to have yielded X-ray quality crystals that enable full structural elucidation are the metalloanthocyanins commelinin from C. communis (131) and protocyanin from C. cyanus. (132) These complexes display a 3-fold symmetry axis and consist of six anthocyanin molecules bound to a core of two metal ions with six flavone copigments intercalated in between (vide infra). (1) Unfortunately, copigmentation and self-association (binary) complexes are usually labile, which make crystal growing virtually impossible and makes X-ray crystallography inapplicable to the analysis of most copigmentation systems with relevance to food. Moreover, significant to dramatic structural modifications from solution to the solid phase should be systematically envisaged, and the geometrical features of the copigmentation complexes should be analyzed with great care.

It is worth noting again that the experimental methods presented in this section are much less used than UV–vis absorption to characterize copigmentation, although NMR titrations are the most often used method to characterize supramolecular complexes and estimate binding constants. Indeed, copigmentation generally induces large changes in the pigment’s visible spectrum; moreover, UV–vis spectroscopy allows working at low pigment concentration (<0.1 mM), for which the competing self-association of anthocyanins can be neglected, and data acquisition is fast enough to investigate many pigment-copigment systems for structure-affinity relationships. This shows however the lack of systematic studies based on advanced experimental methods in supramolecular chemistry, which should be developed in the future to gain further insight in structural and energetic description. At present, the only alternative to X-ray crystallography for directly investigating the 3D structures of anthocyanin complexes at the atomic scale is to perform molecular modeling calculations (see sections 8–10) and combine their results with experimental data from UV–vis absorption, NMR, and CD spectroscopy experiments.

5 Stability in Intermolecular Copigmentation

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5.1 Structure–Affinity Relationships

As mentioned above, copigmentation has mainly been investigated qualitatively by comparing hyperchromic effects observed with different pigment-copigment pairs. However, since the hyperchromic effect may not be simply related to the copigmentation binding constants (vide supra), such data must be interpreted with care. Moreover, copigmentation is strongly pH-dependent, and most works reporting binding constants were conducted at a pH where the flavylium is the dominant-colored species. Despite these limitations, the known copigments can be ranked in order of decreasing binding constants based on the studies reported to date: flavones and flavonols (K_AHCP+ > 10³ M^–1) > hydroxycinnamic acids (K_AHCP+ = 2–4 × 10² M^–1) > flavanols (K_AHCP+ = 1–2 × 10² M^–1) > hydroxybenzoic acids (K_AHCP+ < 10² M^–1) (see Table 2). (29, 31, 46, 49, 102-106, 113) Unexpectedly, the simple aroma component 3,5-dimethoxy-4-hydroxyacetophenone also turned out to be a rather potent copigment of malvin. (133) This ranking suggests that any extension of the π-conjugated system beyond the phenolic ring (e.g., conjugation through the 2,3-double bond of flavonoids, substitution by electron-donating hydroxyl and methoxyl groups, or conjugation with an electron-withdrawing keto groups) has a positive impact on copigmentation. This reflects an enhancement of dispersion interactions to favor π–π stacking (higher copigment polarizability) and subsequently the formation of noncovalent complexes. Interestingly, 7-O-sulfoquercetin is an excellent (negatively charged) copigment of the malvin flavylium ion (K_AHCP+ ≈ 10⁴ M^–1), possibly because of the additional ionic interaction it can form (Table 2). (107) Similarly, the ferulate ion (produced by deprotonating the free carboxyl group of ferulic acid, pK_a ≈ 4.2) binds malvin much more avidly than ferulic acid itself, reflecting a possible combination of ionic interactions and enhanced copigment-to-flavylium CT. (105)

Table 2. Thermodynamic Parameters of Binding in Self-Association and Copigmentation Systems^a

	K (M^–1)^b	ΔG⁰ (kJ/mol)^b	ΔH⁰ (kJ/mol)	ΔS⁰ (J/mol K)	pH	ref
self-association
pelargonin	125	–12.0			1	44
cyanin	265	–13.8			1	44
peonin	325	–14.3			1	44
delphin	310	–14.2			1	44
petunin	625	–16.0			1	44
malvin	620	–15.9			1	44
malvin	900 (22 °C)	–16.9			6	45
malvin	200 (22 °C)	–13.1			9.8	45
myrtillin	1240	–17.7			1	128
oenin	976	–17.1			1	128
oenin	820 (27 °C)	–16.6			1	75
malvidin 3-O-β-d-(6-O-p-coumaroyl)-glucoside	1400 (27 °C)	–18.0			1	75
petunin	900	–16.9			1	128
kuromanin	700	–16.2			1	128
peonin	661	–16.1			1	128
callistephin	404	–14.9			1	128
copigmentation
flavonols and flavones
malvin···rutin	2750	–19.6	–37.2	–59.0	3.5	130
malvin···3‴-O-sulforutin	350	–14.5	–33.0	–62.0	3.5	130
malvin···2‴,3‴-O-(2-carboxy-1-methylethylidene) rutin (2 epimers)	2320	–19.2	–16.7	8.4	3.5	130
malvin···2″,3″,4″,2‴,3‴,4‴-hexa-O-succinylrutin	1060	–17.3	–17.1	0.5	3.5	130
malvin···di-O-succinylrutin (3 regioisomers)	1820	–18.6	–13.6	16.7	3.5	130
malvin··· 4‴-O-succinylrutin	1700	–18.4	–7.9	35.3	3.5	130
malvin···quercetin 3′-O-β-d-(2,3,4,6-tetra-O-succinyl) glucoside	1560	–18.2	–23.6	–18.0	3.5	107
malvin···7-O-sulfoquercetin	14470	–23.8	–37.3	–45.6	3.5	107
malvin···4′,7-di-O-sulfoquercetin	8940	–22.6	–34.7	–40.0	3.5	107
pelargonin···isoquercitrin	1050 (20 °C)	–17.2			0.25	105
pelargonin···quercitrin	1740 (20 °C)	–18.5			0.25	105
delphinidin···baicalin	2020	–18.8	–35.2	–67.8	3.65	104
delphinidin···quercetin-5′-sulfonic acid	3290	–20.0	–51.7	–106.6	3.65	104
delphinidin···rutin	1150	–17.4	–55.2	–163.7	3.65	104
flavanols
oenin···(−)-epicatechin	260	–13.8	–18	–14.2	3.6	31
malvin···catechin	185		–30.4	–58.6	3.5	113
malvin···catechin	215		–25.0	–39.2	5.5	113
oenin··· procyanidin B3	330	–14.4	–9.2	17.2	3.6	31
oenin···(9S,11R) vinylcatechin dimer	1930	–18.7			3.5	110
oenin···(9R,11S) vinylcatechin dimer	5420	–21.3			3.5	110
oenin···procyanidin B3	350	–14.5			3.5	110
catechin-(4→8)-oenin···(9S,11R) vinylcatechin dimer (10% EtOH)	311	–14.2	–17.8	–12.0	3.5	108
catechin-(4→ 8)-oenin···(9R,11S) vinylcatechin dimer (10% EtOH)	516	–15.5	–22.7	–24.2	3.5	108
catechin-(4→ 8)-oenin···procyanidin B3 (10% EtOH)	121	–11.9	–32.5	–69.2	3.5	108
hydroxycinnamic acids
malvin···p-coumaric acid	129	–12.0	–32.1	–62.8	2.5	106
malvin···4-O-β-D-glucopyranosylcoumaric acid	111	–11.7	–26.0	–38.0		106
malvin···caffeic acid	243	–13.6	–25.6	–46.0		106
malvin···4-O-β-d-glucopyranosylcaffeic acid	244	–13.6	–21.6	–31.0		106
malvin···ferulic acid	331	–14.4	–29.0	–50.1	3.6	106
malvin···4-O-β-D-glucopyranosylferulic acid	277	–13.9	–33.8	–71.0		106
peonidin···ferulic acid	155 (20 °C)	–12.5			2.58	105
oenin···ferulic acid	243 (20 °C)	–13.6			2.58	105
pelargonin···ferulic acid	263 (20 °C)	–13.8			2.58	105
cyanin···ferulic acid	210 (20 °C)	–13.3			2.58	105
malvin···chlorogenic acid	220	–13.4	–24.1	–36.1	3.5	113
malvin···chlorogenic acid	140	–12.2	–18.3	–20.1	5.5	113
oenin··· chlorogenic acid	390	–14.8	–14.2	2.04	3.6	31
hydroxybenzoic acids
pelargonin···protocatechuic acid	68 (20 °C)	–10.5			0.25	105
pelargonin···gallic acid	87 (20 °C)	–11.1			0.25	105
malvin···protocatechuic acid	80 (20 °C)	–10.9			3.65	105
oenin···p-hydroxybenzoic acid (12% EtOH)	12.1	–6.2	–10.7	–15.3	3.6	49
oenin···protocatechuic acid (12% EtOH)	14.6	–6.7	–13.5	–23.4	3.6	49
oenin···gallic acid (12% EtOH)	21.2	–7.6	–16.9	–31.9	3.6	49
oenin···vanillic acid (12% EtOH)	35.6	–8.9	–19.7	–37.1	3.6	49
oenin···syringic acid (12% EtOH)	50.6	–9.7	–21.1	–38.8	3.6	49
purines and aromatic amino acids
malvin···caffeine	125	–12.0	–11.7	0.9	3.5	113
malvin···caffeine	180	–12.9	–17.6	–16.0	5.5	113
malvin···Trp	64	–10.3	–6.8	11.8	3.5	113
malvin···TrpOMe	36	–8.9	–12.3	–11.5	3.5	113

All values were obtained in aqueous solution unless otherwise specified (presence of a certain % of EtOH).

Values at 25 °C, unless otherwise specified.

Copigments with multiple phenolic units are more efficient than simpler analogs due to geometrical flexibility, which allows the formation of numerous molecular contacts between the pigment and copigment. For example, catechin dimers (condensed tannins) are slightly better copigments than catechin itself, although much less efficient than the vinylcatechin dimers (K_AHCP+ > 10³ M^–1) found in red wine. (110) Similarly, gallotannin penta-O-galloyl-β-d-glucose forms a much more stable complex with malvin (K_AHCP+ ≈ 10³ M^–1) than does gallic acid, possibly by accommodating the pigment between the galloyl residues at C1-OH and C6-OH of the d-glucose core. (126) The ability of gallotannins to function as copigments in plants was confirmed with sylvatin, which is unusual in that it carries acetyl residues on its d-glucose moiety. (134) By contrast, the more rigid ellagitannins, vescalagin and castalagin, exhibited little affinity for malvin. (126)

The chemical features of the anthocyanin partner, and particularly the difference between 3,5-di-O-glycosides and 3-O-glycosides, had a relatively modest impact on the stability of the copigmentation complexes. (109) A modest impact of B-ring substitution was also observed, although some works reported that pigments having methoxyl substituents on the B-ring tend to bind copigments more strongly than their hydroxylated counterparts, (104) suggesting a weaker role of hydrogen bonding with respect to π–π stacking. Pigments bearing bulky di- or trisaccharides at C3-OH form less stable copigmentation complexes than 3-O-β-d-glucosides. (135, 136) The bulky substituents most probably induce strong steric repulsion that counteracts the stabilizing π–π stacking and hydrogen-bonding interactions. Interestingly, sterically demanding vinylcatechin dimer copigments were reported to bind oenin more strongly than malvin (110) and catechin-(4 → 8)-oenin. (108)

Structure-affinity relationships have further been established with non-natural model anthocyanin analogs (flavylium cations substituted by OH, OMe and/or glycosyloxyl groups) more accessible to chemical synthesis. (109, 116) For a given copigment, the binding constants appeared weakly influenced by the flavylium substitution. It must be noted that unlike anthocyanins, the simple aglycones (anthocyanidins) are accessible from their two faces, as indeed both 1:1 and 1:2 pigment-copigment bindings have been evidenced with chlorogenic acid. Moreover, upon water addition, flavylium ions unsubstituted at C3 give the C_trans as the sole accumulating colorless form (while the main colorless form of natural anthocyanin is by far the hemiketal). As the C_trans is flatter and more polarizable than the hemiketal (thus, more prone to develop dispersive interactions), copigmentation with the colorless forms was also observed with these model pigments, thus limiting the color gain. (109, 116)

5.2 Environmental Effects

The stability of intermolecular copigmentation complexes is highly sensitive to temperature, pH, and the presence of organic cosolvents. As already stressed, the pH dependence of hyperchromic effects largely reflects the sensitivity of anthocyanins to water addition. However, the relative affinities of the flavylium cation and quinonoid bases to the copigment also contribute to the overall process. Although only a few studies have compared K_AHCP+ and K_ACP binding constants, the trend for phenolic copigments (e.g., flavonoids and HCA) is that the flavylium cation binds slightly more strongly that the corresponding quinonoid bases. (102, 113) As an example, the K_AHCP+ and K_ACP binding constants for the malvin···rutin pair were around 3 × 10³ and 10³ M^–1 at 25 °C, respectively. However, the opposite was true for caffeine; for this copigment, the two constants took values of about 10² and 2 × 10² M^–1, respectively, at 25 °C (Table 2). (113) In keeping with this finding, the apparent pK_a value of cyanidin 3-O-β-d-glucoside declined from 3.8 to 3.3 in the presence of a large excess of caffeine (0.08 M), which is consistent with a more efficient stabilization of the bases. (117)

The thermodynamic constants of copigmentation, proton transfer, and hydration can be used to construct distribution diagrams showing the relative abundance of free and bound colored forms as well as colorless forms as a function of pH (Figure 15). Even at high pigment and copigment concentrations, as found in plant vacuoles, a moderately efficient copigment such as HCA only mildly increases pK_h^′CP (i.e., the pH value at which the relative abundances of colored and colorless forms are equal) and hence the pH range in which the colored forms prevail (Figure 15A). By contrast, the effect of flavones and flavonols is much more significant and, for instance, three equivalents of copigment are enough to shift pK_h^′CP by 2 to 3 pH units (Figure 15B).

The temperature dependence of the hyperchromic effect must also be interpreted with care as it may reflect the thermodynamics of both the hydration and copigmentation steps. For instance, raising the temperature of a catechin-(4 → 8)-oenin-vinylcatechin dimer solution (pH = 3.5) leads to an unexpected color gain that is ascribed to the exothermic character of the hydration step. (108) However, copigmentation itself is typically exothermic and thus a color loss is generally observed when temperature is increased. (29, 31, 46, 103, 104, 106, 107, 113)

At pH = 3.6, the association enthalpies of gallic acid, vanillic acid, and syringic acid with oenin were −7.6, −8.9, and −9.7 kJ/mol, respectively (Table 2). (49) The entropy change of the copigmentation process is generally negative. Thus, for the same systems as before, the ΔS⁰ values were −31.9, −37.1, and −38.8 J/mol K, respectively, at pH = 3.6. Similar trends were obtained in ref 32. That is to say, the formation of the noncovalent copigmentation complex driven by π–π stacking and hydrogen bonding is a wholly ordering process.

A separate ¹H NMR investigation provided early evidence of heterodimerization involving colorless forms. (137) Studies on the pH and concentration dependence of the different malvin forms revealed that the flat C_trans (unlike the hemiketal and C_cis) binds the flavylium ion.

The decisive contribution of water to the driving force of copigmentation is evident, and the addition of organic cosolvents is strongly destabilizing. (46) For instance, even the remarkably stable malvin···7-O-sulfoquercetin complex (with its record high binding constant of ca. 10⁴ M^–1 at 25 °C) does not persist in a 1:1 water–methanol mixture. (107) Small concentrations of ethanol (4–6%) tend to increase the exothermicity of the interaction between the malvin flavylium cation and common copigments, suggesting that ethanol molecules preferentially accumulated in the first solvation shells of these complexes. (113) The formation of such organized assemblies would be entropically costly, making the overall thermodynamics of the process less favorable and producing a lower binding constant in the presence of cosolvents. Nevertheless, this result is consistent with the persistence of copigmentation complexes in wine, which contains a moderate percentage of ethanol.

5.3 Self-Association

At relatively high concentration (> 0.1 mM), the flavylium cation of common anthocyanidin 3,5-O-β-d-diglucosides forms noncovalent dimers with a left-handed chiral stacking and association constants in the range of 1 to 6 × 10² M^–1, depending on the B-ring substituents (Table 2). (44) Self-association of the flavylium cation is enhanced when the number of hydroxyl and methoxyl substituents in the B-ring is increased. The same trend was observed with common anthocyanidin 3-O-β-d-glucosides, albeit with slightly higher dimerization constants ranging from 4 to 12 × 10² M^–1 (Table 2). (128)

Interestingly, the self-association of flavylium cation tends to reduce K_h and increase K_a. Thus, self-association protects the flavylium cation against hydration (like copigmentation) and favors its conversion into the quinonoid bases. (128) The latter result suggests that the self-association of the neutral quinonoid bases is stronger than that of flavylium cations. This is not unexpected because the self-association of flavylium cation is impeded by electrostatic repulsion. These data are in agreement with the results of ¹H NMR studies on malvin in acidic to mildly alkaline solutions, (44, 45) which provided the following association constants: K_AH+/AH+ = 600, K_A/A = 900, K_A–/A– = 200 M^–1 (Table 2). Moreover, spectroscopic titrations of malvin around neutrality have shown two successive proton transfers consistent with the sequence A···A → A···A^– → A^–...A^– with pK_a = 7.0 and 8.2 at 5 mM. (43) By contrast, in dilute solution (50 μM), a single proton transfer is observed with pK_a = 7.0. The persistence of the neutral quinonoid bases above neutrality in concentrated solutions is further evidence that noncovalent dimerization is more favorable for neutral than for anionic bases.

It is worth noting that self-association is in competition with intermolecular copigmentation. In such cases, the dominant process, in plant and food, will be determined by the relative concentrations of pigment and copigment. (85) Studies on wine models have suggested that self-association of oenin, the main grape anthocyanin, is more important to color stabilization than copigmentation in young red wine. (31)

5.4 Metal–Anthocyanin Complexes

Metal ions may participate in stabilizing copigmentation complexes. Anthocyanins with a catechol or pyrogallol B-ring (cyanidin, petudinin, and delphinidin derivatives) can bind hard metal ions such as Al³⁺, Fe³⁺, and Mg²⁺ with the simultaneous loss of two protons. (25, 109, 138, 139) Metal-anthocyanin binding is crucial for the expression of blue coloration, although it must be noted that blue coloration can also be achieved with metal-free acylated anthocyanins, especially when the vacuole pH is relatively high. However, metal-anthocyanin binding must typically be combined with intermolecular copigmentation (the other common source of bathochromic shifts in the visible spectrum) to achieve a stable blue. The most intriguing anthocyanin-based supramolecular assemblies that have been examined to date are known as “metalloanthocyanins” and consist of metal-pigment-copigment complexes with a well-defined 2:6:6 stoichiometry; see Table 1. (1) In these complexes, each metal ion is bound to the B-ring of three anthocyanin ligands and anthocyanins bound to different metal ions stack in a left-handed mode. Moreover, pairs of copigment (flavone) molecules, also stacked in a left-handed mode, fill the empty spaces and stack onto anthocyanin moieties in a right-handed arrangement.

The structure of commelinin (Figure 10) was elucidated by X-ray crystallography, which represented a major breakthrough in the understanding of natural coloration due to anthocyanins. (131) The CD spectra associated with anthocyanin complexation were shown to be typical of molecular exciton coupling as first described by Kasha et al., (140) indicating the formation of stacks with right- or left-handed screw axes. (40) In commelinin, malonylawobanin (the acylated anthocyanin pigment) and flavocommelin (the flavone glucoside copigment) are arranged in stacked pairs with interaromatic ring distances of ca. 0.40 and 0.35 nm for pigment and copigment pairs, respectively. Chiral anticlockwise supramolecular arrangements were observed for pigment···pigment and copigment···copigment pairs, whereas a clockwise arrangement was observed for pigment···copigment pairs, with interaromatic distance of 0.45 nm. This supramolecular assembly has been characterized extensively and is now taken as the prototypical example of a distinct class of copigmentation complexes.

Overall, the available data indicate that various π–π stacking interactions coexist in metalloanthocyanins, including anthocyanin self-association, copigment (flavone) self-association, and anthocyanin-copigment association (copigmentation). Moreover, the anthocyanin components of metalloanthocyanins quite often bear a 6-O-p-coumaroyl-d-Glc substituent at C3-OH, which was shown to form long-range NOEs with the flavone nucleus. (59) Here, anthocyanin molecules all interact via their metal-stabilized anionic quinonoid bases.

6 Stability in Intramolecular Copigmentation

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6.1 Conformational Folding of Acylated Anthocyanins

Anthocyanins acylated by HCA are prone to intramolecular copigmentation or self-association (noncovalent dimerization) depending on their structure. (1, 100, 141, 142) Intramolecular stacking requires a flexible acyl link that makes possible close contacts between the anthocyanidin chromophore and copigment moiety (Scheme 2, panels C–E). The interacting partners in such folded conformations are covalently linked but also share a number of noncovalent interactions based on π–π stacking and possibly hydrogen bonding. Conversely to intermolecular copigmentation, the association energies of intramolecular copigmentation are less amenable to experimental determination as they pertain to a conformational equilibrium. The stabilization is typically qualitatively described in terms of structural features, about which NMR analysis can provide precious information.

The observation of long-range NOE correlations between the flavylium nucleus and HCA residues is a direct evidence for the existence of folded conformations in which both moieties are in close (van der Waals) contact (i.e., intermoiety distance of 0.3–0.4 nm). Moreover, the ¹H NMR spectra of HCA residues in contact with a chromophore typically contain proton signals that are shielded relative to those of the equivalent protons in the corresponding HCA methyl esters under the same conditions. It is significant that HCA groups capable of folding back onto the chromophore are typically linked to the primary C6-OH group of a sugar moiety (most frequently, β-d-glucopyranose). Thus, rotation about the C5–C6 bond seems to provide just about enough flexibility for stacking to occur. The folding increases the percentage of gt (gauche–trans) conformers as evidenced by analyzing the J_H5,H6 coupling constants of the linker. (142) Conversely, when acylation occurs at a secondary sugar OH group such as the C4-OH group in the case of the monoacylated anthocyanin petanin, no flavylium-HCA NOE correlations were observed; in such cases, NMR analysis instead suggested the formation of a head-to-head extended dimer in which both flavylium nuclei on the one hand and both HCA residues on the other hand were in close contact. (143, 144) Interestingly, petanin is closely related to alatanin C as both pigments bear a single HCA group at the terminal sugar moiety of a 1,6 disaccharide moiety. However, unlike petanin, alatanin C is acylated via a primary C6-OH group and its NOESY (nuclear overhauser effect spectroscopy) spectrum reveals flavylium-acyl contacts. (145) It is also remarkable that in the triacylated anthocyanin tecophilin, which displays a diacylated d-glucose unit with HCA residues at C2-OH and C6-OH, only the acyl group at C6-OH stacks onto the chromophore. (146) The fact that long-range NOE correlations within acylated anthocyanins can even be observed in nonaqueous environments (DMSO-d₆) emphasizes the stability of such molecular stacks and shows that they do not necessarily require the assistance of the hydrophobic effect to form. (147, 148)

Such arrangements may also form with wine pigments and models in which the C6 and/or C8 atoms of flavylium and flavanol units are linked through a CH₃–CH bridge originating from ethanol after its oxidation to ethanal. (149) These pigments are consistently far more resistant to water addition than the corresponding flavylium cations. Spectroscopic titrations of these pigments are also consistent with sequential proton loss within dimers. (150, 151) Similarly, the wine pigment formed by electrophilic aromatic substitution at oenin’s C8–H position by the carbocation derived from vescalagin (by dehydration at C1-OH), a common ellagitannin transferred from oak barrel to wine upon aging, exhibits long-range NOEs between the flavylium nucleus and a galloyl unit; a moderately improved color stability in aqueous solution and a bathochromic shift of the visible band by ca. 20 nm were observed with respect to oenin. (152) These observations together suggest the formation of a folded conformation allowing intramolecular π–π stacking interactions and CT.

The structural features that predispose a given molecule to intramolecular copigmentation or self-association are subtle and only partially understood. In brief, when HCA residues are linked to the B- or C-ring by short sugar spacers (monosaccharides or 1,2-disaccharides), intramolecular copigmentation seems to be favored. With more extended spacers (e.g., 1,6-disaccharides) or repeating D-Glc-HCA sequences, especially at the A- or C-ring, chiral (left-handed or right-handed) self-association seems to be the rule. It must also be emphasized that depending on the position of the sugar moiety on the chromophore, HCA residues bound to C6-OH sugar groups by acyl linkages do not exhibit the same propensity for π–π stacking. For species with a single D-Glc spacer, the following ranking has been proposed: C3′ ∼ C5′ > C7 > C3. (141, 153)

The capacity of acylated anthocyanins for intermolecular copigmentation has not been studied extensively. In principle, the folding of an internal HCA residue onto the chromophore should make it less available for π–π stacking interactions with external copigments. In other words, intermolecular copigmentation should compete with intramolecular copigmentation and self-association. The CD spectrum of alatanin C and its concentration dependence are suggestive of a strong noncovalent dimerization, even at low pigment concentration (50 μM). (145) However, the addition of a potent flavone copigment (flavocommelin, 8 equiv) cancels the Cotton effect, suggesting that copigmentation outcompetes self-association under these conditions. In the case of the Morning glory anthocyanins (Pharbitis nil), which undergo intramolecular copigmentation, a single HCA residue has little impact on the stability of the copigmentation complexes with chlorogenic acid, perhaps suggesting that one face of the chromophore remains accessible to the copigment. (135) However, the binding of chlorogenic acid to the diacylated anthocyanin was greatly weakened, in agreement with the pigment adopting a sandwich-like conformation that blocks both faces of its chromophore. On the other hand, the monoacylated pigment cyanidin 3-O-β-D-[2-O-β-d-xylosyl-6-O-β-d-(6-O-p-coumaroyl)glucosyl)]-galactoside does not seem to bind free HCAs. (136) However, as this is also true for its deacylated counterpart, it appears that it is the bulky trisaccharide rather than the acyl moiety that is responsible for the chromophore’s inaccessibility to external copigments.

Being quite prone to noncovalent dimerization, the wine pigments, in which anthocyanins are linked to a flavanol unit through a CH₃–CH bridge, show very little affinity for chlorogenic acid. (150, 151) Conversely, the diacylated Ceanothus papillosus anthocyanin, which has two HCA residues that interact with the chromophore (based on the diamagnetic shifts observed in its ¹H NMR spectrum), cannot express the blue color of the flower without its major copigment, kaempferol 3-O-β-xylosyl-(α-1,2)-rhamnoside. (55) Interestingly, this unusual metal-free combination of intermolecular copigmentation with intramolecular copigmentation or self-association is not observed with other (more common) flavonol 3-O-glycosides.

There is relatively little physical-chemical information on acylated anthocyanin dimerization constants or the impact of acylation on the thermodynamics of water addition and proton transfer. A recent ¹H NMR study showed that malvidin 3-O-β-d-(6-O-p-coumaroyl)glucoside is more prone to noncovalent dimerization [K_AH+/AH+ ≈ 1400 M^–1 in D₂O–DMSO-d₆ (7:3)] than its deacylated counterpart (oenin, K_AH+/AH+ ≈ 800 M^–1), see Table 2. (75) Interestingly, even in the most dilute solution, some proton signals of malvidin 3-O-β-D-(6-O-p-coumaroyl)glucoside remain more shielded than the corresponding protons of oenin. This observation suggests that intramolecular copigmentation also plays a role, a conclusion supported by the long-range NOE observed between the malvidin 2′,6′ protons and the vinylic α proton of the acyl residue.

By forcing water away from the chromophores, intramolecular copigmentation and self-association are expected to make them more resistant to water addition. In keeping with this expectation, the pK′_h values of the Morning glory (Pharbitis nil) anthocyanins increase with the number of HCA residues, acylating the primary C6-OH groups of the d-glucosyl-β-1,2-d-glucosyl moiety at C3-OH. (135, 154) Interestingly, the color stability is greatly enhanced on going from the monoacylated to the diacylated pigment. By assuming that the difference in the Gibbs energy of water addition in the series only reflects the selective stabilization provided by the HCA residues to the flavylium ion, it was even possible to estimate the distribution of the diacylated pigment into open, half-folded and fully folded (sandwich) conformations (Figure 16); the latter was estimated to be dominant, with a relative abundance of ca. 60%. Unlike pK_h^′, the pK_a value is not strongly affected by acylation, which suggests that the intramolecular π–π stacking interactions are as strong with the flavylium cation as with the quinonoid bases, and that the conformation distributions of the two species are broadly similar. Other studies on acylated anthocyanins have confirmed that acylation increases pK_h^′. (47, 48) This color-stabilizing effect is also observed with a remarkable pigment in which delphinidin 3-O-β-d-glucoside is covalently linked to apigenin 7-O-β-d-glucoside via a malonyl residue that bridges the two Glc C6-OH groups. (48) Interestingly, pK_a lowering was also observed with Matthiola incana anthocyanins, which are closely related to the Morning glory anthocyanins but also bear a 5-O-β-d-(6-O-malonyl)glucosyl moiety. (47) This may reflect intramolecular hydrogen bonding between the malonyl group and the O atom at C7 of the quinonoid bases. (116) A series of di- and triacylated anthocyanins bearing p-hydroxycinnamic and p-hydroxybenzoic acid residues on the sugar moieties of both the A- and B-rings were found to be so resistant to water addition that no pK_h^′ values could be determined. (155) It is however not clear whether this spectacular color stabilization reflects intramolecular copigmentation or noncovalent dimerization.

Figure 16. Morning glory (*Pharbitis nil*) anthocyanins (inspired from ref 135).

To better appreciate how noncovalent dimerization tends to erase water addition in polyacylated anthocyanins, a distribution diagram as a function of pH can be constructed with tentative stability constants for the different dimers AH⁺···AH⁺, AH⁺···A, and A···A (Figure 17). Even by assuming that the monomer itself is stabilized by intramolecular copigmentation (accounting for a relatively high pK_h^′ value of 3), very high dimerization constants in the range of 10⁴–10⁵ M^–1 are required to minimize the abundance of the colorless forms over the pH range of 3–6.

Figure 17. Distribution diagram for a prototypical acylated anthocyanin forms showing the strong influence of noncovalent dimerization. Parameters: pK′_h = 3.0 (assuming partial protection against water addition owing to intramolecular copigmentation in monomer), pK_a = 4.0, pigment concentration = 10 mM. Tentative values for the dimerization constants: K_AH+/AH+ = 3 × 10⁴, K_AH+/A = 8 × 10⁴, K_A/A = 5 × 10⁴ M^–1.

6.2 Improving the Chemical Stability of Anthocyanins by Copigmentation

The chemical stability of anthocyanins must be clearly distinguished from the stability of their color, which was the subject of the preceding discussion. Color stability relates to the reversible equilibrium between colored and colorless forms, whereas chemical stability relates to the irreversible chemical degradation of pigments, mainly arising from cleavage of the C2–C1′, C2–C3, or C3–C4 bonds of the chromophores. (111, 156-159) The former is fast while the latter takes place over time scales of hours to days, even months, depending on the conditions (e.g., pH, temperature, dioxygen, irradiation, and copigments). (160) Regardless, whether thermal or photochemical, anthocyanin degradation imposes serious limitations on the industrial use of anthocyanins as colorants for food and cosmetic applications. The mechanisms involved have not been fully elucidated but probably involve a combination of hydrolytic and auto- or photo-oxidation steps.

Some works on the photochemistry of anthocyanins have provided information relevant to this issue. Generally, anthocyanins are only weakly fluorescent and simple flavylium ions in their excited state are strong acids (pK_a < 0), rapidly transferring a proton to water. The excited quinonoid base thus formed is then deactivated by a combination of radiative and nonradiative pathways. (161) In the presence of a copigment, a very efficient alternative pathway emerges, namely the direct ultrafast (τ < 1 ps) nonradiative deactivation of the copigmentation complex via a low-lying copigment-to-flavylium CT state. Interestingly, acylated anthocyanins in their excited state are also very efficient at dissipating excess energy to water. In particular, when UV–B light is absorbed by the HCA moiety, an ultrafast energy transfer to the chromophore takes place, which successfully competes with (Z-E)-isomerization of the vinyl moiety. (162) In the sophisticated polyacylated Heavenly blue anthocyanin, this efficient HCA-to-chromophore energy transfer only takes place in neutral conditions (i.e., when the pigment adopts a quinonoid structure). Under acidic conditions, the dominant pathway remains the (Z-E)-isomerization of the most external HCA residues. (60) In parallel with those observations, the Heavenly blue anthocyanin was demonstrated to be chemically much more stable (and also much more fluorescent) at neutral pH than under acidic conditions, whereas the opposite usually holds with common anthocyanins. Overall, these results suggest that π–π stacking in anthocyanins, whether inter- or intramolecular, provides efficient pathways for energy dissipation, thereby competing with alternative pathways for the excited states that may lead to degradation. For instance, it may be noted that monoacylated anthocyanins were shown to accumulate from diacylated anthocyanins upon UV irradiation. (163)

On the other hand, the thermal degradation of anthocyanins is well-known to be slower for acylated anthocyanins or when efficient copigments are present. (164) In some cases, copigmentation by HCAs seems to compete with intramolecular copigmentation, thus leading to a net decrease in pigment stability. (136) Upon thermal treatment of weakly acidic solutions of anthocyanins and anthocyanin-rich extracts, a likely scenario is (i) the endothermic formation of C_trans, (ii) the rate-limiting hydrolysis of the glycosidic bond at C3, and (iii) the fast degradation of the chalcone aglycone to yield the p-hydroxybenzoic acid derived from the B-ring and other cleavage products. (158) The same sequence is much less favorable in acidic conditions, first because the flavylium cation is relatively insensitive to acid-catalyzed hydrolysis and because anthocyanidins are only stable at low pH (under their flavylium form). (165) It may thus be speculated that copigmentation, although typically weaker at high temperature, somewhat still limits the formation of C_trans, thereby slowing down the whole degradation process. This is consistent with the fact that chalcone glycoside intermediates could not be detected during the degradation of acylated anthocyanins. (158)

It must be noted that alternative routes not involving the C_trans intermediate may also occur, for instance oxidative pathways leading to B-ring elimination and formation of the corresponding coumarin. (164) A mechanism starting with addition of hydrogen peroxide (of undetermined origin) at C2 of the flavylium nucleus and subsequent Bayer-Villiger rearrangement was also proposed for the degradation of oenin in a wine model. (157) It may be speculated that copigmentation could protect the chromophore from H₂O₂ addition in the same way it opposes water addition.

7 Driving Forces of Copigmentation

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From the large collection of experimental studies, the driving forces of copigmentation have clearly been identified as π–π stacking interactions. Hydrophobic effects have also been suggested as a crucial contribution, as the most stable copigmentation complexes in water vanish in water:methanol (1:1) mixtures. Although both contributions are interrelated, the different attractive/repulsive contributions should be carefully distinguished. (166)

π–π Stacking had first been described by solvophobic effects of entropic origin mainly, except in water where enthalpic effects are important. Later, electrostatic interactions have been pointed out as a major driving force. (167) In particular, the electrostatic substituent effect is of crucial importance to predict aromatic stacking geometries [e.g., edge-to-face (T-shaped) arrangement vs face-to-face (displaced) parallel stacking]. (168-170) The stability of a given noncovalent stacking involving aromatic rings has exhibited correlation with the Hammett substituent constants. Even substituents at aromatic rings which have little influence on the π-electron distribution [i.e., with only an inductive (± I) but without a mesomeric (±M) effect] might exhibit a clear effect on the electrostatic potential; this allows, for example, parallel stacking of substituted benzene, whereas nonsubstituted benzene forms T-shaped noncovalent dimers. (171) The electrostatic contribution can be seen as pairwise interactions between maxima and minima of the electrostatic potential in both partners, a consideration of importance to quantify such intermolecular interaction. (172) In principle, parallel stacking complexes require one partner bearing strong electron-donor and the other strong electron-acceptor groups. (169, 170) In copigmentation, the (multiple) OH substitution pattern in both pigment and copigment is of crucial electrostatic importance to favor parallel stacking due to the considerable + M effect of the OH group. (173) Here, the relative positioning of both partners is driven by the electrostatic contribution.

In many situations, it became however clear that dispersion forces make the dominant contribution to attractive π–π interactions. The (London) dispersion interactions stem from correlation of transient dipoles among atoms and molecules. (174) They are by far the dominant noncovalent interactions between nonpolar molecules. They also contribute if the molecules are originally polar, although in this case, the noncovalent effects would also incorporate other electrostatic-driven contributions including hydrogen bonding (vide infra). It is known that parallel-displaced arrangements maximize dispersive attraction, (170) which may appear as an indicator of the ideal dispersive-type arrangement in copigmentation complexes; every variation from this geometry is driven by the other contributions. Due to the small polarizability of water molecules, dispersion interactions in intermolecular complexes are maximized in water with respect to other solvents, as in this case, the competition with solvent molecules is weakened. (166)

As said above, the copigmentation complexes are observed mainly in water and highly in polar solvents (i.e., water:alcohol mixtures with excess of water). Therefore, besides the pure pigment–copigment interaction, further contributions arising from solute–solvent interactions are likely to occur. The description of all aspects of this complex process is beyond the scope of the review (details can be found in literature refs 175 and 176), and here we only focus on some aspects which are considered important in copigmentation. Solvents with high cohesive interactions prefer to interact with bulk solvent molecules rather than to solvate the complementary apolar surfaces of solute molecules, (170) hence favoring solute aggregation by the hydrophobic effect. It is not a special type of molecular interaction but a collective effect with entropic (“classical” hydrophobic effect) and enthalpic (“nonclassical” hydrophobic effect) origin. (176) In the vicinity of a hydrophobic solute (or a hydrophobic region of a larger molecule), water molecules form a particularly organized network that maximizes the number of hydrogen-bonding interactions among them. (175) When two hydrophobic surfaces, of both a pigment and a copigment are brought together (in the copigmentation complex), the ordered water molecules are released from the intermolecular region (hydrophobic cavity) into the bulk solvent, causing an increase in entropy; that is to say, the system gains Gibbs energy. In some conditions, this can be reinforced by enthalpy gain due to the formation of new hydrogen bonds upon this water release (“nonclassical” hydrophobic effect). (176) Nonetheless, copigmentation also involves an ordering process, as the rotational and translational contributions to entropy decrease when pigment and copigment associate. This counterbalances entropic changes due to the hydrophobic effect and the overall change in entropy during the copigmentation process results from a subtle balance between these multiple effects, in which the numerous OH groups of polyphenols may participate through the (intra- and intermolecular) hydrogen-bonding network. In most copigmentation systems experimentally studied, the entropy variation is negative (Table 2). Only the negative enthalpy of association enables formation of the copigmentation complexes. This agrees with the fact that with flat molecular surfaces, hydrophobic effects are minor, and the dispersive forces mainly drive stacking. (176) Positive entropy changes were rarely observed, namely, for the interaction of malvin with highly water-soluble rutin derivatives bearing acylated succinyl groups on the sugar moiety. (130)

Hydrogen bonding between the phenolic pigment and copigment may also play a role in stabilizing noncovalent copigmentation complexes. Although its role in copigmentation is not sufficiently documented so far, it is usually weakened in water media. This agrees with the recent QM/MM calculations performed on a prototype copigmentation system, showing more planar OH groups (i.e., weakening intermolecular H-bonds between both the pigment and the copigment) with respect to calculations performed in implicit solvent (see section 10.3 and ref 173). It is thus important to recall that copigmentation is a complex phenomenon resulting from subtle combinations of different noncovalent interactions; since anthocyanins and phenolic copigments can be regarded as amphiphilic compounds, their complexation is influenced by all of these effects. The stability of a mixture of amphiphilic molecules in an aqueous environment can be maximized in two ways, namely by maximizing the solvation of their hydrophilic parts (e.g., via intermolecular hydrogen bonding with water molecules) and by minimizing the exposure of the hydrophobic parts to the polar solvent. This latter factor promotes the formation of intra- and intermolecular stacks driven by dispersion forces and, to a lesser extent, hydrogen bonding. These forces naturally lead to the copigmentation process. In accordance with the thermodynamic balance of complexation, copigmentation complexes can be stable, metastable, or unlikely; usually the entropy decrease associated with complex formation counteracts the negative enthalpy of association, as evidenced experimentally by enthalpy–entropy compensation. (113)

Because the typical intermolecular distances of parallel stacking is about 3.5 Å, a distance also obtained in copigmentation complexes (vide infra), short-range repulsive interactions (exchange term related to the Pauli exclusion principle) are most likely to contribute to the energetic balance of copigmentation. Charge transfer is suggested to contribute mainly in excited state and little in energetic stability of noncovalent complexes; however, exchange can significantly influence interplanarity. (167) One should keep in mind that other contributions could also be at stake in the stability of large copigmentation complexes, namely CH-π interactions (mainly driven by dispersion), OH-π interactions (mainly driven by electrostatics), cation-π interactions, and anion-π interactions. (170, 171, 177)

The available experimental data on physicochemical factors relevant to the formation of copigmentation complexes include information on modes of binding and energies of association. However, theoretical chemistry has become a mandatory support to experimental works, which may help figure out driving forces of copigmentation and subsequent observed changes. So far, little has been made to draw conclusions from the experimental data on the nature of the interactions and to compare the results, for example, with energetic stabilities. Theoretical studies on prototypical copigmentation complexes are required to support such comparison, which would allow a comprehensive distinction of all energetic contributions. In the future, phenolic molecular balances (166, 171, 178) could be designed to investigate and quantify noncovalent interactions in copigmentation. In any event, the molecular recognition between the two partners of a given copigmentation complex should only be interpreted with care in solvent-accessible systems. (178)

The available experimental data suggest that noncovalent copigmentation complexes may exist in various conformations and mutual orientations (i.e., they are not rigid and their structures fluctuate around minima). This makes it necessary to thoroughly sample their conformational space (i.e., the space of all their possible conformations and mutual arrangements) (also known as hypersurface), when attempting to study their behavior with computational tools. The need to explore a large number of structures prohibits the use of QM ab initio methods, necessitating the use of empirical methods in order to obtain stabilizing energies of noncovalent complexes in a reasonable time frame. Moreover, the hydrophobic effect is a collective phenomenon and the only way to properly evaluate its physical-chemical consequences is to describe the solvent explicitly. Given the size of a typical copigmentation complex, the only theoretical chemistry methods suitable for performing such calculations are MM and MD simulations. Such methods account for all of the relevant forces (i.e., electrostatic interactions, dispersion, and repulsion). However, they also face some limitations as discussed in the very next section.

8 Conformation and Thermodynamics in Copigmentation from Molecular Dynamics

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8.1 Molecular Dynamics Challenges

It is assumed that the basic concepts of MM and MD simulations are a prerequisite for comprehensive understanding of this section; more details can be found in literature. (179-181) MM relies on several approximations (179) and compensation of errors to produce useful results. (182) It should be noted that a force field is a rather complex “tool” that sometimes needs reparameterization or even the addition of new parameters, both of which are delicate tasks that can only be achieved with much care. (183) Classical MD simulations can be used to monitor the evolution of a molecular system over time. (184) They are performed using dedicated software tools (e.g., AMBER, (185) CHARMM, (186) NAMD, (187) GROMACS, (188) etc.) and usually last for between hundreds of nanoseconds and a few microseconds depending on system size and the available computational power. It is worth noting that MD simulations provide atomic and femtosecond resolutions simultaneously.

8.1.1 Exploring Conformational Space

A key objective when attempting to sample the conformational space of a system with many degrees of freedom as in copigmentation complexes is to reduce the number of conformations that must be considered by focusing on those that are most heavily populated under the relevant conditions. Conformations with lower energies (ε_i) have greater populations (p_i) according to the Boltzmann distribution (eq 9):

(9)where Q represents the partition function and β equals to 1/k_BT (i.e., inverse product of the Boltzmann constant and the temperature). One way of sampling conformational space is to identify one (or a few) reasonable conformation(s) (e.g., by geometry optimization) and then to run a classical MD simulation starting from that optimized structure.

Since MD simulations are usually carried out at room temperature (ca. 300 K), they produce conformations that are in principle accessible under experimental conditions but only over the time scale of the simulations. This means that MD simulations cannot describe “long-lasting” processes of around the microsecond time scale or above. In the case of copigmentation, nanosecond time scales are sufficient to explore the conformational space of the simplest molecular systems. However, in most real-world copigmentation complexes, jumping the energetic barriers from one potential well to another (i.e., from one conformer to another) would require a longer time. In such cases, classical MD rarely enables robust conformational space sampling. As alternatives, stochastic Monte Carlo methods based on randomly generated geometries (Figure 18) (189) as well as biased methods of MD can be employed.

Figure 18. Schematic (1D) potential energy surface (PES) showing many local minima accessible by 1 ns-long MD simulation and the necessity to properly explore the entire PES to reach the real valley via long MD simulation or biased techniques to force random exploration. (The noncovalent complex represented here is just a pictorial representation.)

8.1.2 Biased vs Unbiased Molecular Dynamics

Many techniques for performing biased MD simulations have been developed. An important one is simulated annealing, which creates bias by performing successive artificial simulated loops of heating/cooling. In this process, the system is quickly heated to a high temperature (up to several thousand Kelvin) then cooled slowly. This enables the molecular system to escape from its initial minimum then to explore the rest of its hypersurface, systematically escaping from local minima. Simulated annealing procedures have been employed regularly in studies on copigmentation (see Section 8.2).

Other more advanced methods have been developed for efficient exploration of the hypersurface, (190) including MD with quenching (MDQ), replica exchange MD (REMD), and meta-dynamics (MetaD). These methods could provide important new insights into the conformational space of copigmentation complexes.

MDQ is a variant of the classical MD, which is carried out at ambient or elevated temperature (e.g., 500 K) to facilitate escape from the initial minimum. (191) The structures along the MDQ trajectory are collected at particular time steps and minimized (quenched) using the applied force field. This technique has been efficiently used to sample the conformational space of small noncovalent complexes (e.g., the acetic acid dimer (192) and microhydration of nucleobases). (193)

In the temperature REMD (T-REMD) method, a set of several parallel MD simulations each at different temperatures are executed simultaneously, and at specific time steps a Monte Carlo step is performed to exchange structures between neighboring temperatures. (194) This method helps to overcome energetic barriers; however, some conformational transitions are not facilitated by the T-REMD method if the system is entropically biased. (195) This behavior may significantly limit the usefulness of T-REMD as a tool for studying the conformational space of copigmentation complexes.

MetaD (196) requires the definition of one or more collective variables, which are typically the root-mean-square-deviation from a given structure, radius of gyration, and number of intermolecular hydrogen bonds. During a MetaD simulation, a biasing potential is deposited at given time steps to the collective variable, filling potential wells of the hypersurface. The biasing potentials are collected and integrated after the MetaD run, enabling reconstruction of the Gibbs energy surface from the obtained negative picture. This method is very effective and many flavors of MetaD have been developed to date. The selection of a suitable collective variable(s) remains the major challenge of MetaD. (197)

8.1.3 Estimation of ΔG_binding

Theoretical modeling of copigmentation mostly focuses on conformations and related stabilities, which are well expressed in terms of Gibbs energies of association (binding), ΔG_binding. In accordance with the first principle of thermodynamics, the Gibbs energy of binding is negative for complexes that form spontaneously; the lower the ΔG_binding, the more stable the complex. As noted above, classical MD simulations enable identification of the favored conformations quite effectively. (198) Because the various copigmentation complex conformers usually differ in Gibbs energy by only a few kcal/mol, (108) the quality of force field is crucial. It may bias the differences among individual conformers and could even create erroneous ordering. In this case, it is recommended to further minimize the different identified conformers using QM methods and to evaluate the differences among individual conformers using high-level QM calculations.

Postprocessing methods have also been developed to estimate the Gibbs energy of association. They are known as MM with Poisson–Boltzmann surface area (MM-PBSA) and MM with generalized Born Surface Area (MM-GBSA). (199) Both methods are based on the thermodynamic cycle (Scheme 3), which makes it possible to split the process into two parts, one corresponding to complex formation in the gas phase and the other to the transfer of the process from the gas phase to a solvent (usually water).

Scheme 3. Thermodynamics Cycle for the Formation of Copigmentation Complexes in Water (Comprising Complex Formation in the Gas Phase and the Transfer of the Process from the Gas Phase to Solvent)

The Gibbs energy of association is then estimated using the following formula:

(10)where ΔH_MM is the MM enthalpy in the gas phase; ΔS_MM is the entropy of the solute in the gas phase; and ΔG_solv is the solvation Gibbs energy and all these terms are averaged along the MD trajectory.

The solute entropy is computed under the quasiharmonic approximation by means of normal mode calculations. (200, 201) The electrostatic contribution to the solvation Gibbs energy is estimated using continuum solvation models based on the generalized Born (GB) (202) or Poisson–Boltzmann (PB) (203) equations, and the nonpolar terms are derived using surface area (SA). (204) In principle, the absolute values of the estimated Gibbs energies of association may be biased by the used approximations; however, they can be more safely used for ranking various complexes or their conformational states (see section 8.2.1 for further details).

8.2 Molecular Picture of Copigmentation

8.2.1 Molecular Dynamics Based Studies: Early Stages

The first MM calculations on copigmentation complexes were performed with the MM+ (205) force field both in vacuo and in a water box. (47) Indirect molecular information was actually available in both these studies because the calculations were performed on the pigments alone (in absence of explicit copigments), namely delphinidin 3-O-gentiobioside and cyanidin 3-O-rutinoside, with both favylium and hemiketal forms being considered. Low intramolecular distances were predicted which supported the possibility of hydrogen bonding between the pigment and the sugar moieties. More recently, Yoshida et al. performed MM calculations on the pigments albireodelphin A and monodeacylgentiodelphin (two acylated gentiodelphin pigments linked, at different locations, to one caffeic acid as copigment). (141) The interacting potential was described by the CHARMM force field, and an implicit water solvent was used. Various geometrical features were constrained according to NMR data. In particular, distances were fixed at 2.5 ± 0.5 Å and 4.0 ± 1.0 Å when strong and weak NOE contacts were observed, respectively. Interestingly, no interaction was observed between the pigment and the copigment for the former compound, whereas some conformers of the caffeoyl moiety approached the pigment at the van der Waals distances. The most stable conformers were obtained from the analysis of several thousand conformers. However, in this case, one can expect that several conformations were relatively close to each other in energy and could have been considered as well.

At about the same period, MM simulations were performed on theaflavin self-association and theaflavin–caffeine complexation. (206) Again NOE-NMR contacts were evidenced between the two partners, which were used to perform constrained simulated annealing. The proposed supramolecular arrangements confirmed the importance of π–π stacking and hydrogen-bonding intermolecular interactions, which was revealed by the predicted formation of a spatial arrangement in which the electron deficient tropolone ring lies directly over the electron-rich catechol ring.

MM calculations were carried out as an initial step to evaluate the conformational features of (i) a series of anthocyanins (peonidin-3-O-glucoside, pelargonin, cyanin, oenin, and malvin) complexed with several phenolic derivatives (gallic acid, protocatechuic acid, ferulic acid, caffeic acid, and quercitrin), using the MM+ force field; (105) (ii) oenin and five phenolic compounds (caffeic acid, catechin, proanthocyanin B, rutine, and ellagic acid), using the AMBER force field; (207) and (iii) oenin and five different hydroxybenzoic acids (p-hydroxybenzoic acid, protocatechuic acid, gallic acid, vanillic acid, and syringic acid). (49) However, these reports included only a few details on the procedures used to ensure comprehensive coverage in the conformational analysis. Some other studies have been reported in which more care was taken to ensure adequate conformational sampling, and more comprehensive details of the MD simulation procedure or simulated annealing protocol were provided. For example, the geometrical features of the cyanidin···baicalein 7-O-glucuronide copigmentation system was explored based on a joint simulated annealing and 300 ps-long MD simulation procedure using the Tripos force field and the SPC explicit solvent model. (208) A thorough conformational analysis of 115 conformations and mapping of hydrophilic and hydrophobic spots on the Connolly surface demonstrated the importance of hydrogen bonding and the hydrophobic effect in this system. Water was excluded from the space between the interacting partners, leading to the formation of a so-called lamellar stacking system (see Figure 19 for similar arrangements).

Figure 19. Molecular dynamics snapshot of the 3-*OMe*-cyanidin···quercetin noncovalent complex (the pigment 3-*OMe*-cyanidin in red; the copigment quercetin in yellow), showing the space between both partners depleted from water molecules.

MD simulations were also performed on the malvidin···ellagic acid complex. (209) The AMBER force field was used to treat the solute, whereas the solvent was treated with the TIP3P model, using different mixtures of solvents to evaluate the effects of ethanol (0% and 14% ethanol in volume). A 100 ns equilibration period was used, which was considered sufficient to characterize all intermolecular reorganizations in the first solvent shell. Over this time scale, the ethanol molecules clearly aggregated around the copigmentation complex, and with the 14%:86% ethanol:water mixture, the first solvent shell consisted of 50%:50% ethanol:water. The authors assigned this behavior to strong entropic effects when water was replaced by ethanol in the first solvent shell, thus modifying subsequent enthalpy–entropy compensation. This is seemingly consistent with the fact that the entropy of water decreases locally around the hydrophilic moieties of the copigmentation complex, which counteracts the noncovalent association. The magnitude of this effect was probably eliminated by replacing water by ethanol in the first solvent shell. This is perfectly consistent with the experimental work described above using malvin and common copigments in the presence of moderate amounts of ethanol molecules and shows that ethanol preferentially accumulate in the first solvation shells. (113)

A conformational search procedure using CONFLEX (conformational analysis of flexible molecules) with the MM3 force field was used to explore the conformational space of three oligomeric pyranoanthocyanin···flavanol pigments isolated from Port wines (pyranomalvidin-3-O-glucoside···procyanidin B3, pyranomalvidin-3-O-glucoside···(+)-catechin and pyranomalvidin-3-O-glucoside···(−)-epicatechin). (16) The authors confirmed intramolecular π–π stacking between the pyranoanthocyanidin chromophore and the second catechin moiety of B3, with an interatomic distance between the aromatic rings of 3.25 Å. Pyranomalvidin-3-O-glucoside···(+)-catechin exhibited a less closed structure than pyranomalvidin-3-O-glucoside···(−)-epicatechin, which impacted the copigmentation process, the latter pigment having a stronger hyperchromic effect.

Regular MD simulations were performed with copigmentation complexes formed by the noncovalent interaction between two pigments (oenin and malvin) and three copigments (two vinylcatechins and procyanidin B3). (110) With the general AMBER force field (GAFF) (180) for the pigment···copigment systems and TIP3P for water, a 100 ps equilibration step was followed by a 10 ns-long simulation, which was suggested to enable exploration of the potential energy hypersurface. The same procedure was applied on oaklin compounds formed in red wines aged in oak barrels, namely guaiacylcatechin-pyrylium and syringylcatechin-pyrylium, with common copigments including catechin, epicatechin, chlorogenic acid, epigallocatechin, and procyanidin B3. (210) The average minimal distances between pigment and copigment were greater than 4.65 Å, which is slightly greater than the optimal distance for efficient π–π stacking. Hydrogen bonding was also observed in all pigment···copigment complexes (indicated by an interatomic distance of ca. 2.7 Å).

The MM-PBSA technique has thus been used successfully in two separate studies to score the relative binding energies of copigmentation association. The MM-PBSA method provided the correct ordering of the formed complexes, thus making it possible to confirm previously proposed structure-affinity relationships. Moreover, it was shown that vinylcatechin and epicatechin provided the most efficient copigmentation stabilization in both studies, respectively. The quantitative description failed with respect to experimental binding Gibbs energies, which was attributed to the approximations underpinning the MM-PBSA method.

Interestingly, classical MD has also been used to study self-association of polyphenols in complex environments. As polyphenols are amphiphilic compounds, they distribute into biological membranes in cells. (211-214) Biased and free MD simulations highlighted the formation of self-association complexes and complexation with vitamins in lipid bilayers (Figure 20). This was confirmed by spectroscopic measurements. In this case, complexation occurred over a time scale of several nanoseconds, between the lipid chains of the bilayer (i.e., in a hydrophobic environment). In this case, the driving force of self-association and complexation was π–π stacking and hydrogen bonding to a lesser extent. It should be noted that MD simulations are sufficiently mature to enable simulation of such complex environments (e.g., lipid bilayers, micelles, etc.) and impact of such environments on copigmentation processes.

Figure 20. π–π Stacking complexes between quercetin (yellow) and vitamin E (green) in lipid bilayer membranes.

8.2.2 Challenges in the Theoretical Description of Copigmentation Complexes

The results presented in the preceding subsection strongly suggest that the precise choice of force field one makes will not necessarily greatly change the conclusions one obtains concerning geometrical features of copigmentation. Indeed, all regular force fields can adequately cover the essential noncovalent interactions occurring during copigmentation. Also the use of explicit solvent enables a qualitative description of the hydrophobic effect. Therefore, one might anticipate that a qualitative description can generally be reached when using regular MM-based calculations. In any case, the exploration of the conformational space, and identification and energy ordering of all possible copigmentation complex arrangements remains the real challenge. Again, the reader should be aware that sampling the conformational space requires sufficiently long MD simulations, properly parametrized simulated annealing procedures or sophisticated-biased MD simulations (see section 8.1.2).

Another critical issue that, in principle, could be addressed using MD is the real capacity to form copigmentation complexes, which is determined by the Gibbs energy of association ΔG_binding (see section 8.1.3). Obtaining accurate estimates of such Gibbs energy changes (with errors of less than 1 kcal/mol) remains an important challenge in contemporary computational chemistry. As noted above, there are several specialized methods that can be used to estimate ΔG_binding from classical and biased MD simulations. The predictive potential of these methods is mostly limited by the robustness of their sampling and the accuracy of the force field used. As the Gibbs energy of association is based on both enthalpic and entropic contributions, the quality of the force field is mostly reflected in the enthalpic term, whereas the sampling is in the entropic term. This is useful when attempting to improve the estimated association energies obtained with empirical methods.

The enthalpy can be estimated using QM calculations. In principle, using high-level QM methods the electronic energy can be accurately calculated, but there are still some uncertainties in calculations of zero-point vibrational energy (ZPVE). ZPVE is usually calculated using the harmonic approximation, which is generally sufficiently accurate around the minima for many molecular systems but might be not valid especially for low-frequency vibration modes (intermolecular breathing modes) of noncovalent complexes. Accounting for anharmonic contributions may improve the estimation of ZPVE. It should be noted that the errors in ZPVE estimation account usually to ∼1 kcal/mol. Anyway, the accurate estimation of the entropy remains difficult for accurate estimation of association energies, especially for QM methods, which assess the entropy using the apparatus of statistical mechanics and adopting the ideal gas, rigid rotor, and harmonic oscillator approximations. (215)

9 Conformation and Thermodynamics in Copigmentation from Quantum Chemistry

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The geometries identified by MM-based calculations can be subsequently used as inputs for QM-based calculations in order to: (i) describe in detail the electronic configurations of both the separated monomers and the weakly bound complex; (ii) study any chemical property (e.g., deprotonation) or bond rearrangements that occur upon complexation; (iii) distinguish between attractive and repulsive energetic contributions, which are governed by the complex’s underlying electronic structure; and (iv) evaluate all kinds of specific optical features, which arise from the properties of excited states (see section 10). It is important to apply QM methods rigorously and on the basis of a sound understanding of the underlying theories and to select methods with care from the wide range that are available. Our aim here is to provide a comprehensive and brief listing of computational methods suitable for studying copigmentation. This is necessary because the field is so broad that it is important to cater to researchers with widely varying levels of expertise in different aspects.

In the context of conformation and thermodynamic stability of copigmentation complexes, dispersion (London) forces must be accurately evaluated. Dispersion interactions originate from electron correlation effects, which are not fully captured by theoretical approaches based on the mean-field approximation, such as Hartree–Fock (HF) theory. This means that it is necessary to study these phenomena using alternative first-principles methods such as density functional theory (DFT) or post-HF methods.

9.1 Computing Copigmentation with DFT

The correlation functionals that are most commonly used in DFT studies are considered semilocal; i.e., they compute the correlation energy as a functional of the electron density at a given point r in space, and its gradient, E_c[ρ(r),∇ρ(r)], as well as higher-order derivatives, E_c[ρ(r),∇ρ(r),∇²ρ(r)]. These approaches neglect long-range electron–electron correlation effects. In this section, we briefly describe how current dispersion-corrected functionals address this problem, making possible an accurate modeling of the interactions that enable copigmentation (for some relevant reviews, see refs 216−226).

The most commonly utilized (semi)classical picture expresses dispersion energy (E_D) as a sum of pairwise interactions between the relevant weakly overlapping entities (atoms, molecules, or atoms-in-molecules):

(11)where R_IJ is the separation of entities I and J, and C₆^IJ is the interatomic dispersion coefficient. We also note that these interactions are not limited to the dipole–dipole case; more generally speaking, the energy can be written as a multipole expansion:

(12)where the different terms represent dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole (or dipole-octupole) effects, respectively. The dispersion coefficients depend on the polarizabilities as described by the Casimir-Polder expression: (227)

(13)with α(iω) being the frequency-dependent polarizability. While C₆^IJ can be computed explicitly, the other coefficients are normally calculated recursively [e.g., C₈^IJ = 3C₆^IJ(Q_IQ_J)^1/2 with Q being related to < Rⁿ> multipole-type expectation values and nuclear charges]. (-228-232) However, these coefficients can be computed using more sophisticated schemes; for example, the XDM method calculates them very accurately from the exchange-hole dipole moment. (233-235) At this point, we would like to note that the distance dependence (R^–6 and beyond) of the dispersion energy is clearly of a long-range nature, meaning that it influences both thermodynamic parameters and chemical reactivity in solvated environments. The energy expression given in eq 12 is asymptotically correct; however, it diverges at small interatomic separations. The simplified form is also used in the Lennard-Jones potential, E_D = 4ϵ[(σ/R_IJ)¹² – (σ/R_IJ)⁶], which is used in many force fields and where the latter term stands for the dispersive (attractive) interaction. Although it is widely used and remarkably accurate for most systems, it is important to recall that this pairwise additivity scheme does not fully reflect the collective nature of the dispersion interactions (i.e., the relevant many-body effects).

The binding (or association) energy (ΔE_binding) for two weakly interacting M and N (sub)systems has a profound effect on the supramolecular self-assembly of copigments. This energy is given simply by

(14)where the M···N notation is used throughout this text to emphasize the key role of weak interactions, and where E(M) and E(N) are the energies of the isolated pigments (which must all be computed at the same level of theory). This expression can be easily generalized to describe the copigmentation association of more than two molecules by using the many-body expansion. (236, 237)

The most popular and reasonably successful DFT-based methods describing dispersion are those which include pairwise additive corrections. The direct application of a classical dispersion correction, E_D ∝ – R^–6, is inappropriate because it will lead to a double-counting of the energy at intermediate distances and a divergence at shorter distances. Coupling the energy terms with some parameter fitting can avoid the double-counting problem, whereas introducing a damping function (238-240) allows managing the transition from short-to-long distances in order to avoid the problem of divergence.

Actually, the reparameterized -D3(BJ) method (241-243) illustrates the state-of-the-art of current corrections. There are also various simplified versions of this correction; while the primitive -D1 variant has gradually been discarded, (244) the -D2 method (245, 246) is still widely and successfully used. To further illustrate the use of the above correction in the field of natural polyphenols, taking into account the diversity of this review’s intended readership, Figure 21 shows the magnitude and shape of the dispersion energy as a function of the interatomic distance for three pairs of interacting IJ atoms: C–C, C–H, and H–H. Note that we have truncated the expression for E_D at first-order and used a value of s₆ = 1.0 for the sake of readability. Broadly speaking, we can clearly see that: (i) the energy peaks at approximately the average van der Waals radii of the two atoms involved; (ii) less energy is introduced for less polarizable atoms; (iii) the expression displays the correct asymptotic behavior; and (iv) it augments the electronic energy for all of the interacting atoms, at a negligible computational cost.

Figure 21. Dispersion energy as a function of the interatomic distance for a set of selected atomic pairs.

We also wish to mention some other approaches, namely the vdW-TS method; (247) the density-dependent energy correction (dDsC) which introduces a density-dependent damping function (248) and reduces the severity of intramolecular errors without perturbing the good performance achieved for long-range dispersion interactions; (249, 250) and the DFT-lg method. (251, 252) Seamless additive corrections have also been developed, in which the missing dispersion energy can be obtained by considering the coupling of the electronic densities ρ(r) and ρ(r′) at two different points within the electronic coordinate space, r and r′. The corresponding general correlation functional expression (253-256) includes a coupling function Φ(r, r′) partially accounting for nonlocality (DFT-NL methods), which naturally vanishes at short electron–electron distances and concomitantly describes intramolecular dispersion interactions. (257-261) Other recent refinements have been proposed (262, 263) whose development has led to the VV10 final form. (264-269) This approach has yielded some remarkably accurate results. (270-272)Figure 22 outlines the two approximations (DFT-D3 and DFT-NL) discussed so far. Finally, we mention that nonpairwise effects may be important in inhomogeneous systems or in cases where there is a large region of vacuum between weakly interacting molecular fragments. Furthermore, it has recently been shown that the size dependence of the dispersion interactions deviates from the expected rule E_D ∝ k² (where k is the number of weakly interacting entities), with some unusual behavior observed depending on the dimensionality of the system. (273, 274)

Figure 22. Sketch of the two main DFT-based corrections discussed: the statically averaged interaction (top) and the dynamically interacting densities (bottom).

9.2 Other Methods to Compute Copigmentation

Post-HF methods can minimally describe the dispersion energy by truncated perturbation theory, in which the intermolecular correlation energy is introduced by coupling both monomers with their respective excited-state via a long-range term that has a stabilizing effect. Double excitations are very important for electronic correlation, and therefore the simplest size-extensive ab initio method (e.g., Møller–Plesset perturbation theory truncated at second-order, MP2) can at least partially describe dispersion effects. However, this method cannot be used to simultaneously describe multiple excitations within and between the interacting molecules, and it is thus not recommended for an accurate description of the copigmentation process due to its well-known overestimation of binding energies.

Coupled-cluster single and double (CCSD), or more appropriately the extension known as CCSD(T), including a perturbative-like correction Δ(T), is considered to be the “gold-standard” method of computational chemistry. (275) Other perturbative corrections that have been investigated, such as the CCSD[T] method, are also very accurate (276) and reaffirm the excellent trade-off between accuracy and computational cost inherent to CCSD(T).

We hasten to note that the CCSD(T) method seamlessly covers all types of noncovalent interactions in an accurate way. Unfortunately, its computational cost is very high because it formally scales with system size as O(N⁷), where N is related to the system size. This makes it difficult to use CCSD(T) to model large (real-world) copigmentation complexes. Furthermore, the performance of these high-level techniques is strongly dependent on the manifold of virtual orbitals available for excitations (the larger, the better), so it is important to use very large basis sets to achieve nearly converged results at the complete basis set (CBS) limit. This truncation of the basis sets space leads to the undesired basis set superposition error (BSSE), which is known to overestimate artificially the strength of the binding energy. Even when the use of a counter-poise corrections is sometimes recommended, which simply aims at subtracting that additional energy by a set of additional calculations, it has been recently questioned too. Various strategies have been proposed, but their description is beyond the scope of the review. One can mention MP2-F12 and CCSD(T)-F12; (277-281) domain-based local pair-natural-orbitals (DLPNO) CCSD(T) method; (282-295) and spin-component-scaled (SCS) variants of MP2 and CCSD. (296, 297) The latter approach (SCS-MP2) has been theoretically rationalized (298, 299) and leaves the opportunity to reweigh each contribution specifically for noncovalent interactions (e.g., SCSN-MP2, (300, 301) SCS-MP2-D2, (302) SCS(MI)-MP2, (303) DW-MP2, (304) SCS-S66-MP2, (305) and SCS(MI)-CCSD (306) to name just a few applications). (307-313)

Table 3 stresses again the computational demands of the available post-HF methods, showing their formal scaling. All DFT-based methods formally scale from O(N³) (pure) to O(N⁴) (hybrid) to O(N⁵) (double-hybrid) in the worst case, so their scaling is a few orders of magnitude lower than the wave function-based methods discussed previously.

Table 3. Formal Scaling of Different Methods Belonging to the Wavefunction Family

method	CCSD(T), CCSD[T]	CCSD, SCS-CCSD	MP2.5, MP2.X	MP2, SCS-MP2
scaling	O(N⁷)	O(N⁶)	O(N⁶)	O(N⁵)

The interaction between molecules typically involves electrostatic, polarization, dispersion, and repulsion contributions. It is worth noting that these contributions are difficult to separate experimentally, and to this end, the symmetry adapted perturbation theory (314, 315) may assess the role of individual contributions. (316-318)

While density-fitting or resolution-of-the-identity techniques can substantially alleviate the computational costs of wave function-based calculations, they are also applicable to DFT methods, so the latter will always be favored in terms of their balance between accuracy and cost. However, there might be situations where even DFT is too costly for rapidly screening noncovalently bound systems, in solvated or unsolvated environments, and so alternative low-cost methods may be needed. If we also take the need for large basis sets when using common ab initio methods into account, it is clear that major savings can be achieved by using methods that can provide qualitatively (or better still, semiquantitatively) correct results with minimal basis sets. The recently developed HF-3c method (319-321) (the suffix -3c denotes a triple pairwise correction) is an outstanding method of this kind. A valence variant (HF-3cv) also exists, in which the core electrons are treated with pseudopotentials (relativistic effective core potentials) reducing the computational cost even further. (322) We should note that a density-based variant, dubbed as PBEh-3c, has been also recently proposed. (323)

The only way to achieve greater computational speedups would be to neglect three- and four-center integrals in the HF treatment, leading to the semiempirical OMx or PMx methods (324-326) with some supplementary corrections for dispersion and/or hydrogen bonding. This approach has resulted in the development of improved semiempirical methods such as OM3-D3 (327, 328) and PM6-DH(2). (329, 330) The density functional tight binding (DFTB) method also uses a minimal basis set and provides reasonably accurate results at a fraction of the cost of a standard calculation thanks again to some parametrization of the integrals. (331, 332) Novel features are the use of dispersion corrections (333) and the self-consistent charge density functional tight binding method (SCC-DFTB) for the treatment of charged systems. (334)

It is important to note that the list of methods and applications presented herein is not exhaustive because of the vast and rapidly growing number of possibilities in this vast field. We have nevertheless tried to give a first comprehensive (although necessarily limited) view of the complex and rich physics of dispersion interactions and to demonstrate why there is such a large range of available methods with very different formal scalings with respect to system size.

9.3 Quantum Chemistry Studies on Copigmentation: Failures and Successes

9.3.1 Conformational Analysis

Only a few purely QM studies on the conformational analysis of copigmentation complexes have been published so far. (114) QM calculations (mainly using DFT) are typically performed on the most stable conformers, which are generally identified using MD (see section 8.2). Indeed, for most real-world copigmentation systems, the number of degrees of freedom is too high to permit random exploration of their conformational space using robust but costly QM methodologies. However, such approaches are viable for systems with a very limited number of degrees of freedom. For example, we recently reported a systematic scan of the 3D space of intermolecular coordinates for the copigmentation pair consisting of 3-OMe-cyanidin (with the pigment in its flavylium form) and quercetin (the copigment). (114) Scanning along the z-axis, which was defined as being perpendicular to the coplanar and cofacially oriented partners, revealed an energy minimum at an intermolecular separation of 3.3 Å, which is typical for π–π stacking interactions. Scanning in the xy plane then resulted in the identification of five conformers (named conformers 1–5 in the related publication), which may be stabilized by a combination of π–π stacking and (in some cases) intermolecular hydrogen-bonding interactions [e.g., between the OH groups of the two partner’s B-rings in the most stable conformer (conformer 5) or involving the keto group at C5 of quercetin (conformer 2)] (see Figure 23, panels A and B). Even with such a simple binary copigmentation system, there is considerable flexibility in the stacking of the two partners. As was suggested previously, the system was shifted slightly away from pure cofacial stacking, with both B-rings being parallel-displaced (Figure 23A). Note also that, as suggested by Hondo et al., (131) chiral (clock-wise or anticlockwise) rearrangements are likely, as confirmed by this QM study (Figure 23C). In addition, the individual partners sometimes “bend” away from purely coplanar stacking arrangements, mainly because of intermolecular hydrogen bonding (Figure 23D). The identification of these different geometries prompted further MD simulations in a box of water, (173) which confirmed the coexistence of the five conformers and revealed large hydrophobic effects, with the space between the two fragments being completely devoid of water molecules (Figure 19).

Figure 23. Five stable conformations of the 3-*OMe*-cyanidin··· quercetin noncovalent complex (A) side-view and top view showing the parallel-displaced arrangement; (B) side-view showing the intermolecular hydrogen bonding of conformers 2 and 5; (C) top view showing the supramolecular chirality in conformers 3 and 5; and (D) side-view showing the slight bending in conformers 1 and 5.

We wish to stress that with the 3-OMe-cyanidin···quercetin copigmentation prototype, the only way to obtain a potential well along the z-axis within the DFT framework was to include dispersion forces, through the DFT-D correction. The use of uncorrected hybrid functionals, such as B3P86 or B3LYP, precluded the description of a stable complex (Figure 24). Interestingly, the copigmentation complex of oenin and ellagic acid, with and without the presence of ferrous and ferric ions, has also recently been studied with great success using B3LYP. (209, 335) The presence of such ions clearly enhanced the electrostatic interactions between the two partners and helped drive the stacking that was ultimately identified, with the cation thus promoting the formation of a sandwiched structure in which it is “trapped” between the two active partners (e.g., malvidin-Fe(II)-ellagic acid). The incorporation of the cation increased the stacking distance between the two partners from roughly 2.6 to 5.0 Å, again demonstrating its important effect. These results demonstrate that such through-space cation-π interactions can be (semi)quantitatively described by uncorrected DFT-based methods. Note, however, that the distance between the stacked molecules in the absence of ions is generally below the sum of their van der Waals radii, (336) and thus indicates some mismatch between electrostatic and dispersion interactions. This again highlights the need to use dispersion-corrected methods that adequately balance all kinds of noncovalent interactions when studying this type of complexes.

Figure 24. Potential energy curve along the z-axis defined perpendicular to the planar π-conjugated system, as obtained by three methods of calculation.

Systematic QM evaluations of the potential energy curve along the z-axis would be particularly instructive when studying copigmentation. However, such methodologies cannot be recommended as standard tools for describing the geometrical features of copigmentation complexes. Combining QM with MD simulations appears a much better way of dealing with these complexes’ geometrical flexibility; the MD simulation is performed first (it should generally be unbiased, but biased simulations may be preferable if reliable experimental data can be used to constrain the geometries) followed by QM calculations on selected geometries to confirm their relative stabilities.

9.3.2 Association Energies

So far little has been made to establish a quantitative comparison between experimental and theoretical ΔE_binding, which, as detailed above, remains a complex challenge. Nonthermally corrected association energies were computed for the five conformers found for 3-OMe-cyanidin···quercetin at the B3P86-D2/cc-pVDZ level, yielding values of −13.3, −13.1, −12.8, −13.4, and −13.9 kcal/mol, respectively. (114) From these results obtained at the dispersion-corrected DFT level, the Boltzmann distribution was predicted to be 16.2%, 12.9%, 7.0%, 19.9%, and 44.4% for the five conformers, respectively. This distribution gave a weighted association energy of −13.3 kcal/mol, which was rather close to the experimental enthalpy (−13.9 kcal/mol) obtained for a similar system. (30)

Interestingly, self-association was also observed between the two partners, with a slightly higher association energy (corresponding to a lower stability) of ca. −12.7 kcal/mol being determined for the self-association of the flavylium form of 3-OMe-cyanidin. As previously suggested, the self-association between two flavylium cations appeared feasible based on our dispersion-corrected calculations, confirming that noncovalent interactions can counteract the repulsive electrostatic interactions between two positively charged species.

Table 4. Calculated Association Energies (kcal/mol) for the Prototypical Copigmentation System 3-OMe-Cyanidin···quercetin, in Their Five Stable Conformers

	conformer	conformer	conformer	conformer	conformer
	1	2	3	4	5
HF-3c	–15.8	–18.1	–17.8	–15.8	–20.1
B3P86-D2/def2-QZVP	–12.6	–16.5	–14.1	–13.8	–17.3
B3P86-D3(BJ)def2-QZVP	–14.5	–18.2	–16.6	–15.8	–19.2
B3P86-NL/def2-QZVP	–17.6	–21.7	–19.9	–19.2	–23.4
SCS-S66-MP2/def2-QZVP	–17.6^a	–22.6^a	–20.0^a	–19.4^a	–23.5^a
COSMO-B3P86-D2/def2-QZVP	–6.9^b	–8.6^b	–6.8^b	–7.5^b	–10.6^b
COSMO-B3P86-D3(BJ)/def2-QZVP	–8.8^b	–10.3^b	–9.3^b	–9.5^b	–12.5^b
COSMO-B3P86-NL/def2-QZVP	–11.7^b	–13.6^b	–12.4^b	–12.8^b	–16.5^b

Values may be considered as reference for gas phase estimates.

Values for the water phase represented by a continuum solvent.

Table 4 lists some energies computed for the five conformers of the 3-OMe-cyanidin···quercetin system using the DFT-D2, DFT-D3, and DFT-NL variants with the very large def2-QZVP basis set, in the presence and absence of solvent effects. We can clearly see the pronounced influence of the solvation shell (even when described using a continuum model) and, concomitantly, the robust behavior of all the dispersion corrections considered. For example, the (solvated) weighted association energy is predicted to be −12.4 kcal/mol at the COSMO-B3P86-D3(BJ)/def2-QZVP level, with conformer 5 (the most stable) of 3-OMe-cyanidin···quercetin contributing most heavily to this value. Interestingly, the low-cost HF-3c method performs rather well. Note, however, that further and more detailed benchmark studies are required to establish a global consensus concerning method selection for the accurate description of copigmentation complexes.

Evaluating the Gibbs energy of association of copigmentation complexes is even more challenging than estimating their electronic energy and enthalpy, not least because of the difficulty of estimating the entropy correction. The translational, rotational, and vibrational contributions to entropy are evaluated using expressions from statistical thermodynamics, subject to the ideal gas, rigid rotor, and harmonic approximations. However, some features of copigmentation complexes go beyond these approximations. It is also important to note that QM calculations are performed either in vacuo or using implicit solvent models, mainly polarizable continuum models (e.g., PCM or COSMO) in which the solute is placed in a shape-adapted cavity surrounded by a continuum dielectric medium. This approach usually accounts for mean-field polarizable effects reasonably well but all specific interactions with water are ignored, which can be critical in the case of copigmentation. It also means that hydrophobic effects and related entropic contributions cannot be accounted for directly. An explicit description of the first solvent shell would enhance the results but dramatically increase the computational effort. The use of implicit solvent also has direct consequences for the evaluation of energies and enthalpies of binding because stabilizing hydrogen bonds between the pigment and copigment may compete with intermolecular hydrogen bonding between the two partners and water molecules. Again, further developments based on combining QM and MM calculations (QM/MM) are probably required to improve the prediction of ΔG_binding.

10 Underlying Concepts of Spectral Shifts in Copigmentation

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Having identified QM methodologies based on cost-effective dispersion-corrected DFT methods as particularly appropriate tools for studying pigment-copigment systems, (337) we now turn our attention to the prediction of their electronic and optical properties with the aim of better understanding their UV–vis absorption spectra. This is particularly important because, as noted above, UV–vis spectroscopy is the most important experimental tool for studying copigmentation. There have only been a few publications reporting the successful interpretation of copigmentation complexes’ spectral behavior on the basis of computational investigations. (105, 108, 114) However, several investigations along these lines have been initiated because copigmentation is a complex electronic process (vide infra). On one hand, it involves electronic properties arising from the pigment and the effects of the copigment, such as the stabilization of specific (de/protonated) pigment forms at a specific pH values due to its close contact with the copigment. Moreover, it involves cooperative pigment-copigment electronic interactions that enable the formation of energetically low-lying CT states. Both factors can significantly, and simultaneously, contribute to energetic (bathochromic) shifts and hyperchromic effects affecting the pigment’s UV–vis spectrum. The understanding of experimental UV–vis spectra is further complicated by the fact that electronic transitions in the visible range, including the CT states, are close in energy. (114) Moreover, the corresponding bandwidths are large, so the apparent “main” absorption is actually a collective response of different electronic excitations. Consequently, spectral shifts and intensity enhancements cannot necessarily be interpreted using a simple scheme.

10.1 Charge Transfer and Underlying Theory

For anthocyanins not engaged in copigmentation complexes, various QM-based studies have calculated the UV–vis absorption features, mainly of their flavylium cation forms, which were the subject of a recent review. (173) These studies have highlighted the crucial importance of: (i) the choice of method and (ii) the description of the environment (water solvation mainly). With respect to the first of these points, the available options include the semiempirical ZINDO method, (152, 338) post-HF methods for excited states (e.g., configuration interaction: CI, CIS(D), CC2, or CASPT2) (339) and TD-DFT methods. (50, 69, 108, 114, 340-343) In terms of computational feasibility and accuracy, TD-DFT appears to currently represent the optimal compromise between computational cost and accuracy when studying the optical properties of anthocyanins.

The electronic description of the excited states presents an additional challenge due to the potential for the existence of CT states. These states can form because of the energetic offset between the frontier MOs of the pigment (which commonly acts as the electron acceptor, A) and the copigment (typically the donor, D), as shown in Scheme 4. In the simplest approximation (i.e., a one-electron case with no mixing of the D and A MOs), the energy of the CT state is given by

(15)

Scheme 4. (A) Simplified MO diagram for CT and exciton formation of a DA and AA pair (H = HOMO, L = LUMO)^a

In reality, MO mixing, configuration interaction (CI), and mixing with higher allowed excited states through perturbation significantly change this picture, which is highly dependent on the electronic natures of D and A as well as their mutual orientation (intermolecular distance, rotation, and lateral displacements). However, as a rule of thumb, the energy of the CT state is still mainly driven by E_L^A – E_H^D, and the oscillator strength by the degree of MO mixing (i.e., mainly by the energetic offsets ΔE_L = E_L^A – E_L^D and ΔE_H = E_H^A – E_H^D). (344) This also suggests a basic correlation between the amount of bathochromic shift and decrease of the oscillator strength for the CT state.

This facile picture is significantly altered in more accurate time-dependent approaches such as TD-DFT. In fact, CT states are usually predicted to have very unrealistically low energies, (345, 346) which renders the standard TD-DFT treatment almost meaningless. This behavior can be understood by combining purely electrostatic arguments with the underlying TD-DFT equations that are routinely employed. (347) Assuming that, during CT excitations, some charge density is transferred from one region to another that is distant in space, and that these separated charge densities can be approximated as point charges separated by a distance R, the distance-dependent excitation energy is estimated as

(16)where IP_D is the ionization potential of the donor, EA_A is the electron affinity of the acceptor, and 1/R is the electrostatic separation at the distance R between pigment and copigment. However, when one applies and develops the TD-DFT linear-response equations for a pure functional, taken here as an example, and assuming that the relevant CT excitation is dominated by a HOMO to LUMO transition, this energy is estimated in terms of one-electron orbitals as

(17)with f_XC being the exchange-correlation kernel (i.e., the functional derivative of the exchange-correlation potential) defined by the selected functional. However, due to the orbital localization imposed, φ_i → 0 in the limit of large separation between pigment and copigment, which also implies a small density overlap in the intermolecular region, due to the exponential decay of the latter property, so that the previous expression indeed simply (and wrongly) collapses to

(18)with ε_i being the corresponding eigenvalues in a one-electron picture. This clearly shows how and why the TD-DFT excitation energy underestimates the real value; it misses not only the −1/R component, but it approximates IP_D – EA_A as ε_LUMO^A – ε_HOMO^D rather than giving the correct expression ε_LUMO^A – ε_HOMO^D + Δ_xc, with Δ_xc being the correction to the HOMO–LUMO gap (also known as the derivative discontinuity).

Note that within this one-electron scheme, the bathochromic shift against the monomer, say the acceptor A (with excitation energy roughly equals to ε_LUMO^A – ε_HOMO^D), is given by

(19)Eq 19 corresponds to the energetic offset of the HOMO of the weakly bound donor and acceptor molecules. When this approximation is used, the CT state is predicted to be dark (i.e., oscillator strength f^CT = 0) since CT is complete (i.e., transfer of 1|e| from D to A), and no dependency on the mutual orientation is expected.

Experience has also shown that for short-range (e.g., intramolecular) CT excitation, the use of hybrid functionals (including a certain percentage of exact-like exchange (e.g., 50% for BH and HLYP) can partly alleviate this drawback. This alleviation can be traced back to TD-HF, the HF-analogue of TD-DFT, for which at large separations:

(20)reproducing (qualitatively) the CT excitations since now E_CT^TD–HF = ε_LUMO^A – ε_HOMO^D – 1/R. Thus, the use of a hybrid functional, where a HF-like exchange term is weighted by a value C_HF, in practical calculations would lead to E_CT^TD–HF → ε_LUMO^A – ε_HOMO^D – C_HF/R, partially correcting the error. One disadvantage of this procedure is that the weight of the HF-like exchange is often system-dependent, demonstrating a need for more accurate and general solutions that can be applied to all systems.

Furthermore, in the case of long-range (e.g., intermolecular) CT excitations, a more efficient and conceptually correct model would enable automatic switching from short- to long-range regions, with the full HF-like term being dominant in the latter. In this correction, the two-electron operator 1/|r – r′| = 1/r₁₂ is divided by the error function into two separate contributions (short- and long-range):

(21)μ is a parameter to be determined, or even fine-tuned from first-principles, for each functional. This has led to the family of range-separated functionals (e.g., CAM-B3LYP (348) or ωB97XD (349, 350)), which are applied below. Note also that not only excitation energies but also oscillator strengths are more accurately predicted by these methods than with standard hybrid functionals, as demonstrated by a recent comparison to benchmark EOM-CCSD values. (351)

It should be noted that the theoretical treatment of the pigment-copigment CT states differs from the molecular exciton picture for self-aggregation of pigments (i.e., AA systems). For a simple rotation of two pigments, one starts with H-aggregates (with the relevant transition dipole moments, μ, oriented in parallel to give a bathochromically shifted, symmetry-forbidden state, and a hypsochromically i.e., blue-shifted, allowed state) and moves to a situation in which the dipole moments are perpendicular (no shift); see Scheme 4. Starting again from the H-aggregates, lateral displacements lead successively to the formation of J-aggregates corresponding to permitted lower energetic states. At π–π stacking distances (∼3.5 Å), the H/J inversion point and the extent of the splitting cannot be described in terms of classical dipoles as attempted by Kasha (140) and must instead be handled using an appropriate QM treatment that incorporates all of the relevant (inter)molecular parameters. (120)

In accordance with the considerations discussed above, the CT character depends critically on the electronic nature of the co/pigments as well as the intermolecular geometrical parameters. For a reliable description of CT states, it is therefore essential to use a theoretical method capable of reflecting and reproducing this structural sensitivity.

10.2 Theoretical Investigations of Spectral Shifts in Copigmentation

Methodologies that exclude long-range interactions have failed to reproduce the bathochromic shifts associated with copigmentation. For example, ZINDO//AM1 and TD-B3LYP calculations were performed for the two hybrid pigments, 1-deoxyvescalagin-(1β → 8)-oenin and 1-deoxyvescalagin-(1β → 8)-malvidin. At wine pH, these two pigment-copigment systems exhibit a bathochromic shift compared to the corresponding anthocyanin and anthocyanidin derivatives, which is responsible for the well-evidenced red-to-purple hue evolution. (152) On the basis of experimental data, these spectral effects were clearly assigned to noncovalent interactions between the pigment and copigment moieties. However, neither of the two tested computational methods could properly describe the excited state (ES), in which CT was expected to play a significant role.

Post-HF methods are known to correctly account for CT. In one notable example pertaining to phenolic compounds that are not strictly related to copigmentation, a post-HF method, namely the second-order approximate coupled cluster (CC2) approach CC2/aug-cc-pVDZ, was used to successfully predict CT effects in isoflavonoid fluorescence, using geometries computed at the PBE0/TZVP level. (352) However, such methodologies are very time-consuming when applied to copigmentation systems. A rather delocalized MO with components on both fragments was identified in PCM-MP2/6-311++G(d,p) calculations on the malvidin···ellagic acid complex (Figure 4 of ref 209). However, it is difficult to establish a link between this MO description and CT excited states because the cited work did not focus on optical properties, and so no ES calculations were reported.

Remaining within the TD-DFT framework, the XC functional is known to have a major impact on the quality of the results, particularly when studying CT systems. Hybrid DFT (PCM-mPW1PW91/6-31+G(d,p)) calculations showed that the first ES of 4-methyl-7-methoxyflavylium chloride···ferulic acid, which is described by a HOMO → LUMO transition, has strong CT character with the HOMO and LUMO being localized on the copigment and pigment, respectively. (105) Consequently, this ES (S₀ → S₁), lying at 594 nm, was essentially dark in optical terms, with an oscillator strength of 0.002. The other two ES (without CT character), S₀ → S₂ and S₀ → S₃, were only slightly shifted (402 and 390 nm, respectively). Unfortunately, as in many cases, there are no conclusive experimental data available with which to verify the computational conclusion because weak low-lying CT states are difficult to detect under the broad features of the intense pigment-localized transition.

CT states can be properly characterized using range-separated hybrid (RSH) functionals such as ωB97X and CAM-B3LYP that (mathematically) split the particle–particle interaction operator into short- and long-range interactions, as it was previously explained. These functionals have only recently been developed but have made obsolete the use of hybrid functionals for extended π-conjugated systems and systems in which CT plays a determinant role. DFT calculations employing long-range corrections (SS-PCM-ωB97XD/cc-PVDZ) confirmed the bathochromic shift occurring in the copigmentation complex of 3-O-methylcyanidin···quercetin. (114) UV–vis absorption spectra were predicted for the five stable conformers of this complex (Figure 23) on the basis of COSMO-B3P86-D2(s₆ = 0.780)/cc-pVDZ geometry optimizations. The bathochromic shift, obtained from a Boltzmann-weighted analysis of the five conformers, was predicted to be 0.14 eV (23 nm), which is consistent with the experimental result (11.7 nm) presented in ref 30 given that complete complexation would not have been achieved under the reported experimental conditions. (107) In accordance with the calculations, the main absorption band was assigned to the first excited state, which exhibited considerable CT character. The HOMO is mainly delocalized on quercetin, whereas the LUMO is on the pigment (Figure 25) and CT occurred from the copigment to the pigment. The global bathochromic shift that had been observed for many years was thus rationalized as a new band originating from the noncovalent π–π stacking arrangement. Also, in this case, high-energy lying states such as S₀ → S₂ contribute to the global bathochromic shift. In this model 3-O-methylcyanidin···quercetin copigmentation system, it was clearly seen that the MO and ES description was strongly conformation-dependent. Specifically, the CTs for the five conformers were 0.09, 0.06, 0.13, 0.30, and 0.73 |e|, respectively, and the corresponding bathochromic shifts were 3.7, 5.7, 10.8, 20.9, and 37.8 nm, respectively; the correlation between the bathochromic shift and the CT character confirms the rule of thumb stated above.

Figure 25. MO orbital diagram related to the maximum absorption wavelength HOMO and LUMO (left) and NTO analysis (right). Both schemes show the strong CT character of S₀ → S₁.

Thus, all of the molecular conformational arrangements and conformational diversity of pigment···copigment complexes must be identified and characterized in order to understand the spectral shifts associated with copigmentation. This point has also been made by other authors, many of whom also stressed the role of thermally activated intramolecular vibrations. (353) The 3-O-methylcyanidin···quercetin complex exhibits rather few degrees of freedom, so a systematic evaluation of its conformational space can be performed using QM-based approaches. However, for most real-world copigmentation systems, such approaches are too computationally demanding, and the identification of all possible conformers requires the application of MM-based approaches. We have recently used such an approach with the catechin-(4 → 8)-oenin pigment, which is copigmented with two vinylcatechins and procyanidin B3. (108) A 10 ns MD simulation was used to sample the conformational space, yielding a set of averaged geometries. DFT-D optimization of these geometries provided three conformers on which TD-ωB97XD/6-31+G(d,p) calculations were performed. Interestingly in this system, new UV–vis absorption bands were identified. Theoretical calculations predicted that the B- or E-rings of the pigment participated in parallel-displaced π–π stacking interactions with the C-, A-, D-, and F-rings of the copigment. While the main absorption (λ_MAX) was assigned to the S₀ → S₁ transition (which exhibits CT character), the new absorption bands were mainly attributed to the S₀ → S₂ and S₀ → S₃ excited states. The electronic transitions describing these two ESs appeared to be complex, involving lower-lying occupied MO but were always to the LUMO, and for most of them there was evidence for a contribution from intramolecular CT within the hybrid pigment (catechin-(4 → 8)-oenin). We believe a posteriori that the sampling in this study was not sufficient, since the 10 ns time scale of the MD simulation is unlikely to have been sufficient to permit escape from local minima. However, the overall qualitative description of the experimentally observed optical properties clearly was sufficient.

10.3 Environmental Effects and Peak Broadening

Even more than conformational diversity, the description of the environment is a matter of utmost importance when studying molecular spectroscopy in solution. The rearrangement of the solvent in response to changes in the solute’s charge distribution induces inhomogeneous polar broadening. (354) Most theoretical works on anthocyanins and copigmentation have described the solvent using implicit models, mainly COSMO (355) and PCMs (356) mainly IEFPCM and (C)PCM; some gas phase (i.e., in vacuo) studies have been reported, although these are becoming less common. However, it is important to stress that the conventional application of PCM in TD-DFT calculations is in principle not physically relevant because the effective Hamiltonian is defined in a static way, whereas the electronic vertical transition is a dynamical process. Simply applying PCM within TD-DFT fails to capture the time dependence of solvent relaxation. Therefore, even though this approach is attractive due to its very competitive accuracy/computational cost ratio, great care must be taken when interpreting results obtained in this way. Various approaches have been developed to circumvent this problem. (356) These techniques can be divided into two families, namely state-specific (SS) and linear-response (LR) methods. SS methods solve the effective Schrödinger equation for each state of interest. LR-methods aim to directly compute the vertical excitation energies, describing the time-dependent wave function as a linear perturbation of the time-independent wave function. In one case, SS-PCM and PCM were found to provide similar qualitative descriptions of the spectral shifts occurring in a copigmentation complex (i.e., both predicted the occurrence of a bathochromic shift) but the quantitative description was different in that PCM underestimated the shift compared to SS-PCM. (114)

Whatever progress may be made in the development of implicit models, such models are inherently incapable of describing specific solute–solvent interactions. Copigmentation is a phenomenon associated with pigments and copigments that are both phenolic and which mainly occurs in aqueous solution. Therefore, as noted above, hydrogen-bonding interactions are expected to play important roles in stabilizing the complexes and structuring the first solvent shell surrounding them. These supramolecular structures are dynamic in nature and may strongly influence the complex’s optical properties. Implicit solvents cannot capture this aspect of the system, so the only way to investigate these dynamic supramolecular architecture at present is to perform MD-based calculations, and in this case, the optical properties cannot be calculated. So the MD simulations must be somehow combined to QM-based calculations of the excited states.

In an evaluation of CT in the isoflavonoid daidzein, the system was microsolvated with different numbers of water molecules (limiting to one water molecule per OH group), which may contribute to its intermolecular hydrogen-bonding network. (352) The S. Baroni group has rationalized the spectral shifts of cyanidin 3-O-glucoside using an explicit solvent description: they performed ab initio MD (within the Car–Parrinello scheme) within TD-DFT using the plane wave pseudopotential approach and periodic boundary conditions in a 20 × 20 × 12 Å³ supercell. (353) Their results indicated that the first solvent shell is highly anisotropic, featuring water molecules interacting both (i) in-plane with the OH groups of the anthocyanidin moiety and (ii) out-of-plane with the π orbitals of the aromatic rings; the former interaction is attractive, whereas the latter is repulsive. The authors concluded that static models such as QM calculations with a PCM model may not be appropriate for characterizing the spectral changes observed with these pigments. The dynamic solvent description appeared to be crucial but mainly because it influenced intramolecular thermal fluctuations, which dramatically impact the energies and π-character of the frontier MOs involved in light absorption. Band broadening and modifications of UV–vis absorption spectra were mainly attributed to these dynamic distortions of the (co)pigment’s structures rather than direct solvation effects. This again highlights the importance of sampling conformational space: not just that of the solutes, but also that of the supramolecular solute–solvent assembly. Interestingly, only a few water molecules appeared to directly influence absorption in the visible range (i.e., had detectable effects on the π-conjugated frontier MOs).

On the basis of similar calculations, the same authors developed a color morphing procedure to expedite the theoretical evaluation of anthocyanins’ optical properties in solution. (357) Rather than providing absorption wavelengths and oscillator strengths, the TD-DFT results can also be expressed in terms of three-color parameters XYZ using the transmitted light intensity:

(22)where I₀ is the incident light; κ is the absorption coefficient as obtained from the theoretical (TD-DFT) oscillator strengths; l is the actual path length of light through the sample; x̅ y̅ z̅ are the tristimulus color matching function giving the chromatic response of an observer as defined by CIE; and N is a normalization factor.

As regards simulations with explicit solvent, we recently performed QM/MM-MD simulations on the prototypical 3-OMe-cyanidin···quercetin copigmentation system. This method predicted a bathochromic shift of 0.36 eV, which is very close to that obtained using SS-PCM-TD-ωB97XD/cc-PVDZ calculations (0.41 eV, see above). (173) This case study confirmed that the direct impact of the solvent on the absorption properties of anthocyanin systems is relatively weak, and that conformational fluctuations are important. In addition, these simulations also revealed five copigmentation conformers arranged in very similar ways to those identified in our earlier systematic pure-QM search. The dynamic network of intermolecular solute–solvent hydrogen bonding appeared to weaken all of the intramolecular hydrogen bonds (C3-OH···O4, C3′–OH···O4′, and C4′–OH···O3′) except for the strong C5-OH···O4 intramolecular hydrogen bond in quercetin (which was present for 98.6% of the MD simulation time). This QM/MM approach is based on a fully self-consistent polarizable embedding (PE) scheme. (358, 359) A series of snapshots along the MD simulation is collected, and TD-DFT calculations are performed on each snapshot to evaluate the optical properties that are averaged on the whole collection of geometries. As far as the series of snapshots is sufficiently characteristic of rearrangements occurring in real solutions, this technique is adapted for calculations of UV–vis as well as CD spectra. (360) It is much relevant and promising to tackle unresolved questions of copigmentation.

The spectral shifts observed in copigmentation are usually small, on the order of 0.01–0.2 eV (i.e., 2–40 nm at ca. 500 nm). Therefore, the method must be as accurate as possible and any potential sources of error should be accounted for and controlled. We wish to strongly emphasize that an inappropriate choice of XC functional combined with classical PCM models may result in error compensation, producing a seemingly correct qualitative description that must be interpreted with great care. Such approaches are very unlikely to produce reliable quantitative predictions other than by pure chance. Ideally, such error compensation should be avoided and recent theoretical studies have paved the way toward a safe method based on coupled TD-DFT/MM approaches. (173, 353, 357)

Last but not the least, the vibrational structure of copigmentation spectra must be analyzed. To minimize computational time, most works in this field focus on computing the vertical transition energy, which is then compared to the experimental E_MAX (λ_MAX). However, estimating the performance of a QM method based on vertical transition calculations is likely to systematically bias the conclusion. A rough 0.1–0.3 eV shift is expected when comparing a vertical transition wavelength to the maximum absorption wavelength, simply because these two values do not actually provide the same information. (361) The comparison to experimental data is affected by conformational and solvent broadening and also by vibrational corrections (via the Franck–Condon factor). The first-moment ¹M therefore appears to be a more robust parameter for such purposes; it can be compared to experimental λ_MAX, values using the expression: (361, 362)

(23)where υ is the frequency and L(υ) is the absorption spectrum line shape, which can be obtained by

(24)where ρ_i(T) is the Boltzmann distribution of the vibrational state i; ⟨w_i|μ_if|w_f⟩ is the transition dipole moment; |w_i⟩ and |w_f⟩ are the initial and final states, respectively; and E_i and E_f are their respective energies. In other words, ¹M is the center of gravity of the spectrum in a given region.

11 Concluding Remarks, Future Needs, and Applications

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There is everlasting interest for safe and efficient ways to prepare foods with a wider variety of dyes and pigments that are stable under the conditions used in food preparation and conservation, as well as safe and suitable for consumption. Copigmentation has recently attracted great interest in food industry. The reason for this interest can be attributed to the recent advances in the field, which offer opportunities to design new combinations of natural pigment and copigment (dye and co-dye) with stable and finely tuned colors. The joint theoretical and experimental studies can now provide a molecular understanding of copigmentation with the sake of such real-world applications. However, although experimental techniques have provided insight into many aspects of copigmentation, there remain a number of major challenges to be addressed. Namely, comprehensive structure affinity relationships have still to be established and the different contributions to copigmentation complex stability should be better unraveled. This is a complex issue as this process is particularly environment-dependent (solvent, pH, temperature, and metal ions), which is of crucial importance in food applications. This underdeveloped field should benefit from the application of advanced techniques (e.g., isothermal titration calorimetry, NMR with NOE, and molecular balances), which have already provided useful insights in the field of supramolecular chemistry. Further research may also benefit from the systematic design of model copigmentation complexes to better establish structure-affinity and structure-optical-property relationships.

State-of-the-art theoretical calculations are increasingly capable of addressing the conformations and supramolecular bonding arrangements of pigment-copigment pairs. To accurately evaluate the Gibbs energy of association and spectral features of such copigmentation complexes, it is necessary to adopt a combination of (biased) MD simulations and DFT with modern functionals, including corrections for dispersion and/or long-range separation. The advanced theoretical calculations may support experimental data in the identification of individual contributions to copigmentation complex stability (e.g., hydrophobic effect, dispersion forces, π–π-stacking, exchange term, and hydrogen bonding). By understanding these interactions, we can rationalize their spectral consequences (i.e., bathochromic and hyperchromic shifts). Many theoretical challenges remain to be addressed, however, including: (i) identifying factors that favor self-association over copigmentation or vice versa; (ii) characterizing metal-mediated copigmentation, which has only been addressed by a few computational investigations (335) and which is poorly understood in many respects, it is not clear how flavylium deprotonation and metal binding (which itself induces proton loss) affect the thermodynamics of copigmentation and induce spectral change; and (iii) coming to a better understanding of band broadening in the UV–vis spectra of copigmentation complexes, which significantly influence their perceived color.

Author Information

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Corresponding Authors
- Patrick Trouillas - INSERM UMR 850, Univ. Limoges, Faculty of Pharmacy, 2 rue du Dr. Marcland, F-87025 Limoges, France; Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of Science, Palacký University Olomouc, tr. 17. listopadu 12, 771 46 Olomouc, Czech Republic; Email: [email protected]
- Michal Otyepka - Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of Science, Palacký University Olomouc, tr. 17. listopadu 12, 771 46 Olomouc, Czech Republic; Email: [email protected]
Authors
- Juan C. Sancho-García - Departamento de Química Física, Universidad de Alicante, Apartado de Correos 99, E-03080 Alicante, Spain
- Victor De Freitas - REQUIMTE/LAQV − Research Unit, Faculty of Science, Porto University, Rua do Campo Alegre, 4169-007 Porto, Portugal
- Johannes Gierschner - Madrid Institute for Advanced Studies - IMDEA Nanoscience, C/Faraday 9, Ciudad Universitaria de Cantoblanco, E-28049 Madrid, Spain
- Olivier Dangles - University of Avignon, INRA, UMR408 SQPOV, F-84000 Avignon, France
Notes
The authors declare no competing financial interest.

Biographies

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Patrick Trouillas received his Ph.D. degree in solid-state physics (optoelectronic properties of fullerene) at the University of Limoges (France). He then joined CEA for a postdoctoral position dealing with thermal exchanges in thin solid films. In 2000, he reoriented his research toward natural compounds (e.g., polyphenols) and pharmaceutical/cosmetic applications. He is currently Assistant Professor at the University of Limoges, jointly affiliated to (i) INSERM-U850 (Limoges) and (ii) the Regional Centre of Advanced Technologies and Materials in Olomouc (Czech Republic). Within active EU networks, he has extensively worked on Molecular Modeling as a tool to rationalize: (i) drug-lipid bilayer interaction and membrane crossing; (ii) biological (antioxidant) properties of natural compounds; and (iii) pigments and dyes' molecular properties. This gave P.T. the opportunity to meet J-C.S-G, J.G., and M.O., with whom he has developed many research projects; he met V.F. and O.D. within the international polyphenol community.

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Juan-Carlos Sancho-Garcı́a completed a Ph.D. in Quantum and Computational Chemistry in 2001. During that period, he also held (1999) a Research Fellowship of the J. Heyrovský Institute of Physical Chemistry in Prague (Czech Republic). He later worked (2002–2004) as a Marie Curie Fellowship at the Laboratory for Chemistry of Novel Materials in Mons (Belgium). He obtained (2005) a tenured-track “Ramón y Cajal” Postdoctoral Senior Grant at the University of Alicante, becoming next (2010) an Associate Professor and Lecturer in Physical Chemistry. He has also recently served as an external scientific advisor for high-tech companies and research hubs, such as the Samsung Advanced Institute of Technology, and led as Principal Investigator research projects uninterruptedly from 2004. His main research interest has always been the development and application of DFT methods to challenging systems, in various fields of Chemistry and Materials Science. He met Patrick Trouillas in 2009 and started to work on pigmentation and copigmentation issues, after some preliminary theoretical studies on polyphenol compounds. This fruitful collaboration crystallized in joint publications and in the associated training of young researchers.

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Victor De Freitas graduated in Chemistry from the Faculty of Science of the University of Porto (FCUP) in 1984. In 1995, he obtained his Ph.D. in Biological and Medical Sciences in the University of Bordeaux II (France), with a specialization in Oenology. After his Ph.D., he returned to the Department of Chemistry and Biochemistry (DQB) of FCUP, where he has been developing his teaching and research activities. He is currently Full Professor at the University of Porto and member of the REQUIMTE-LAQV Research Centre, where he has been developing an independent area of research on polyphenol compounds: (i) chemical transformations resulting from oxidation processes of polyphenolic pigments, including technological applications in the food industry; (ii) interaction of different classes of polyphenols with proteins in the sensory and nutritional context; and (iii) antioxidant and biological properties of polyphenolic compounds.

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Johannes Gierschner received his Ph.D. in Physical Chemistry in Tübingen, Germany (2000). After stays in Tübingen, Mons, and Georgia Tech, Atlanta, GA, he joined IMDEA Nanoscience in 2008 as a senior researcher (Ramón y Cajal fellow, 2008–2013). From 2008–2010, he was a visiting researcher at the University of Valencia, and since 2009, he is regular visiting researcher at Seoul National University. In 2013, he completed his habilitation (Priv. Doz., University Tübingen). His work integrates optical spectroscopy and computational chemistry to elucidate structure–property relationships in conjugated organic materials.

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Michal Otyepka received his Ph.D. degree in Physical Chemistry at the Palacký University, Olomouc, Czech Republic (2004). Currently, he is a head of the Department of Physical Chemistry and vice-director of the Regional Centre of Advanced Technologies and Materials, both at the Palacký University, Olomouc. His research is mostly focused on modeling of biomacromolecules, 2D materials and their interactions, and chemistry of graphene derivatives.

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Olivier Dangles studied chemistry at the Ecole Normale Supérieure of Cachan, France (1981–1985), and he obtained a Ph.D. in organic chemistry at the University of Paris-Orsay (1989). He was an assistant professor at the University of Strasbourg (1989–1992), and then a researcher at the National Center of Scientific Research (CNRS, 1992–1995), where he devoted his research to the chemistry of anthocyanins in relation to the expression of natural colors (group of Prof. R. Brouillard). In 1995, he was appointed a Prof. of chemistry at the University of Lyon. Since 2000, he has been a Prof. of chemistry at the University of Avignon, and he works in a joint research unit of Avignon University and the National Institute for Agricultural Research (INRA). His main research topics deal with the chemistry of polyphenols and carotenoids in relation to their coloring properties and their effects on human health: (i) mechanisms of oxidation and antioxidant activity; (ii) interactions with proteins; and (iii) lipids and metal ions and chemical synthesis of metabolites.

Acknowledgment

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P.T. thanks the “Conseil Régional du Limousin” for financial support and CALI (CAlcul en LImousin). Financial support from the Czech Science Foundation (P208/12/G016), the Ministry of Education, Youth and Sports of the Czech Republic (project LO1305), and the Operational Program Education for Competitiveness-European Social Fund (project CZ.1.07/2.3.00/20.0058 of the Ministry of Education, Youth and Sports of the Czech Republic) is also gratefully acknowledged. The work at IMDEA was supported by the Spanish Ministerio de Economı́a y Competitividad (MINECO; project CTQ2014-58801). P.T. thanks F. Di Meo and G. Fabre for fruitful discussions on noncovalent interactions and B. Chantemargue for giving a last minute helping hand.

Abbreviations and Symbols

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AH⁺	flavylium cation
A	neutral quinonoid base
A^–	anionic neutral quinonoid base
B	hemiketal
BSSE	basis set superposition error
BJ	Becke-Johnson
C_cis	cis-chalcone
C_trans	trans-chalcone
CC2	second-order approximate coupled cluster singles and doubles
CBS	complete basis set
CCSD	coupled-cluster singles and doubles
CCSD(T)	coupled-cluster singles, doubles, and triples
CD	circular dichroism
CI	configuration interaction
CIE	commission international de l’éclairage
CASPT2	complete-active-space perturbation theory
COSMO	conductor-like solvation model
CP	copigment
CT	charge transfer
dDsC	density-dependent energy dispersion energy correction
DFT	density functional theory
DFTB	density functional tight binding
DLPNO	domain-based local pair-natural-orbitals
DSSC	dye-sensitized solar cells
ES	excited state
GB	generalized born
HCA	hydroxycinnamic acid
HF	Hartree−Fock
IEFPCM	integral equation formalism polarizable continuum model
LR	linear-response
MAD	mean absolute deviation
MD	molecular dynamics
MDQ	MD with quenching
MetaD	meta-dynamics
MM	molecular mechanics
MM-GBSA	molecular mechanics- Poisson–Boltzmann/surface area
MM-PBSA	molecular mechanics-generalized born/surface area
MO	molecular orbital
MP2	second order Møller–Plesset perturbation theory
NMR	nuclear magnetic resonance
NOE	nuclear Overhauser effect
NTO	natural transition orbital
PCM	polarizable continuum model
PB	Poisson–Boltzmann
QM	quantum mechanics
REMD	replica exchange MD (REMD)
RSH	range-separated hybrid functionals
SA	surface area
SCS	spin-component-scaled
SS-PCM	state-specific polarizable continuum model
SS	state-specific
TD-DFT	time-dependent density functional theory
TD-HF	time-dependent Hartree−Fock
vdW-TS	van der Waals Tkatchenko-Scheffler correction
VV10	Vydrov-Voorhis nonlocal correlation functional
XC	exchange-correlation
XDM	exchange-hole dipole moment
ZINDO	Zerner’s intermediate neglect of differential overlap-ZINDO

References

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Asen, S.; Stewart, R. N.; Norris, K. H. Anthocyanin, Flavonol Copigments, and pH Responsible for Larkspur Flower Colour Phytochemistry 1975, 14 (12) 2677– 2682 DOI: 10.1016/0031-9422(75)85249-6
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Castañeda-Ovando, A.; Pacheco-Hernández, M.; de, L.; Páez-Hernández, M. E.; Rodríguez, J. A.; Galán-Vidal, C. A. Chemical Studies of Anthocyanins: A Review Food Chem. 2009, 113 (4) 859– 871 DOI: 10.1016/j.foodchem.2008.09.001
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Chemical studies of anthocyanins: A review
Castaneda-Ovando, Araceli; Pacheco-Hernandez, Ma. de Lourdes; Paez-Hernandez, Ma. Elena; Rodriguez, Jose A.; Galan-Vidal, Carlos Andres
Food Chemistry (2009), 113 (4), 859-871CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier B.V.)
A review. Anthocyanins are natural colorants which have raised a growing interest due to their extensive range of colors, innocuous and beneficial health effects. Despite the great potential of application that anthocyanins represent for food, pharmaceutical and cosmetic industries, their use has been limited because of their relative instability and low extn. percentages. Currently, most investigations on anthocyanins are focused on solving these problems, as well as their purifn. and identification. In this paper, the most recent advances in the chem. investigation of the anthocyanins are summarized, emphasizing the effects of pH, co-pigmentation, metal ion complexation and antioxidant activity on their stability.
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He, F.; Liang, N.-N.; Mu, L.; Pan, Q.-H.; Wang, J.; Reeves, M. J.; Duan, C.-Q. Anthocyanins and Their Variation in Red Wines I. Monomeric Anthocyanins and Their Color Expression Molecules 2012, 17 (12) 1571– 1601 DOI: 10.3390/molecules17021571
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Andersen, O. M.; Markham, K. R. Flavonoids: Chemistry, Biochemistry and Applications; CRC Press, 2005.
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Fulcrand, H.; Dueñas, M.; Salas, E.; Cheynier, V. Phenolic Reactions during Winemaking and Aging Am. J. Enol. Vitic. 2006, 57 (3) 289– 297
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Phenolic reactions during winemaking and aging
Fulcrand, Helene; Duenas, Montserrat; Salas, Erika; Cheynier, Veronique
American Journal of Enology and Viticulture (2006), 57 (3), 289-297CODEN: AJEVAC; ISSN:0002-9254. (American Society for Enology and Viticulture)
A review. The reactivity of polyphenols is due to the position of the hydroxyl groups on their arom. nuclei. Ortho-hydroxyl groups promote oxidn. while meta-hydroxyl groups induce electrophilic arom. substitution. Both hydroxylation patterns are encountered in flavonoid structures, on the B and A rings, resp. In addn. to oxidn. and electrophilic arom. substitution, flavonoids undergo nucleophilic addn. on the central C ring when it is pos. charged. Reactions of the A and C rings are pH-dependent. The A ring of flavonoids undergoes a polycondensation reaction mediated by an aldehyde. The products are anthocyanin and flavanol polymers and copolymers constituted of both. Flavanol polymers are not stable and rearrange into vinyl flavanols and xanthylium pigments. Vinyl flavanols can react with the pos. charged C ring of anthocyanins, yielding pyranoanthocyanins, which can also be formed from components that have a reactive double bond, such as carbonyl and ethylene bonds. The pos. charged C ring primarily undergoes direct reactions. Since the pos. charge on the C ring of anthocyanins and flavanols is pH-dependent, their dehydration and interflavan bond cleavage reactions are also pH-dependent. This leads to flavanol-anthocyanin (F-A+) adducts at lower pH values and anthocyanin-flavanol (A+-F) adducts above pH 3.8. Temp. seems to favor formation of the latter.
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Cheynier, V.; Dueñas-Paton, M.; Salas, E.; Maury, C.; Souquet, J.-M.; Sarni-Manchado, P.; Fulcrand, H. Structure and Properties of Wine Pigments and Tannins Am. J. Enol. Vitic. 2006, 57 (3) 298– 305
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Structure and properties of wine pigments and tannins
Cheynier, Veronique; Duenas-Paton, Montserrat; Salas, Erika; Maury, Chantal; Souquet, Jean-Marc; Sarni-Manchado, Pascale; Fulcrand, Helene
American Journal of Enology and Viticulture (2006), 57 (3), 298-305CODEN: AJEVAC; ISSN:0002-9254. (American Society for Enology and Viticulture)
A review. Grape phenolics are structurally diverse, from simple mols. to oligomers and polymers that are usually designated "tannins," referring to their ability to interact with proteins. Anthocyanin pigments and tannins are particularly important for red wine quality. Their extn. depends on their location in the berry and their soly. All phenolic compds. are unstable and undergo numerous enzymic and chem. reactions. Color and taste changes during red wine aging have been ascribed to anthocyanin-tannin reactions. The structures and properties of tannins and pigmented tannins from these reactions are often misunderstood. Current research on wine phenolic compn. is reviewed, with emphasis on the following issues: (1) reactions of tannins yield both larger polymers and smaller species; (2) anthocyanin reactions can generate colorless species as well as polymeric and small various pigments; (3) some polymeric pigments undergo sulfite bleaching while some low mol. wt. pigments do not; (4) polymers are both sol. and astringent, so the astringency loss during aging may involve cleavage rather than polymn.; and (5) sensory properties of anthocyanins and tannins are modulated by interactions with other wine components.
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de Freitas, V.; Mateus, N. Formation of Pyranoanthocyanins in Red Wines: A New and Diverse Class of Anthocyanin Derivatives Anal. Bioanal. Chem. 2011, 401 (5) 1463– 1473 DOI: 10.1007/s00216-010-4479-9
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Formation of pyranoanthocyanins in red wines: a new and diverse class of anthocyanin derivatives
de Freitas Victor; Mateus Nuno
Analytical and bioanalytical chemistry (2011), 401 (5), 1463-73 ISSN:.
Pyranoanthocyanins constitute one of the most important classes of anthocyanin-derived pigments occurring naturally in red wine. Nonetheless, correct assignment of their structures and pathways of formation in red wine has been relatively recent--less than two decades. Study of these newly discovered pigments is progressively unfolding the chemical pathways that drive the evolution of red wine colour during ageing. The objective of this paper is to review current knowledge regarding the pathway of formation in red wine of a great variety of pyranoanthocyanin structures, namely carboxypyranoanthocyanins, methylpyranoanthocyanins, pyranoanthocyanin-flavanols, pyranoanthocyanin-phenols, portisins, oxovitisins, and pyranoanthocyanin dimers. The chromatic features of some of the compounds, for example their colour expression and acid-base equilibria in aqueous media, are also discussed.
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Mateus, N.; Silva, A. M. S.; Santos-Buelga, C.; Rivas-Gonzalo, J. C.; de Freitas, V. Identification of Anthocyanin-Flavanol Pigments in Red Wines by NMR and Mass Spectrometry J. Agric. Food Chem. 2002, 50 (7) 2110– 2116 DOI: 10.1021/jf0111561
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Mateus, N.; Oliveira, J.; Haettich-Motta, M.; de Freitas, V. New Family of Bluish Pyranoanthocyanins J. Biomed. Biotechnol. 2004, 2004 (5) 299– 305 DOI: 10.1155/S1110724304404033
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He, J.; Carvalho, A. R. F.; Mateus, N.; De Freitas, V. Spectral Features and Stability of Oligomeric Pyranoanthocyanin-Flavanol Pigments Isolated from Red Wines J. Agric. Food Chem. 2010, 58 (16) 9249– 9258 DOI: 10.1021/jf102085e
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He, J.; Oliveira, J.; Silva, A. M. S.; Mateus, N.; De Freitas, V. Oxovitisins: A New Class of Neutral Pyranone-Anthocyanin Derivatives in Red Wines J. Agric. Food Chem. 2010, 58 (15) 8814– 8819 DOI: 10.1021/jf101408q
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Chassaing, S.; Isorez, G.; Kueny-Stotz, M.; Brouillard, R. En Route to Color-Stable Pyranoflavylium Pigments—a Systematic Study of the Reaction between 5-Hydroxy-4-Methylflavylium Salts and Aldehydes Tetrahedron Lett. 2008, 49 (49) 6999– 7004 DOI: 10.1016/j.tetlet.2008.09.139
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Oliveira, J.; Mateus, N.; Freitas, V. de. Synthesis of a New Bluish Pigment from the Reaction of a Methylpyranoanthocyanin with Sinapaldehyde Tetrahedron Lett. 2011, 52 (16) 1996– 2000 DOI: 10.1016/j.tetlet.2011.02.079
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Brouillard, R.; Dubois, J.-E. Mechanism of the Structural Transformations of Anthocyanins in Acidic Media J. Am. Chem. Soc. 1977, 99 (5) 1359– 1364 DOI: 10.1021/ja00447a012
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Mechanism of the structural transformations of anthocyanins in acidic media
Brouillard, Raymond; Dubois, Jacques-Emile
Journal of the American Chemical Society (1977), 99 (5), 1359-64CODEN: JACSAT; ISSN:0002-7863.
In acidic aq. media (pH 1-6), there are three forms of malvin: the flavylium cation I (R = β-D-glucopyranosyl), the carbinol, and the quinonoidal base. Equilibrium between the two neutral forms occurs via the flavylium cation and the equil. const. [carbinol]/[base] is 1.6 (± 0.5) × 102 at 4° ;a relaxation technique was used to det. the rate consts for neutralization (endotherm) of the base, for hydration ofI via formation of a C-O bond and proton transfer,and for the reverse of the reactions.
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McClelland, R. A.; Gedge, S. Hydration of the Flavylium Ion J. Am. Chem. Soc. 1980, 102 (18) 5838– 5848 DOI: 10.1021/ja00538a024
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Hydration of the flavylium ion
McClelland, Robert A.; Gedge, Sherrin
Journal of the American Chemical Society (1980), 102 (18), 5838-48CODEN: JACSAT; ISSN:0002-7863.
Spectral and kinetic studies were carried out on the transformations undergone in aq. soln. by flavylium ions and I (R = H, Me, MeO). Seven species were identified under various pH conditions, i.e., the flavylium ion, 2 pseudobases, 4-hydroxy adducts and the cis-2-hydroxychalcones and their ionized forms. Equil. between the various species are described and rate and equil. consts. were detd.
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Pina, F.; Melo, M. J.; Laia, C. A. T.; Parola, A. J.; Lima, J. C. Chemistry and Applications of Flavylium Compounds: A Handful of Colours Chem. Soc. Rev. 2012, 41 (2) 869– 908 DOI: 10.1039/C1CS15126F
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Chemistry and applications of flavylium compounds: a handful of colours
Pina, Fernando; Melo, Maria J.; Laia, Cesar A. T.; Parola, A. Jorge; Lima, Joao C.
Chemical Society Reviews (2012), 41 (2), 869-908CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
A review. Flavylium compds. are versatile mols. that comprise anthocyanins, the ubiquitous colorants used by Nature to confer color to most flowers and fruits. They have found a wide range of applications in human technol., from the millenary color paints described by the Roman architect Vitruvius, to their use as food additives, combining color and antioxidant effects, and even as light absorbers in solar cells aiming at a greener solar energy conversion. Their rich complexity derives in part from their ability to switch between a variety of species (flavylium cations, neutral quinoidal bases, hemiketals and chalcones, and neg. charged phenolates) by means of external stimuli, such as pH, temp. and light. This crit. review describes (i) the historical advancements in the understanding of the equil. of their chem. reaction networks; (ii) their thermodn. and kinetics; (iii) the mechanisms underlying their color development, such as co-pigmentation and host-guest interactions; (iv) the photophysics and photochem. that lead to photochromism; and (v) applications in solar cells, models for optical memories, photochromic soft materials such as ionic liqs. and gels, and their properties in solid state materials (274 refs.).
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Pina, F. Chemical Applications of Anthocyanins and Related Compounds. A Source of Bioinspiration J. Agric. Food Chem. 2014, 62 (29) 6885– 6897 DOI: 10.1021/jf404869m
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Chemical Applications of Anthocyanins and Related Compounds. A Source of Bioinspiration
Pina, Fernando
Journal of Agricultural and Food Chemistry (2014), 62 (29), 6885-6897CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
A review. Independently of the natural or synthetic origin, flavylium derivs. follow the same network of chem. reactions. Actually, the flavylium cation is stable only at low pH values. Increasing the pH gives rise to the formation of several species: quinoidal bases, hemiketal, cis- and trans-chalcones, and their deprotonated forms. A deep knowledge of the thermodn. and kinetics of these species is an essential tool to practical applications of these compds., in particular, in the domain of food chem. In this work the network of chem. reactions involving flavylium derivs. is presented, and the resp. thermodn. and kinetics are discussed in detail, including the math. expressions and a step-by-step procedure to calc. all of the rate and equil. consts. of the system. Examples of systems possessing a high or low cis-trans isomerization barrier are shown. Recent practical applications of anthocyanins and related compds. illustrate the potential of the flavylium-based family of compds.
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Nave, F.; Petrov, V.; Pina, F.; Teixeira, N.; Mateus, N.; de Freitas, V. Thermodynamic and Kinetic Properties of a Red Wine Pigment: Catechin-(4,8)-Malvidin-3- O -Glucoside J. Phys. Chem. B 2010, 114 (42) 13487– 13496 DOI: 10.1021/jp104749f
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Mora-Soumille, N.; Al Bittar, S.; Rosa, M.; Dangles, O. Analogs of Anthocyanins with a 3′,4′-Dihydroxy Substitution: Synthesis and Investigation of Their Acid–base, Hydration, Metal Binding and Hydrogen-Donating Properties in Aqueous Solution Dyes Pigm. 2013, 96 (1) 7– 15 DOI: 10.1016/j.dyepig.2012.07.006
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Analogs of anthocyanins with a 3',4'-dihydroxy substitution: Synthesis and investigation of their acid-base, hydration, metal binding and hydrogen-donating properties in aqueous solution
Mora-Soumille, Nathalie; Al Bittar, Sheiraz; Rosa, Maxence; Dangles, Olivier
Dyes and Pigments (2013), 96 (1), 7-15CODEN: DYPIDX; ISSN:0143-7208. (Elsevier Ltd.)
Glycosides of hydroxylated flavylium ions are proposed as pertinent analogs of anthocyanins, a major class of polyphenolic plant pigments. Anthocyanins with a 3',4'-dihydroxy substitution on the B-ring (catechol nucleus) are esp. important for their metal chelating and electron-donating (antioxidant) capacities. In this work, an efficient chem. synthesis of 3',4'-dihydroxy-7-O-β-D-glucopyranosyloxyflavylium chloride and its aglycon is reported. Then, the ability of the two pigments to undergo proton transfer (formation of colored quinonoid bases) and add water (formation of a colorless chalcone) is investigated: at equil. the colored quinonoid bases (kinetic products) are present in very minor concns. (<10% of the total pigment concn.) compared to the colorless chalcone (thermodn. product). The glucopyranosyloxyflavylium ion appears significantly less acidic than the aglycon. The thermodn. of the overall sequence of flavylium-chalcone conversion is not affected by the β-D-glucosyl moiety while the kinetics appears slower by a factor ca. 8. Although the glucopyranosyl-oxyflavylium ion and its aglycon display similar affinities for Al3+, the Al3+-glucoside complex is more stable than the Al3+-aglycon complex due to the higher sensitivity of the latter to water addn. and conversion into the corresponding chalcone. Finally, the glucopyranosyl-oxyflavylium ion and its aglycon are compared for their ability to reduce the 1,1-diphenyl-2-picrylhydrazyl radical in a mildly acidic water/MeOH (1:1) mixt. as a first evaluation of their antioxidant activity. Glycosidation at C7-OH results in a lower rate const. of first electron transfer to DPPH and a lower stoichiometry (total no. of 1,1-diphenyl-2-picrylhydrazyl radicals reduced per pigment mol.). Anthocyanins are difficult to ext. from plants in substantial amt. However, the analogs investigated in this work are of easy access by chem. synthesis and express the physico-chem. properties typical of anthocyanins. They can thus be regarded as valuable models for investigating the coloring, metal-binding and antioxidant properties of these important natural pigments.
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Yan, Q.; Zhang, L.; Zhang, X.; Liu, X.; Yuan, F.; Hou, Z.; Gao, Y. Stabilization of Grape Skin Anthocyanins by Copigmentation with Enzymatically Modified Isoquercitrin (EMIQ) as a Copigment Food Res. Int. 2013, 50 (2) 603– 609 DOI: 10.1016/j.foodres.2011.04.007
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Stabilization of grape skin anthocyanins by copigmentation with enzymatically modified isoquercitrin (EMIQ) as a copigment
Yan, Qiuli; Zhang, Linhan; Zhang, Xiaofei; Liu, Xuan; Yuan, Fang; Hou, Zhanqun; Gao, Yanxiang
Food Research International (2013), 50 (2), 603-609CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
The thermal and light stability of grape skin anthocyanins with enzymically modified isoquercitrin (EMIQ) as a copigment was investigated at different pH levels of 3, 4 and 5. The ratios of anthocyanins to EMIQ were 2:1, 1:1, and 1:2 (wt./wt.), resp., in the thermal expts. at 90 °C, and EMIQ concns. (0.25, 0.5, and 1%, wt./wt.) were evaluated resp. in the light expts. Results revealed that the degrdn. of anthocyanins copigmented with EMIQ followed first-order reaction kinetics. The half life of anthocyanins extended significantly with the increase of EMIQ concn. (p < 0.05), moreover, the color stability increased due to the addn. of EMIQ as the total color difference values ΔE* were smaller for the copigmented anthocyanins. The magnitude of the bathochromic (λmax) shifted to the longest wavelength absorption band with the increasing copigment concn. for all pH levels. Results demonstrated that EMIQ was an effective copigment to stabilize grape skin anthocyanins.
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Fanzone, M.; González-Manzano, S.; Pérez-Alonso, J.; Escribano-Bailón, M. T.; Jofré, V.; Assof, M.; Santos-Buelga, C. Evaluation of Dihydroquercetin-3-O-Glucoside from Malbec Grapes as Copigment of Malvidin-3-O-Glucoside Food Chem. 2015, 175, 166– 173 DOI: 10.1016/j.foodchem.2014.11.123
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Evaluation of dihydroquercetin-3-O-glucoside from Malbec grapes as copigment of malvidin-3-O-glucoside
Fanzone, Martin; Gonzalez-Manzano, Susana; Perez-Alonso, Joaquin; Escribano-Bailon, Maria Teresa; Jofre, Viviana; Assof, Mariela; Santos-Buelga, Celestino
Food Chemistry (2015), 175 (), 166-173CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
Malbec is a wine grape variety of great phenolic potential characterized for its high levels of anthocyanins and dihydroflavonols. To evaluate the possible implication of dihydroflavonols in the expression of red wine color through reactions of copigmentation or condensation, assays were carried out in wine model systems with different malvidin-3-O-glucoside:dihydroquercetin-3-O-glucoside molar ratios. The addn. of increasing levels of dihydroquercetin-3-O-glucoside to a const. malvidin-3-O-glucoside concn. resulted in a hyperchromic effect assocd. with a darkening of the anthocyanin solns., greater quantity of color and visual satn., perceptible to the human eye. Copigmentation and thermodn. measurements showed that dihydroquercetin-3-O-glucoside can act as an anthocyanin copigment, similar to other usual wine components like flavanols or phenolic acids, although apparently less efficient than flavonols. The high levels of dihydroflavonols existing in Malbec wines in relation to other non-anthocyanin phenolics should make this family of compds. particularly important to explain the color expression in Malbec young red wines.
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Baranac, J. M.; Petranovic, N. A.; Dimitric-Markovic, J. M. Spectrophotometric Study of Anthocyan Copigmentation Reactions. 2. Malvin and the Nonglycosidized Flavone Quercetin J. Agric. Food Chem. 1997, 45 (5) 1694– 1697 DOI: 10.1021/jf9606114
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Spectrophotometric Study of Anthocyan Copigmentation Reactions. 2. Malvin and the Nonglycosidized Flavone Quercetin
Baranac, Jelisaveta M.; Petranovic, Nadezda A.; Dimitric-Markovic, Jasmina M.
Journal of Agricultural and Food Chemistry (1997), 45 (5), 1694-1697CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
Using UV-vis spectrophotometry we have established that a process of copigmentation takes place between an anthocyan mol., malvin chloride (malvidin 3,5-diglucoside), and a nonglycosidized pentahydroxyflavone, quercetin (3,5,7,3',4'-pentahydroxyflavone). The kinetic and thermodn. parameters, by which the process is characterized, were correlated to the structure, i.e., the nature and position of the substituents in the interacting mols.
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Dimitrić-Marković, J. M.; Petranović, N. A.; Baranac, J. M. A Spectrophotometric Study of the Copigmentation of Malvin with Caffeic and Ferulic Acids J. Agric. Food Chem. 2000, 48 (11) 5530– 5536 DOI: 10.1021/jf000038v
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Dimitrić-Marković, J. M.; Baranac, J. M.; Brdaric, T. P. Electronic and Infrared Vibrational Analysis of Cyanidin-Quercetin Copigment Complex Spectrochim. Acta, Part A 2005, 62, 673– 680 DOI: 10.1016/j.saa.2005.02.036
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Electronic and infrared vibrational analysis of cyanidin-quercetin copigment complex
Dimitric Markovic, Jasmina M.; Baranac, Jelisaveta M.; Brdaric, Tanja P.
Spectrochimica Acta, Part A: Molecular and Biomolecular Spectroscopy (2005), 62A (1-3), 673-680CODEN: SAMCAS; ISSN:1386-1425. (Elsevier B.V.)
Copigment complex formation between cyanidin and quercetin, in aq. buffered solns., was studied by electronic absorption and IR vibrational spectroscopies. It was found that the assocn. of cyanidin with quercetin occurred at pH 3.0 and pH 5.0 including cyanidin flavylium ion and anhydrobase transformation forms, resp. The obtained copigmentation const. values of K = 2726.7 (pH 3.0) and K = 1093.1 (pH 5.0) indicated good assocn. ability of the investigated mols. IR spectra revealed the existence of hydrogen bonds in the copigment complexes structures. The anal. of the deconvoluted IR spectra indicated several types of hydrogen bonds, differently formed: the H-O ··· H bonds with the corresponding bands around 3500 cm-1 and bonds formed via H3O+, oxonium, ion of the mols. with the corresponding bands below 3000 cm-1.
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Lambert, S. G.; Asenstorfer, R. E.; Williamson, N. M.; Iland, P. G.; Jones, G. P. Copigmentation between Malvidin-3-Glucoside and Some Wine Constituents and Its Importance to Colour Expression in Red Wine Food Chem. 2011, 125 (1) 106– 115 DOI: 10.1016/j.foodchem.2010.08.045
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Copigmentation between malvidin-3-glucoside and some wine constituents and its importance to colour expression in red wine
Lambert, Stephanie G.; Asenstorfer, Robert E.; Williamson, Natalie M.; Iland, Patrick G.; Jones, Graham P.
Food Chemistry (2011), 125 (1), 106-115CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
Thermodn. parameters for intermol. copigmentation interactions involving malvidin-3-glucoside were detd. by UV/visible spectroscopy at wine pH (pH 3.6). These included assocn. consts., enthalpy and entropy changes, which were measured for chlorogenic acid, caffeic acid, quercetin, quercetin-3-glucoside, (-)-epicatechin, (+)-catechin, procyanidin dimer and seed tannin. Quercetin produced the strongest copigment (KCP = 2900 ± 1300), while the addn. of glucose at position 3 (quercetin-3-glucoside) reduced its effect by almost 10-fold. Malvidin-3-glucoside self-assocn. (KD = 3300 ± 300 mol-1 l) was thermodynamically favored over intermol. interaction with any of the copigments tested. No color enhancement due to self-assocn. was obsd. for malvidin-3-glucoside-derived pigments that cannot enter hydration reactions. In addn., malvidin-3-(6-O-p-coumaryl)glucoside did not show color enhancement suggesting that the p-coumaryl group prevents self-assocn. The malvidin-3-glucoside CD spectrum was not affected by indicated changes in malvidin-3-glucoside concn. These observations demonstrate that self-assocn. of malvidin-3-glucoside is more important than copigmentation in young red wine.
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Malaj, N.; De Simone, B. C.; Quartarolo, A. D.; Russo, N. Spectrophotometric Study of the Copigmentation of Malvidin 3-O-Glucoside with P-Coumaric, Vanillic and Syringic Acids Food Chem. 2013, 141 (4) 3614– 3620 DOI: 10.1016/j.foodchem.2013.06.017
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Willstätter, R.; Zollinger, E. H. XVI. Über Die Farbstoffe Der Weintraube Und Der Heidelbeere, II Justus Liebigs Ann. Chem. 1917, 412 (2) 195– 216 DOI: 10.1002/jlac.19174120207
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Robinson, G. M.; Robinson, R. A Survey of Anthocyanins. I Biochem. J. 1931, 25 (5) 1687– 1705 DOI: 10.1042/bj0251687
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Asen, S.; Stewart, R. N.; Norris, K. H.; Massie, D. R. A Stable Blue Non-Metallic Co-Pigment Complex of Delphanin and C-Glycosylflavones in Prof. Blaauw Iris Phytochemistry 1970, 9 (3) 619– 627 DOI: 10.1016/S0031-9422(00)85702-7
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Asen, S.; Stewart, R. N.; Norris, K. H. Co-Pigmentation Effect of Quercetin Glycosides on Absorption Characteristics of Cyanidin Glycosides and Color of Red Wing Azalea Phytochemistry 1971, 10 (1) 171– 175 DOI: 10.1016/S0031-9422(00)90266-8
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Copigmentation effect of quercetin glycosides on absorption characteristics of cyanidin glycosides and color of red wing azalea
Asen, Sam; Stewart, Robert N.; Norris, Karl H.
Phytochemistry (Elsevier) (1971), 10 (1), 171-5CODEN: PYTCAS; ISSN:0031-9422.
A quercetin 5-methyl ether and 5 quercetin glycosides were isolated from flowers of Red Wing azalea but were found only in trace amts. in an orange sport of this cultivar. The anthocyanins (cyanidin glycosides) extd. from the orange and red flowers were identical, even though the absorbance spectra of the intact cells differed. The absorbance spectrum of the orange sport was simulated with a 10-3M aq. soln. of cyanidin 3,5-diglucoside at the pH of the tissue, 2.8. The absorbance spectrum of Red Wing was matched with cyanidin 3,5-diglucoside at the same concn. and pH, copigmented with the 3-rhamnoside or galactoside of quercetin.
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Asen, S.; Stewart, R. N.; Norris, K. H. Co-Pigmentation of Anthocyanins in Plant Tissues and Its Effect on Color Phytochemistry 1972, 11 (3) 1139– 1144 DOI: 10.1016/S0031-9422(00)88467-8
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Copigmentation of anthocyanins in plant tissues and its effect on color
Asen, S.; Stewart, R. N.; Norris, K. H.
Phytochemistry (Elsevier) (1972), 11 (3), 1139-44CODEN: PYTCAS; ISSN:0031-9422.
Glycosides of the 6 common anthocyanidins all formed copigment complexes with flavonoids and other compds. at pH 2-5. The formation of copigment complexes resulted in a bathochromic shift in the visible λmax. of the anthocyanins and a large increase in extinction at pH 3 and higher. These complexes apparently formed with both the red flavylium salts and the purple anhydro bases. The increase in extinction at pH 3-5 was attributed to the stabilizing effect copigmentation had on the anhydro bases. The degree of copigmentation was a function of the concn. of the anthocyanins and the molar ratio of copigments to anthocyanins. Copigmentation offers an explanation for the infinite color variations that occur in flowers in a pH range where anthocyanins alone are virtually colorless.
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Asen, S.; Norris, K. H.; Stewart, R. N. Copigmentation of Aurone and Flavone from Petals of Antirrhinum Majus Phytochemistry 1972, 11 (9) 2739– 2741 DOI: 10.1016/S0031-9422(00)86505-X
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Hoshino, T.; Matsumoto, U.; Goto, T. Self-Association of Some Anthocyanins in Neutral Aqueous Solution Phytochemistry 1981, 20 (8) 1971– 1976 DOI: 10.1016/0031-9422(81)84047-2
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40
Hoshino, T.; Matsumoto, U.; Harada, N.; Goto, T. Chiral Exciton Coupled Stacking of Anthocyanins: Interpretation of the Origin of Anomalous CD Induced by Anthocyanin Association Tetrahedron Lett. 1981, 22 (37) 3621– 3624 DOI: 10.1016/S0040-4039(01)81976-6
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41
Hoshino, T.; Matsumoto, U.; Goto, T. Evidences of the Self-Association of Anthocyanins I. Circular Dichroism of Cyanin Anhydrobase Tetrahedron Lett. 1980, 21 (18) 1751– 1754 DOI: 10.1016/S0040-4039(00)77827-0
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42
Hoshino, T.; Matsumoto, U.; Goto, T.; Harada, N. Evidence for the Self-Association of Anthocyanins IV. PMR Spectroscopic Evidence for the Vertical Stacking of Anthocyanin Molecules Tetrahedron Lett. 1982, 23 (4) 433– 436 DOI: 10.1016/S0040-4039(00)86852-5
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43
Hoshino, T.; Goto, T. Effects of pH and Concentration on the Self-Association of Malvin Quinonoidal Base: Electronic and Circular Dichroic Studies Tetrahedron Lett. 1990, 31 (11) 1593– 1596 DOI: 10.1016/0040-4039(90)80025-H
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44
Hoshino, T. Self-Association of Flavylium Cations of Anthocyanidin 3,5-Diglucosides Studied by Circular Dichroism and 1H NMR Phytochemistry 1992, 31 (2) 647– 653 DOI: 10.1016/0031-9422(92)90053-S
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Anthocyanin self-aggregates. Part 7. Self-association of flavylium cations of anthocyanidin 3,5-diglucosides studied by circular dichroism and proton NMR
Hoshino, Tsutomu
Phytochemistry (1992), 31 (2), 647-53CODEN: PYTCAS; ISSN:0031-9422.
Exciton coupling type CD was induced by increasing anthocyanin concn. in strongly acidic media. The higher the concn., the larger the CD magnitude. All anthocyanidin 3,5-diglucosides exhibited neg. signs in the first Cotton effect, which indicates that all the anthocyanins self-assoc. in a left-handed screw manner. Concn. dependence of proton chem. shifts were also obsd. with increase of anthocyanidin 3,5-diglucosides in a strongly acidic medium; upfield shifts of arom. rings by increasing pigment concns. demonstrated that anthocyanidin nuclei stack vertically. Analyses of proton chem. shifts based on the Dimicoli and Helene equation made possible the detn. of the self-assocn. of flavylium cations. The self-assocn. consts. for the most common natural anthocyanidin 3,5-diglucosides are given.
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Hoshino, T. An Approximate Estimate of Self-Association Constants and the Self-Stacking Conformation of Malvin Quinonoidal Bases Studied by 1H NMR Phytochemistry 1991, 30 (6) 2049– 2055 DOI: 10.1016/0031-9422(91)85065-8
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46
Brouillard, R.; Mazza, G.; Saad, Z.; Albrecht-Gary, A. M.; Cheminat, A. The Co-Pigmentation Reaction of Anthocyanins: A Microprobe for the Structural Study of Aqueous Solutions J. Am. Chem. Soc. 1989, 111 (7) 2604– 2610 DOI: 10.1021/ja00189a039
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The co-pigmentation reaction of anthocyanins: a microprobe for the structural study of aqueous solutions
Brouillard, R.; Mazza, G.; Saad, Z.; Albrecht-Gary, A. M.; Cheminat, A.
Journal of the American Chemical Society (1989), 111 (7), 2604-10CODEN: JACSAT; ISSN:0002-7863.
Visible absorption spectrometry shows that, in acidic aq. solns., chlorogenic acid (I) forms a loose 1:1 complex with malvin chloride (II). The mol. interaction taking place between these two chem. species is characteristic of the copigmentation reaction of anthocyanins. For the first time the mechanism assocd. with this reaction is established. The equation describing the copigment effect is also given. The copigmentation reaction is a very fast process which is extremely influenced by temp. Increasing the temp. or adding MeOH, HCONH2, or NaCl always reduces the copigment effect. In fact, the extent of copigmentation is strictly under the control of the unique mol. structure of liq. water. Finally, the copigmentation phenomenon, which is widespread in higher plants, constitutes a simple, inexpensive, and very sensitive, microprobe for the structural studies of aq. solns.
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Figueiredo, P.; Elhabiri, M.; Saito, N.; Brouillard, R. Anthocyanin Intramolecular Interactions. A New Mathematical Approach To Account for the Remarkable Colorant Properties of the Pigments Extracted from Matthiola Incana J. Am. Chem. Soc. 1996, 118 (20) 4788– 4793 DOI: 10.1021/ja9535064
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Figueiredo, P.; Elhabiri, M.; Toki, K.; Saito, N.; Dangles, O.; Brouillard, R. New Aspects of Anthocyanin Complexation. Intramolecular Copigmentation as a Means for Colour Loss? Phytochemistry 1996, 41 (1) 301– 308 DOI: 10.1016/0031-9422(95)00530-7
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49
Zhang, B.; Liu, R.; He, F.; Zhou, P.-P.; Duan, C.-Q. Copigmentation of Malvidin-3-O-Glucoside with Five Hydroxybenzoic Acids in Red Wine Model Solutions: Experimental and Theoretical Investigations Food Chem. 2015, 170, 226– 233 DOI: 10.1016/j.foodchem.2014.08.026
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Copigmentation of malvidin-3-O-glucoside with five hydroxybenzoic acids in red wine model solutions: Experimental and theoretical investigations
Zhang, Bo; Liu, Rui; He, Fei; Zhou, Pan-Pan; Duan, Chang-Qing
Food Chemistry (2015), 170 (), 226-233CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
In the present research, the copigmentations of malvidin-3-O-glucoside with five hydroxybenzoic cofactors (p-hydroxybenzoic acid, protocatechuic acid, gallic acid, vanillic acid, and syringic acid) were investigated. The influence of the concn. of these cofactors and the reaction temp. was examd. The equil. const. (K), stoichiometric ratio (n) and the thermodn. parameters (ΔG°, ΔH°, ΔS°) related to the copigmentation were also reported here. Theor. calcns. were performed to identify the relative arrangement between the pigment and cofactors in the copigmentation complexes. Besides, the comparison of the relative binding free energies (ΔΔGbinding) derived from the theor. calcns. and exptl. data were made, and the binding strength of these copigmentation complexes was discussed with the interaction energies (ΔE). AIM anal. was also used to explore the main driving forces contributing to the copigmentation. In the comparison of the five studied cofactors, syringic acid had a stronger copigmentation effect than the other four phenolic acids investigated.
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Teixeira, N.; Cruz, L.; Brás, N. F.; Mateus, N.; Ramos, M. J.; de Freitas, V. Structural Features of Copigmentation of Oenin with Different Polyphenol Copigments J. Agric. Food Chem. 2013, 61 (28) 6942– 6948 DOI: 10.1021/jf401174b
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Structural Features of Copigmentation of Oenin with Different Polyphenol Copigments
Teixeira, Natercia; Cruz, Luis; Bras, Natercia F.; Mateus, Nuno; Ramos, Maria Joao; de Freitas, Victor
Journal of Agricultural and Food Chemistry (2013), 61 (28), 6942-6948CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
The copigmentation binding consts. (K) for the interaction of different copigments with oenin (major red wine anthocyanin) were detd. All tests were performed in a 12% ethanol citrate buffer soln. (0.2 M) at pH 3.5, with an ionic strength adjusted to 0.5 M by the addn. of sodium chloride. Over the past years, several copigmentation studies were made and many copigments were tested, but none of them included prodelphinidin B3 or a dimeric-type adduct like oenin-(O)-catechin, probably due to the difficulty in obtaining them. The data yielded from this study allowed concluding that (a) the presence of a pyrogallol group in the B ring of the flavan-3-ol structure slightly increases the copigmentation potential and (b) within all copigments tested oenin-(O)-catechin was revealed to be the best. According to computational studies performed on epicatechin/oenin, epigallocatechin/oenin, procyanidin B3/oenin, and oenin-(O)-catechin/oenin complexes, the ΔGbinding energy of the oenin-(O)-catechin/oenin complex is the most neg. compared to the other copigmentation complexes, hence being more stable and thermodynamically favored. All structural data show that oenin-(O)-catechin and epigallocatechin are closer to the pigment mol., which is in accordance with these two copigments having the highest exptl. copigmentation binding consts. for oenin.
51
Fossen, T.; Rayyan, S.; Holmberg, M. H.; Nimtz, M.; Andersen, Ø. M. Covalent Anthocyanin–flavone Dimer from Leaves of Oxalis Triangularis Phytochemistry 2007, 68 (5) 652– 662 DOI: 10.1016/j.phytochem.2006.10.030
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Saito, N.; Nakamura, M.; Shinoda, K.; Murata, N.; Kanazawa, T.; Kato, K.; Toki, K.; Kasai, H.; Honda, T.; Tatsuzawa, F. Covalent Anthocyanin–flavonol Complexes from the Violet-Blue Flowers of Allium “Blue Perfume. Phytochemistry 2012, 80, 99– 108 DOI: 10.1016/j.phytochem.2012.04.011
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Hayashi, K.; Abe, Y.; Mitsui, S. Blue Anthocyanin from the Flowers of Commelina, the Crystallisation and Some Properties Thereof Proc. Jpn. Acad. 1958, 34 (6) 373– 378
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Anthocyanins. XXX. Blue anthocyanin from flowers of Commelina, the crystallization and some properties thereof
Hayashi, Kozo; Abe, Yukihide; Mitsui, Seiji
Proceedings of the Japan Academy (1958), 34 (), 373-8CODEN: PJACAW; ISSN:0021-4280.
cf. C.A. 50, 16935g. Brilliant blue, prismatic crystals obtained after repeated fractionation and pptn. with water and EtOH were subjected to qual. chem. analysis and behavior. The substance contained an appreciable amt. of metallic elements of which Mg and K were inherent to the pigment mol. It is readily sol. in water but does not retain its color in org. solvents and is neither acid nor base. Paper electrophoresis indicated the existence of essential structural difference between the blue and red forms of anthocyanin. The org. components seemed to be delphinidin, glucose, and p-coumaric acid.
54
Shibata, K.; Shibata, Y.; Kasiwagi, I. Studies on Anthocyanins: Color Variationin Anthocyanins J. Am. Chem. Soc. 1919, 41 (2) 208– 220 DOI: 10.1021/ja01459a008
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Bloor, S. J. Blue Flower Colour Derived from Flavonol-Anthocyanin Co-Pigmentation in Ceanothus Papillosus Phytochemistry 1997, 45 (7) 1399– 1405 DOI: 10.1016/S0031-9422(97)00129-5
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Tamura, H.; Kondo, T.; Goto, T. The Composition of Commelinin, a Highly Associated Metalloanthocaynin Present in the Blue Flower Petals of Commelina Communis Tetrahedron Lett. 1986, 27 (16) 1801– 1804 DOI: 10.1016/S0040-4039(00)84379-8
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Kondo, T.; Ueda, M.; Isobe, M.; Goto, T. A New Molecular Mechanism of Blue Color Development with Protocyanin, a Supramolecular Pigment from Cornflower, Centaurea Cyanus Tetrahedron Lett. 1998, 39 (45) 8307– 8310 DOI: 10.1016/S0040-4039(98)01858-9
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Kondo, T.; Oyama, K.; Yoshida, K. Chiral Molecular Recognition on Formation of a Metalloanthocyanin: A Supramolecular Metal Complex Pigment from Blue Flowers of Salvia Patens Angew. Chem., Int. Ed. 2001, 40 (5) 894– 897 DOI: 10.1002/1521-3773(20010302)40:5<894::AID-ANIE894>3.3.CO;2-#
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Mori, M.; Kondo, T.; Yoshida, K. Cyanosalvianin, a Supramolecular Blue Metalloanthocyanin, from Petals of Salvia Uliginosa Phytochemistry 2008, 69 (18) 3151– 3158 DOI: 10.1016/j.phytochem.2008.03.015
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Yoshida, K.; Toyama-Kato, Y.; Kameda, K.; Kondo, T. Sepal Color Variation of Hydrangea Macrophylla and Vacuolar pH Measured with a Proton-Selective Microelectrode Plant Cell Physiol. 2003, 44 (3) 262– 268 DOI: 10.1093/pcp/pcg033
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Kondo, T.; Toyama-Kato, Y.; Yoshida, K. Essential Structure of Co-Pigment for Blue Sepal-Color Development of Hydrangea Tetrahedron Lett. 2005, 46 (39) 6645– 6649 DOI: 10.1016/j.tetlet.2005.07.146
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Tanaka, M.; Fujimori, T.; Uchida, I.; Yamaguchi, S.; Takeda, K. A Malonylated Anthocyanin and Flavonols in Blue Meconopsis Flowers Phytochemistry 2001, 56 (4) 373– 376 DOI: 10.1016/S0031-9422(00)00357-5
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Yoshida, K.; Kitahara, S.; Ito, D.; Kondo, T. Ferric Ions Involved in the Flower Color Development of the Himalayan Blue Poppy, Meconopsis Grandis Phytochemistry 2006, 67 (10) 992– 998 DOI: 10.1016/j.phytochem.2006.03.013
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Markham, K. R.; Mitchell, K. A.; Boase, M. R. Malvidin-3-O-Glucoside-5-O-(6-Acetylglucoside) and Its Colour Manifestation in “Johnson”s Blue’ and Other “Blue” Geraniums Phytochemistry 1997, 45 (2) 417– 423 DOI: 10.1016/S0031-9422(96)00831-X
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Yabuya, T.; Nakamura, M.; Iwashina, T.; Yamaguchi, M.; Takehara, T. Anthocyanin-Flavone Copigmentation in Bluish Purple Flowers of Japanese Garden Iris (Iris Ensata Thunb.) Euphytica 1997, 98 (3) 163– 167 DOI: 10.1023/A:1003152813333
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66
Bimpilas, A.; Tsimogiannis, D.; Balta-Brouma, K.; Lymperopoulou, T.; Oreopoulou, V. Evolution of Phenolic Compounds and Metal Content of Wine during Alcoholic Fermentation and Storage Food Chem. 2015, 178, 164– 171 DOI: 10.1016/j.foodchem.2015.01.090
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Evolution of phenolic compounds and metal content of wine during alcoholic fermentation and storage
Bimpilas, Andreas; Tsimogiannis, Dimitrios; Balta-Brouma, Kalliopi; Lymperopoulou, Theopisti; Oreopoulou, Vassiliki
Food Chemistry (2015), 178 (), 164-171CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
Changes in the principal phenolic compds. and metal content during the vinification process and storage under modified atm. (50% N2, 50% CO2) of Merlot and Syrah wines, from grapes cultivated in Greece, have been investigated. Comparing the variation of metals at maceration process, with the variation of monomeric anthocyanins and flavonols, an inverse relationship was noticed, that can be attributed to complexing reactions of polyphenols with particular trace elements. Cu decreased rapidly, whereas a similar behavior that could be expected for Fe and Mn was not confirmed. Differences in the profile of anthocyanins and flavonols in the fresh Merlot and Syrah wines are reported. During 1 yr of storage monomeric anthocyanins declined almost tenfold, probably due to polymn. reactions and copigmentation. Also, a decrease in flavonol glycosides and increase in the resp. aglycons was obsd., attributed to enzymic hydrolysis. The concn. of total phenols and all metals remained practically const.
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Hermosín Gutiérrez, I. Influence of Ethanol Content on the Extent of Copigmentation in a Cencibel Young Red Wine J. Agric. Food Chem. 2003, 51 (14) 4079– 4083 DOI: 10.1021/jf021029k
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Monagas, M.; Bartolomé, B. Anthocyanins and Anthocyanin-Derived Compounds. In Wine Chemistry and Biochemistry; Moreno-Arribas, M. V.; Polo, M. C., Eds.; Springer: New York, 2009; pp 439– 462.
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69
Rustioni, L.; Bedgood, D. R.; Failla, O.; Prenzler, P. D.; Robards, K. Copigmentation and Anti-Copigmentation in Grape Extracts Studied by Spectrophotometry and Post-Column-Reaction HPLC Food Chem. 2012, 132 (4) 2194– 2201 DOI: 10.1016/j.foodchem.2011.12.058
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De Rosso, M.; Tonidandel, L.; Larcher, R.; Nicolini, G.; Dalla Vedova, A.; De Marchi, F.; Gardiman, M.; Giust, M.; Flamini, R. Identification of New Flavonols in Hybrid Grapes by Combined Liquid Chromatography–mass Spectrometry Approaches Food Chem. 2014, 163, 244– 251 DOI: 10.1016/j.foodchem.2014.04.110
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Kelebek, H.; Canbas, A.; Selli, S. HPLC-DAD–MS Analysis of Anthocyanins in Rose Wine Made From Cv. Öküzgözü Grapes, and Effect of Maceration Time on Anthocyanin Content Chromatographia 2007, 66 (3–4) 207– 212 DOI: 10.1365/s10337-007-0277-8
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Gordillo, B.; Rodríguez-Pulido, F. J.; González-Miret, M. L.; Quijada-Morín, N.; Rivas-Gonzalo, J. C.; García-Estévez, I.; Heredia, F. J.; Escribano-Bailón, M. T. Application of Differential Colorimetry To Evaluate Anthocyanin–Flavonol–Flavanol Ternary Copigmentation Interactions in Model Solutions J. Agric. Food Chem. 2015, 63 (35) 7645– 7653 DOI: 10.1021/acs.jafc.5b00181
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Somers, T. C.; Vérette, E. Phenolic Composition of Natural Wine Types. In Wine Analysis; Linskens, P. D. H.-F.; Jackson, P. D. J. F., Eds.; Modern Methods of Plant Analysis; Springer: Berlin, 1988; pp 219– 257.
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74
González-Manzano, S.; Dueñas, M.; Rivas-Gonzalo, J. C.; Escribano-Bailón, M. T.; Santos-Buelga, C. Studies on the Copigmentation between Anthocyanins and Flavan-3-Ols and Their Influence in the Colour Expression of Red Wine Food Chem. 2009, 114 (2) 649– 656 DOI: 10.1016/j.foodchem.2008.10.002
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Studies on the copigmentation between anthocyanins and flavan-3-ols and their influence in the colour expression of red wine
Gonzalez-Manzano, Susana; Duenas, Montserrat; Rivas-Gonzalo, Julian C.; Escribano-Bailon, M. Teresa; Santos-Buelga, Celestino
Food Chemistry (2009), 114 (2), 649-656CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier B.V.)
With the aim of evaluating the importance of the copigmentation process between anthocyanins and flavanols on the color expression of red wine, assays were carried out in wine model systems with mixts. of compds. obtained from two Vitis vinifera grape varieties (Graciano and Tempranillo). Spectrophotometric and chromatic analyses were performed to evaluate the magnitude of the copigmentation and the modifications induced in the color of the solns. Measurement of the changes in the anthocyanin hydration const. (Kh) was also used to det. the strength of the copigmentation process. All the flavanols assayed induced significant changes in the color, perceptible to the human eye, of the wine-like anthocyanin solns. at concns. similar to those that can exist in red wines. The percentage contribution of the copigmentation with flavanols to the color of the anthocyanin solns. was found to range from 2% to 20%. The extent of this effect was related not only to the concn. of flavanols but also to the qual. compn. of the flavanol prepns., as influenced by the part of the grape (either skin or seed) and the variety considered. Divergences were found between the evaluation of the copigmentation based on chromatic parameters in the CIELAB color space and that based on the measurement at visible λ max, as the latter does not consider the integral color changes produced in the visible spectrum. The results obtained confirmed the importance of the qual. phenolic compn., detd. in the wine by the type of grape and winemaking practices, to the prodn. of an effective copigmentation process.
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Fernandes, A.; Brás, N. F.; Mateus, N.; Freitas, V. de. A Study of Anthocyanin Self-Association by NMR Spectroscopy New J. Chem. 2015, 39 (4) 2602– 2611 DOI: 10.1039/C4NJ02339K
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76
Heras-Roger, J.; Pomposo-Medina, M.; Díaz-Romero, C.; Darias-Martín, J. Copigmentation, Colour and Antioxidant Activity of Single-Cultivar Red Wines Eur. Food Res. Technol. 2014, 239 (1) 13– 19 DOI: 10.1007/s00217-014-2185-0
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Copigmentation, colour and antioxidant activity of single-cultivar red wines
Heras-Roger, J.; Pomposo-Medina, M.; Diaz-Romero, C.; Darias-Martin, J.
European Food Research and Technology (2014), 239 (1), 13-19CODEN: EFRTFO; ISSN:1438-2377. (Springer)
A hundred and thirty-six single-cultivar red wines of different vintages were collected from several wineries in the Canary Islands in order to study the magnitude of the copigmentation phenomenon and the antioxidant activity. The contribution of free anthocyanins, copigmented anthocyanins and polymeric pigments to the color of wine, as well as the total phenols, the antioxidant activity (2,2-diphenyl-1-picrylhydrazyl, DPPH method) and the chromatic characteristics of the wines were detd. The influence of ageing time and the climatic conditions on these parameters was also studied. The wines made with Merlot, Ruby Cabernet and Syrah cultivars showed the highest parameters of color, and the largest contribution to the copigmented anthocyanins was from the Ruby Cabernet, Listan negro and Syrah cultivars. The copigmented anthocyanins and the free anthocyanins decrease with the age of the wine, and the antioxidant activity of the samples appears to be related to the total phenol content. An influence of the climatic conditions on color parameters has been found. The correlation study between parameters suggests that the parameters b* and L* could be used as suitable indicators of evolution or oxidn. stage of red wines.
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García-Marino, M.; Escudero-Gilete, M. L.; Heredia, F. J.; Escribano-Bailón, M. T.; Rivas-Gonzalo, J. C. Color-Copigmentation Study by Tristimulus Colorimetry (CIELAB) in Red Wines Obtained from Tempranillo and Graciano Varieties Food Res. Int. 2013, 51 (1) 123– 131 DOI: 10.1016/j.foodres.2012.11.035
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Color-copigmentation study by tristimulus colorimetry (CIELAB) in red wines obtained from Tempranillo and Graciano varieties
Garcia-Marino, Matilde; Escudero-Gilete, Maria Luisa; Heredia, Francisco Jose; Escribano-Bailon, Maria Teresa; Rivas-Gonzalo, Julian Carlos
Food Research International (2013), 51 (1), 123-131CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
A study of the changes of copigmentation phenomenon in wines elaborated from different varieties has been undertaken. Colorimetric measurement of Tempranillo (T) and Graciano (G) monovarietal wines, and two 80:20 blend wines: M, (grape blending T and G, co-maceration) and W (wine blending T and G, co-vinification) was performed by spectrophotometry. Significant differences (p < 0.05) were found among the color of the wines. The Graciano cv. afforded somewhat darker and more colorful wines than the other wines. The color difference values, ΔE*ab suggested that co-vinification (W) led to wines being more similar to T than the co-maceration (M). The ΔE*ab[w-c] between untreated wines - whole wines, w - and the wines dild. to eliminate copigmentation - cor. wines, c - was 14.2 CIELAB units in the initial stages of winemaking and 6.7 in the final stages. M had a greater proportion of color due to copigmentation than the monovarietal wines. Evaluation of this parameter confirms the importance of copigmentation process into wine color during the early stages of the vinification. Also, through the full spectrum, quant. data obtained allow a visual interpretation of the changes involved. In addn., with the aging in bottle, M wines had more stable color and more different color than W wines.
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Schwarz, M.; Picazo-Bacete, J. J.; Winterhalter, P.; Hermosín-Gutiérrez, I. Effect of Copigments and Grape Cultivar on the Color of Red Wines Fermented after the Addition of Copigments J. Agric. Food Chem. 2005, 53 (21) 8372– 8381 DOI: 10.1021/jf051005o
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Aleixandre-Tudó, J. L.; Álvarez, I.; Lizama, V.; García, M. J.; Aleixandre, J. L.; Du Toit, W. J. Impact of Caffeic Acid Addition on Phenolic Composition of Tempranillo Wines from Different Winemaking Techniques J. Agric. Food Chem. 2013, 61 (49) 11900– 11912 DOI: 10.1021/jf402713d
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Gris, E. F.; Ferreira, E. A.; Falcão, L. D.; Bordignon-Luiz, M. T. Influence of Ferulic Acid on Stability of Anthocyanins from Cabernet Sauvignon Grapes in a Model System and a Yogurt System Int. J. Food Sci. Technol. 2007, 42 (8) 992– 998 DOI: 10.1111/j.1365-2621.2006.01335.x
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Influence of ferulic acid on stability of anthocyanins from Cabernet Sauvignon grapes in a model system and a yogurt system
Gris, Eliana Fortes; Ferreira, Eduardo Antonio; Falcao, Leila Denise; Bordignon-Luiz, Marilde Terezinha
International Journal of Food Science and Technology (2007), 42 (8), 992-998CODEN: IJFTEZ; ISSN:0950-5423. (Blackwell Publishing Ltd.)
The influence of different factors on the stability of the anthocyanin crude ext. from Cabernet Sauvignon grape skins was investigated. In a model system, the factors evaluated were as follows: temp. 4 ± 1 °C and 29 ± 3 °C, presence and absence of light, pH 3.0 and 4.0 and presence of ferulic acid. The influence of the addn. of ferulic acid to anthocyanins was investigated in a yogurt system stored at 4 ± 1 °C. The results obtained for anthocyanin degrdn. velocity const. and for the half-life time of anthocyanins in a model system and in a yogurt system showed that ferulic acid significantly increased the stability of the anthocyanins crude ext.
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Talcott, S. T.; Peele, J. E.; Brenes, C. H. Red Clover Isoflavonoids as Anthocyanin Color Enhancing Agents in Muscadine Wine and Juice Food Res. Int. 2005, 38 (10) 1205– 1212 DOI: 10.1016/j.foodres.2005.05.004
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Red clover isoflavonoids as anthocyanin color enhancing agents in muscadine wine and juice
Talcott, Stephen T.; Peele, Janelle E.; Brenes, Carmen H.
Food Research International (2005), 38 (10), 1205-1212CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
Isoflavonoid exts. from red clover (Trifolium pratense) leaves were found to enhance overall color and stability of anthocyanin 3,5-diglucosides present in muscadine grape (Vitis rotundifolia) juice and wine through intermol. copigmentation reactions. Predominant isoflavonoids present in red clover included formononetin, biochanin A, and prunetin and were the major polyphenolics identified to influence anthocyanin color and stability. Since red clover isoflavonoids have poor water soly. characteristics, this allowed for removal of extraneous non-isoflavonoid compds. using hot water and subsequent extn. with ethanol. Isoflavonoid soly. was evaluated as a function of ethanol concn. with recoveries up to 57% found in 20% solns. Changes in max. absorbance, total sol. phenolics, isoflavonoids, and anthocyanins were evaluated in muscadine juice and wine following the addn. of isoflavonoid exts. with max. color enhancement found at an anthocyanin to cofactor ratio of 1:8, after which their soly. was prohibitive. Addnl., dried leaves and ethanolic exts. of red clover were added prior to and following fermn. of muscadine wine (11% ethanol) stimulating the natural copigmentation that takes place during red wine fermn. and aging processes. Once fermn. was complete, finished wines were evaluated over a 9-wk storage period at 20 and 37°. Despite low levels of isoflavonoids present, color improvement and anthocyanin stability was obsd. in the wines during storage. Little information is available on copigmentation reactions occurring in actual food systems, yet red clover isoflavonoids proved to be novel and effective color enhancing compds. when used in low concns. in young muscadine wines.
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Liu, S.; Fu, Y.; Nian, S. Buffering Colour Fluctuation of Purple Sweet Potato Anthocyanins to Acidity Variation by Surfactants Food Chem. 2014, 162, 16– 21 DOI: 10.1016/j.foodchem.2014.04.029
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Buffering color fluctuation of purple sweet potato anthocyanins to acidity variation by surfactants
Liu, Songbai; Fu, Yuanqing; Nian, Si
Food Chemistry (2014), 162 (), 16-21CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
Anthocyanins are intriguing natural pigments with beneficial bioactivities and their color is extremely susceptible to acidity variation. Minimization of color fluctuation is essential to maintain quality consistency in food industry. A new strategy employing surfactants to mimic encapsulation was attempted with typical anionic, cationic and nonionic surfactants and proved effective although the traditional copigmentation method was inactive. The exceptional color fluctuation buffering effect of anionic surfactants esp. SDS was revealed and then carefully analyzed by colorimetric and spectroscopic methods. The outstanding activity of SDS presumably resulted from effective shielding of anthocyanins from external acidity through strong interaction with the pos. charged flavylium cations owing to its anionic nature. These results suggest SDS is a valuable additive for buffering color fluctuation of anthocyanins. The strategy of surfactant will be useful for buffering color fluctuation of natural colorants.
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Kovac, V.; Alonso, E.; Bourzeix, M.; Revilla, E. Effect of Several Enological Practices on the Content of Catechins and Proanthocyanidins of Red Wines J. Agric. Food Chem. 1992, 40 (10) 1953– 1957 DOI: 10.1021/jf00022a045
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Canals, R.; del Carmen Llaudy, M.; Canals, J. M.; Zamora, F. Influence of the Elimination and Addition of Seeds on the Colour, Phenolic Composition and Astringency of Red Wine Eur. Food Res. Technol. 2008, 226 (5) 1183– 1190 DOI: 10.1007/s00217-007-0650-8
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Influence of the elimination and addition of seeds on the colour, phenolic composition and astringency of red wine
Canals, Roser; del Carmen Llaudy, Maria; Canals, Joan Miquel; Zamora, Fernando
European Food Research and Technology (2008), 226 (5), 1183-1190CODEN: EFRTFO; ISSN:1438-2377. (Springer GmbH)
Several winemaking techniques were developed to eliminate seeds to prevent the release of high amts. of very astringent proanthocyanidins, esp. when the grapes are unripe. However, there is no scientific information on the effects of this practice. The aim of this paper is to study how the elimination and addn. of seeds influence the color, phenolic compn. and astringency of red wine. The elimination of around 80% of the seeds led to a significant decrease of color intensity and anthocyanin concn. The addn. of seeds originated wines with a greater concn. of total anthocyanin, but did not significantly affect the wine color. These wines also presented significantly higher levels of proanthocyanidins, a greater proportion of epicatechin-3-gallate, a lower mean d.p., and, in particular, a drastic increase in astringency. Wines obtained with the elimination of seeds, on the other hand, had exactly the opposite characteristics.
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Escribano-Bailon, M. T.; Santos-Buelga, C. Anthocyanin Copigmentation - Evaluation, Mechanisms and Implications for the Colour of Red Wines Curr. Org. Chem. 2012, 16 (6) 715– 723 DOI: 10.2174/138527212799957977
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Anthocyanin copigmentation - evaluation, mechanisms and implications for the colour of red wines
Escribano-Bailon, Maite T.; Santos-Buelga, Celestino
Current Organic Chemistry (2012), 16 (6), 715-723CODEN: CORCFE; ISSN:1385-2728. (Bentham Science Publishers Ltd.)
A review. Copigmentation is the main color-stabilizing mechanism in plants and in food products of vegetable origin. It is a spontaneous and exothermic process that consists of the stacking of an org. mol., called copigment, on the planar polarizable moieties of the anthocyanin colored forms. Although this phenomenon has long been described, there are some aspects that are still not well understood or controversial like the nature of the interaction pigment to copigment, the way to quantify the extent of the process, its effect on other anthocyanin properties like astringency or reactivity. In this article a review of the most significant advances achieved in the last years in the field of intramol. and intermol. copigmentation is presented. Also, the most recent findings regarding wine copigments and their effects on the color of red wines are revised.
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Quijada-Morín, N.; Dangles, O.; Rivas-Gonzalo, J. C.; Escribano-Bailón, M. T. Physico-Chemical and Chromatic Characterization of Malvidin 3-Glucoside-Vinylcatechol and Malvidin 3-Glucoside-Vinylguaiacol Wine Pigments J. Agric. Food Chem. 2010, 58 (17) 9744– 9752 DOI: 10.1021/jf102238v
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Oliveira, J.; Mateus, N.; Silva, A. M. S.; de Freitas, V. Equilibrium Forms of Vitisin B Pigments in an Aqueous System Studied by NMR and Visible Spectroscopy J. Phys. Chem. B 2009, 113 (32) 11352– 11358 DOI: 10.1021/jp904776k
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Brouillard, R.; Dangles, O. Anthocyanin Molecular Interactions: The First Step in the Formation of New Pigments during Wine Aging? Food Chem. 1994, 51 (4) 365– 371 DOI: 10.1016/0308-8146(94)90187-2
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Wrolstad, R. E.; Erlandson, J. A. Effect of Metal Ions on the Color of Strawberry Puree J. Food Sci. 1973, 38 (3) 460– 463 DOI: 10.1111/j.1365-2621.1973.tb01454.x
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Starr, M. S.; Francis, F. J. Effect of Metallic Ions on Color and Pigment Content of Cranberry Juice Cocktail J. Food Sci. 1973, 38 (6) 1043– 1046 DOI: 10.1111/j.1365-2621.1973.tb02144.x
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Kallio, H.; Pallasaho, S.; Kärppä, J.; Linko, R. R. Comparison of the Half-Lives of the Anthocyanins in the Juice of Crowberry, Empetrum Nigrum J. Food Sci. 1986, 51 (2) 408– 410 DOI: 10.1111/j.1365-2621.1986.tb11142.x
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Osawa, Y. Chapter 2 - Copigmentation of Anthocyanins. In Anthocyanins As Food Colors; Markakis, P., Ed.; Academic Press, 1982; pp 41– 68.
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Rein, M. J.; Heinonen, M. Stability and Enhancement of Berry Juice Color J. Agric. Food Chem. 2004, 52 (10) 3106– 3114 DOI: 10.1021/jf035507i
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Maccarone, E.; Maccarrone, A.; Rapisarda, P. Stabilization of Anthocyanins of Blood Orange Fruit Juice J. Food Sci. 1985, 50 (4) 901– 904 DOI: 10.1111/j.1365-2621.1985.tb12976.x
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Wilska-Jeszka, J.; Korzuchowska, A. Anthocyanins and Chlorogenic Acid Copigmentation - Influence on the Colour of Strawberry and Chokeberry Juices Z. Lebensm.-Unters. Forsch. 1996, 203 (1) 38– 42 DOI: 10.1007/BF01267767
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Anthocyanins and chlorogenic acid copigmentation. Influence on the color of strawberry and chokeberry juices
Wilska-Jeszka, Jadwiga; Korzuchowska, Anna
Zeitschrift fuer Lebensmittel-Untersuchung und -Forschung (1996), 203 (1), 38-42CODEN: ZLUFAR; ISSN:0044-3026. (Springer)
The effect of copigmentation on chlorogenic acid with anthocyanins in strawberry and chokeberry juices was investigated. Chlorogenic acid, at concns. greater than that of anthocyanins, enhanced the color intensity of these juices. The max. copigmentation effect in both juices was obsd. at pH 3.4. In the investigated range of the copigment/pigment ratio, i.e. 1:1 to 50:1, absorbance increased (ΔA) linearly with copigment content, ΔA/g chlorogenic acid was greater in chokeberry than in strawberry juices. In solns. of purified pigments of these fruits, smaller copigmentation effects were obsd. than in juices under the same conditions, which indicated the participation of natural copigments present in fruits in the copigmentation process.
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Hernández-Herrero, J. A.; Frutos, M. J. Influence of Rutin and Ascorbic Acid in Colour, Plum Anthocyanins and Antioxidant Capacity Stability in Model Juices Food Chem. 2015, 173, 495– 500 DOI: 10.1016/j.foodchem.2014.10.059
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Sari, P.; Wijaya, C. H.; Sajuthi, D.; Supratman, U. Colour Properties, Stability, and Free Radical Scavenging Activity of Jambolan (Syzygium Cumini) Fruit Anthocyanins in a Beverage Model System: Natural and Copigmented Anthocyanins Food Chem. 2012, 132 (4) 1908– 1914 DOI: 10.1016/j.foodchem.2011.12.025
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Fischer, U. A.; Carle, R.; Kammerer, D. R. Thermal Stability of Anthocyanins and Colourless Phenolics in Pomegranate (Punica Granatum L.) Juices and Model Solutions Food Chem. 2013, 138 (2–3) 1800– 1809 DOI: 10.1016/j.foodchem.2012.10.072
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Pan, Y.-Z.; Guan, Y.; Wei, Z.-F.; Peng, X.; Li, T.-T.; Qi, X.-L.; Zu, Y.-G.; Fu, Y.-J. Flavonoid C-Glycosides from Pigeon Pea Leaves as Color and Anthocyanin Stabilizing Agent in Blueberry Juice Ind. Crops Prod. 2014, 58, 142– 147 DOI: 10.1016/j.indcrop.2014.04.029
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Flavonoid C-glycosides from pigeon pea leaves as color and anthocyanin stabilizing agent in blueberry juice
Pan, You-Zhi; Guan, Yue; Wei, Zuo-Fu; Peng, Xiao; Li, Ting-Ting; Qi, Xiao-Lin; Zu, Yuan-Gang; Fu, Yu-Jie
Industrial Crops and Products (2014), 58 (), 142-147CODEN: ICRDEW; ISSN:0926-6690. (Elsevier B.V.)
The influences of flavonoid C-glycoside exts. from pigeon pea leaves (FCGE) and its main components vitexin and orientin on the color and anthocyanins stability of blueberry juice were investigated in the thermal expts. The color of juice was enhanced by FCGE and its main components in a molar ratio of 1:1 (anthocyanins/copigment). The satd. color of juice with FCGE and its main components could hold for a significantly longer time. Addnl., copigment FCGE, vitexin and orientin significantly enhanced the stability of anthocyanins. Half-life of anthocyanins in juice samples with FCGE (1:1), orientin and vitexin increased 87%, 79%, and 62%, resp. These results indicated FCGE showed dramatic effect on the color and anthocyanins stability of juice. Furthermore, juice samples with copigments possessed higher total phenolics content and higher DPPH radical-scavenging activity. Therefore, natural, easily available, inexpensive FCGE has potential as color enhancer and anthocyanins stabilizer in food industry.
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Goto, T.; Kondo, T. Struktur Und Molekulare Stapelung von Anthocyanen—Variation Der Blütenfarben Angew. Chem. 1991, 103 (1) 17– 33 DOI: 10.1002/ange.19911030105
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101
Liao, H.; Cai, Y.; Haslam, E. Polyphenol Interactions. Anthocyanins: Co-Pigmentation and Colour Changes in Red Wines J. Sci. Food Agric. 1992, 59 (3) 299– 305 DOI: 10.1002/jsfa.2740590305
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Polyphenol interactions. Part 6. Anthocyanins: co-pigmentation and color changes in red wines
Liao, Hua; Cai, Ya; Haslam, Edwin
Journal of the Science of Food and Agriculture (1992), 59 (3), 299-305CODEN: JSFAAE; ISSN:0022-5142.
Anthocyanin co-pigmentation is reviewed and its relevance to the color and appearance of young red wines is outlined. Reactions between flavan-3-ols, such as are present in red wines, and the anthocyanin malvin to give yellow-orange pigments (absorbance max. ∼440 nm) are reported. Possible structures for these new pigments are discussed as is their probable contribution to the changing hues of red wines as they age.
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Brouillard, R.; Wigand, M.-C.; Dangles, O.; Cheminat, A. pH and Solvent Effects on the Copigmentation Reaction of Malvin with Polyphenols, Purine and Pyrimidine Derivatives J. Chem. Soc., Perkin Trans. 2 1991, 8) 1235– 1241 DOI: 10.1039/p29910001235
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The pH and solvent effects on the copigmentation reaction of malvin with polyphenols, purine and pyrimidine derivatives
Brouillard, Raymond; Wigand, Marie Claude; Dangles, Olivier; Cheminat, Annie
Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1972-1999) (1991), (8), 1235-41CODEN: JCPKBH; ISSN:0300-9580.
The influence of pH on the copigmentation reaction of malvin has been investigated from an exptl. and theor. viewpoint. The general equation for the copigment effect, when monitored by visible absorption spectrometry, is derived and is in good agreement with results obtained in the case of three different copigments, namely chlorogenic acid, caffeine and adenosine. In particular, it is demonstrated that assocn. of malvin with the copigment occurs for all colored malvin species and the corresponding stability consts. are given. Some tannins and purine or pyrimidine derivs. have also been tested for their ability to act as copigments; some assoc. quite strongly with malvin. Water exerted the greatest effect on the extent of the copigmentation phenomenon. Such a result seems to indicate that the strength of the copigment effect parallels the cohesion of the H-bonded tetrahedral network of water mols.
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Baranac, J. M.; Petranovic, N. A.; Dimitric-Markovic, J. M. Spectrophotometric Study of Anthocyan Copigmentation Reactions J. Agric. Food Chem. 1996, 44 (5) 1333– 1336 DOI: 10.1021/jf950420l
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104
Oszmiański, J.; Bakowska, A.; Piacente, S. Thermodynamic Characteristics of Copigmentation Reaction of Acylated Anthocyanin Isolated from Blue Flowers ofScutellaria Baicalensis Georgi with Copigments J. Sci. Food Agric. 2004, 84 (12) 1500– 1506 DOI: 10.1002/jsfa.1815
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Thermodynamic characteristics of copigmentation reaction of acylated anthocyanin isolated from blue flowers of Scutellaria baicalensis Georgi with copigments
Oszmianski, Jan; Bakowska, Anna; Piacente, Sonia
Journal of the Science of Food and Agriculture (2004), 84 (12), 1500-1506CODEN: JSFAAE; ISSN:0022-5142. (John Wiley & Sons Ltd.)
Anthocyanin exts. are increasingly used as food colorants. So far, anthocyanins have not been broadly used in foods and beverages, since they are not as stable as synthetic dyes. Copigmentation between anthocyanins and copigments is the main color-stabilizing mechanism. The process of copigmentation between isolated acylated anthocyanin and rutin, QSA or baicalin has been obsd. using UV-vis spectrophotometry. The thermodn. parameters were correlated to the structure and position of the substituents in the interacting mols. The acylated anthocyanin was isolated from cultivars of Scutellaria baicalensis Georgi flowers and purified by column chromatog. by our own method and has been identified by 1H-/13C-NMR spectroscopy and electrospray mass spectrometry as delphinidin-3-O-(6-O-malonyl)-β-D-glucopyranosyl-5-O-β-D-glucopyranoside.
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Ferreira da Silva, P.; Lima, J. C.; Freitas, A. A.; Shimizu, K.; Maçanita, A. L.; Quina, F. H. Charge-Transfer Complexation as a General Phenomenon in the Copigmentation of Anthocyanins J. Phys. Chem. A 2005, 109 (32) 7329– 7338 DOI: 10.1021/jp052106s
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Charge-Transfer Complexation as a General Phenomenon in the Copigmentation of Anthocyanins
Ferreira da Silva, Palmira; Lima, Joao C.; Freitas, Adilson A.; Shimizu, Karina; Macanita, Antonio L.; Quina, Frank H.
Journal of Physical Chemistry A (2005), 109 (32), 7329-7338CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Color intensification of anthocyanin solns. in the presence of natural polyphenols (copigmentation) is re-interpreted in terms of charge transfer from the copigment to the anthocyanin. Flavylium cations are shown to be excellent electron acceptors (Ered ≈ -0.3 V vs SCE). It is also demonstrated, for a large series of anthocyanin-copigment pairs, that the std. Gibbs free energy of complex formation decreases linearly with EAAnthoc-IPCop, the difference between the electron affinity of the anthocyanin, EAAnthoc, and the ionization potential of the copigment, IPCop. Based on this correlation, copigmentation strengths of potential candidates for copigments can be predicted.
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Galland, S.; Mora, N.; Abert-Vian, M.; Rakotomanomana, N.; Dangles, O. Chemical Synthesis of Hydroxycinnamic Acid Glucosides and Evaluation of Their Ability To Stabilize Natural Colors via Anthocyanin Copigmentation J. Agric. Food Chem. 2007, 55 (18) 7573– 7579 DOI: 10.1021/jf071205v
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Chemical synthesis of hydroxycinnamic acid glucosides and evaluation of their ability to stabilize natural colors via anthocyanin copigmentation
Galland, Stephanie; Mora, Nathalie; Abert-Vian, Maryline; Rakotomanomana, Njara; Dangles, Olivier
Journal of Agricultural and Food Chemistry (2007), 55 (18), 7573-7579CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
This work describes the chem. synthesis of O-aryl-β-D-glucosides and 1-O-β-D-glucosyl esters of hydroxycinnamic acids. In particular, O-aryl-β-D-glucosides were efficiently prepd. via a simple diastereoselective glycosylation procedure using phase transfer conditions. Despite the lability of its ester linkage, 1-O-β-D-caffeoylglucose could also be obtained using a Lewis acid catalyzed glycosylation step and a set of protective groups that can be removed under neutral conditions. Hydroxycinnamic acid O-aryl-β-D-glucosides were then quant. investigated for their affinity for the naturally occurring anthocyanin malvin (pigment). Formation of the π-stacking mol. complexes (copigmentation) was characterized in terms of binding consts. and enthalpy and entropy changes. The glucosyl moiety did not significantly alter these thermodn. parameters, in line with a binding process solely involving the polyphenolic nuclei.
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Alluis, B.; Dangles, O. Quercetin (=2-(3,4-Dihydroxyphenyl)-3,5,7-Trihydroxy-4H-1-Benzopyran-4-One) Glycosides and Sulfates: Chemical Synthesis, Complexation, and Antioxidant Properties Helv. Chim. Acta 2001, 84 (5) 1133– 1156 DOI: 10.1002/1522-2675(20010516)84:5<1133::AID-HLCA1133>3.3.CO;2-Q
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108
Nave, F.; Brás, N. F.; Cruz, L.; Teixeira, N.; Mateus, N.; Ramos, M. J.; Di Meo, F.; Trouillas, P.; Dangles, O.; De Freitas, V. Influence of a Flavan-3-Ol Substituent on the Affinity of Anthocyanins (Pigments) toward Vinylcatechin Dimers and Proanthocyanidins (Copigments) J. Phys. Chem. B 2012, 116 (48) 14089– 14099 DOI: 10.1021/jp307782y
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Influence of a Flavan-3-ol Substituent on the Affinity of Anthocyanins (Pigments) toward Vinylcatechin Dimers and Proanthocyanidins (Copigments)
Nave, Frederico; Bras, Natercia F.; Cruz, Luis; Teixeira, Natercia; Mateus, Nuno; Ramos, Maria J.; Di Meo, Florent; Trouillas, Patrick; Dangles, Olivier; De Freitas, Victor
Journal of Physical Chemistry B (2012), 116 (48), 14089-14099CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
The aim of this study is to investigate interactions possibly taking place in red wine between three flavanols (copigments, CP), i.e., two epimeric vinylcatechin dimers (CP1 and CP2) and catechin dimer B3 (CP3), and a specific pigment resulting from the condensation between the main grape anthocyanin malvidin 3-O-glucoside (oenin) and catechin, catechin-(4→8)-oenin. By comparison with our previous work on oenin itself, the influence of the catechin moiety of the anthocyanin in the binding is established. The thermodn. parameters show that both vinylcatechin dimers exhibit a higher affinity for catechin-(4→8)-oenin, in comparison with proanthocyanidin B3, as previously obsd. with oenin. However, the corresponding binding consts. are weaker, probably due to steric hindrance in the anthocyanin brought by the flavanol nucleus. Consequently, catechin-(4→8)-oenin should be much less stabilized by copigmentation in hydroalcoholic soln. than oenin. Quantum mechanics and mol. dynamics simulations are also performed to interpret the binding data, to specify the relative arrangement of the pigment and copigment mols. within the complexes, and to interpret their absorption properties in the visible range.
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Dangles, O.; Elhajji, H. Synthesis of 3-Methoxy-and 3-B-D-Glucopyranosy1oxy) Flavylium Ions. Influence of the Flavylium Substitution Pattern on the Reactivity of Anthocyanins in Aqueous Solution Helv. Chim. Acta 1994, 77 (6) 1595– 1610 DOI: 10.1002/hlca.19940770616
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Cruz, L.; Brás, N. F.; Teixeira, N.; Mateus, N.; Ramos, M. J.; Dangles, O.; De Freitas, V. Vinylcatechin Dimers Are Much Better Copigments for Anthocyanins than Catechin Dimer Procyanidin B3 J. Agric. Food Chem. 2010, 58 (5) 3159– 3166 DOI: 10.1021/jf9037419
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Vinylcatechin Dimers Are Much Better Copigments for Anthocyanins than Catechin Dimer Procyanidin B3
Cruz, Luis; Bras, Natercia F.; Teixeira, Natercia; Mateus, Nuno; Joao Ramos, Maria; Dangles, Olivier; De Freitas, Victor
Journal of Agricultural and Food Chemistry (2010), 58 (5), 3159-3166CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
The binding consts. (K) for the interaction of three copigments (CP), two epimeric vinylcatechin dimers (CP1 and CP2), and catechin dimer B3 (CP3) with two pigments, malvidin-3-glucoside (oenin) and malvidin-3,5-diglucoside (malvin), were detd. The K values clearly show that both vinylcatechin dimers have much higher affinity for oenin and malvin than dimer B3: KCP2 > KCP1 » KCP3. Quantum mechanics and mol. dynamics calcns. were also performed to interpret the binding data and specify the relative arrangement of the pigment and copigment mols. within the complexes.
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Malien-Aubert, C.; Dangles, O.; Amiot, M. J. Influence of Procyanidins on the Color Stability of Oenin Solutions J. Agric. Food Chem. 2002, 50 (11) 3299– 3305 DOI: 10.1021/jf011392b
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Influence of Procyanidins on the Color Stability of Oenin Solutions
Malien-Aubert, Celine; Dangles, Olivier; Amiot, Marie Josephe
Journal of Agricultural and Food Chemistry (2002), 50 (11), 3299-3305CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
The aim of the present work was to specify the influence of the polymn. degree on the color stability of anthocyanins using model solns. under higher thermal conditions simulating rapid food aging. Results showed that an increase in polymeric degree improves the color stability of oenin. Solns. contg. a catechin tetramer, purified from brown rice, displayed a remarkable stability. Flavanols as monomers, (+)-catechin and (-)-epicatechin, appeared to decrease stability with the formation of a xanthylium salt leading to yellowish solns. For the dimers, procyanidin B2 and B3, different behaviors on red color stability have been obsd. corresponding to their different susceptibility to cleavage upon heating. In the presence of the trimeric procyanidin C2, the red color appeared more stable. However, the HPLC chromatograms showed a decrease in the amplitude of the peaks of oenin and procyanidin C2. Concomitantly, a new peak appeared with a maximal absorption in the red region. This newly formed pigment probably came from the condensation of oenin and procyanidin C2.
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Benesi, H. A.; Hildebrand, J. H. A Spectrophotometric Investigation of the Interaction of Iodine with Aromatic Hydrocarbons J. Am. Chem. Soc. 1949, 71 (8) 2703– 2707 DOI: 10.1021/ja01176a030
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A spectrophotometric investigation of the interaction of iodine with aromatic hydrocarbons
Benesi, H. A.; Hildebrand, J. H.
Journal of the American Chemical Society (1949), 71 (), 2703-7CODEN: JACSAT; ISSN:0002-7863.
cf. C.A. 42, 8172g. The absorption spectra of I2 in C6H5CF3, benzene, toluene, o- and p-xylene, and mesitylene were measured in the region 270-700 mμ. In the visible region, the absorption peaks of these solns. showed moderate shifts toward shorter wave lengths in the order listed above. With the exception of I2 in C6H5CF3, each of the aromatic hydrocarbon solns. had an intense absorption band in the ultraviolet region which was shown to be characteristic of a complex contg. one I2 and one aromatic hydrocarbon mol. The equil. between I2 and the aromatic hydrocarbons was investigated in the neutral solvents CCl4 and C7H14, and the results show that the iodine-mesitylene complex is more stable than the iodine-benzene complex. These findings are strong evidence for an acid-base interaction between I2 and aromatic hydrocarbons. Absorption measurements also were made of I2 in CCl4, CS2, C7H14, Et2O, Me2CO, and 1,1-dichloroethane. No absorption bands analogous to those of the aromatic hydrocarbon solns. were found in the region 270-400 mμ.
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Dangles, O.; Brouillard, R. Polyphenol Interactions. The Copigmentation Case: Thermodynamic Data from Temperature Variation and Relaxation Kinetics. Medium Effect Can. J. Chem. 1992, 70 (8) 2174– 2189 DOI: 10.1139/v92-273
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114
Di Meo, F.; Sancho Garcia, J. C.; Dangles, O.; Trouillas, P. Highlights on Anthocyanin Pigmentation and Copigmentation: A Matter of Flavonoid Π-Stacking Complexation To Be Described by DFT-D J. Chem. Theory Comput. 2012, 8 (6) 2034– 2043 DOI: 10.1021/ct300276p
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Highlights on Anthocyanin Pigmentation and Copigmentation: A Matter of Flavonoid π-Stacking Complexation To Be Described by DFT-D
Di Meo, Florent; Sancho Garcia, Juan Carlos; Dangles, Olivier; Trouillas, Patrick
Journal of Chemical Theory and Computation (2012), 8 (6), 2034-2043CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Anthocyanidins are a class of π-conjugated systems responsible for red, blue, and purple colors of plants. They exhibit the capacity of aggregation in the presence of other natural compds. including flavonols. Such complexations induce color modulation in plants, which is known as copigmentation. It is largely driven by π-interactions existing between pigments and copigments. In this work, the energies of copigmentation-complexation and self-assocn. are systematically evaluated for an anthocyanidin/flavonol couple prototype (3-O-methylcyanidin/quercetin). To describe noncovalent interactions, DFT-D appears mandatory to reach a large accuracy. Due to the chem. complexity of this phenomenon, we also aim at assessing the relevance of both B3P86-D2 and ωB97X-D functionals. The benchmarking has shown that B3P86-D2 possesses enough accuracy when dealing with π-π interactions with respect to both spin component scaled Moller-Plesset second-order perturbation theory post Hartree-Fock method and exptl. data. UV-vis absorption properties are then evaluated with time-dependent DFT for the different complexes. The use of range-sepd. hybrid functionals, such as ωB97X-D, helped to correctly disentangle and interpret the origin of the UV-vis exptl. shifts attributed to the subtle copigmentation phenomenon.
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Awika, J. M. Behavior of 3-Deoxyanthocyanidins in the Presence of Phenolic Copigments Food Res. Int. 2008, 41 (5) 532– 538 DOI: 10.1016/j.foodres.2008.03.002
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Behavior of 3-deoxyanthocyanidins in the presence of phenolic copigments
Awika, Joseph M.
Food Research International (2008), 41 (5), 532-538CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
Anthocyanin stability and color intensity are generally improved in the presence of copigments in moderately acidic environments. The 3-deoxyanthocyanins on the other hand are fairly stable to color loss due to change in pH. It is unknown, therefore, how they behave in the presence of copigments. We studied the effects of common phenolic copigments, tannic, ferulic, and O-coumaric acids, and rutin on behavior and stability of six 3-deoxyanthocyandins over 4.5 mo. Tannic and ferulic acid produced the most significant bathochromic shift, whereas rutin had no bathochromic effect. None of the copigments produced a significant hyperchromic shift with the pigments, implying colored species of the pigments were predominant under conditions used. Ferulic and tannic acids were the most effective at improving color stability of 5-hydroxylated pigments, whereas tannic acid and rutin improved the stability of 5-methoxylated pigments the most. Substitution at C-5 was key to overall behavior of the 3-deoxyanthocyanidins.
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El Hajji, H.; Dangles, O.; Figueiredo, P.; Brouillard, R. 3′-(β-D-Glycopyranosyloxy) Flavylium Ions: Synthesis and Investigation of Their Properties in Aqueous Solution. Hydrogen Bonding as a Mean of Colour Variation Helv. Chim. Acta 1997, 80 (2) 398– 413 DOI: 10.1002/hlca.19970800206
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Limón, P. M.; Gavara, R.; Pina, F. Thermodynamics and Kinetics of Cyanidin 3-Glucoside and Caffeine Copigments J. Agric. Food Chem. 2013, 61 (22) 5245– 5251 DOI: 10.1021/jf4006643
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Melo, M. J.; Moncada, M. C.; Pina, F. On the Red Colour of Raspberry (Rubus Idaeus) Tetrahedron Lett. 2000, 41 (12) 1987– 1991 DOI: 10.1016/S0040-4039(00)00080-0
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Gierschner, J.; Lüer, L.; Milián-Medina, B.; Oelkrug, D.; Egelhaaf, H.-J. Highly Emissive H-Aggregates or Aggregation-Induced Emission Quenching? The Photophysics of All-Trans Para-Distyrylbenzene J. Phys. Chem. Lett. 2013, 4 (16) 2686– 2697 DOI: 10.1021/jz400985t
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Highly Emissive H-Aggregates or Aggregation-Induced Emission Quenching? The Photophysics of All-Trans para-Distyrylbenzene
Gierschner, Johannes; Luer, Larry; Milian-Medina, Begona; Oelkrug, Dieter; Egelhaaf, Hans-Joachim
Journal of Physical Chemistry Letters (2013), 4 (16), 2686-2697CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The present Perspective critically reexamines the photophysics of para-distyrylbenzene (DSB) as a prototype of herringbone-arranged H-aggregates to resolve the apparent contradiction of the frequently reported aggregation-induced emission quenching in H-aggregates on one side and highly emissive DSB crystals on the other and discusses the signatures and fate of excitons in single- and polycryst. samples, including size and polarization effects.
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Gierschner, J.; Park, S. Y. Luminescent Distyrylbenzenes: Tailoring Molecular Structure and Crystalline Morphology J. Mater. Chem. C 2013, 1 (37) 5818– 5832 DOI: 10.1039/c3tc31062k
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Luminescent distyrylbenzenes: tailoring molecular structure and crystalline morphology
Gierschner, Johannes; Park, Soo Young
Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2013), 1 (37), 5818-5832CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
A review. The last few years have seen a steady increase in small mol. based conjugated materials, which promise innovative (opto)electronic applications. This requires however a systematic understanding of structure-property relationships, which can only be achieved via libraries of structurally well-defined single cryst. materials based on systematically designed mol. structures. In this feature article, we are presenting structure-property relationships of functionalized distyrylbenzene (DSB), which is one of the most extensively investigated π-conjugated mol. materials. This will provide a general insight into the specific implications of intermol. arrangements on their solid state optoelectronic properties, discussing H- vs. J-aggregation, herringbone vs. π-stacks, the occurrence of excimers, size effects, and polycrystallinity. The systematic insight into DSB functionalization will then suggest pathways towards targeted mol. design strategies, with special focus on the cyano-vinylene motif (DCS materials) which allows for highly fluorescence solid state samples due to synergetic packing effects promoted by its twist elasticity and secondary bonding interaction. Finally, recent advances in the application of DSB-/DCS-based materials are shortly reviewed.
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Gonnet, J.-F. Colour Effects of Co-Pigmentation of Anthocyanins revisited—1. A Colorimetric Definition Using the CIELAB Scale Food Chem. 1998, 63 (3) 409– 415 DOI: 10.1016/S0308-8146(98)00053-3
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Gordillo, B.; Rodríguez-Pulido, F. J.; Escudero-Gilete, M. L.; González-Miret, M. L.; Heredia, F. J. Comprehensive Colorimetric Study of Anthocyanic Copigmentation in Model Solutions. Effects of pH and Molar Ratio J. Agric. Food Chem. 2012, 60 (11) 2896– 2905 DOI: 10.1021/jf2046202
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122
Comprehensive Colorimetric Study of Anthocyanic Copigmentation in Model Solutions. Effects of pH and Molar Ratio
Gordillo, Belen; Rodriguez-Pulido, Francisco J.; Escudero-Gilete, M. Luisa; Gonzalez-Miret, M. Lourdes; Heredia, Francisco J.
Journal of Agricultural and Food Chemistry (2012), 60 (11), 2896-2905CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
New colorimetric variables were defined in the uniform CIELAB color space to assess the quant. and qual. color changes induced by copigmentation and their incidence on visual perception. The copigmentation process was assayed in model solns. between malvidin 3-glucoside and 3 phenolic compds. (catechin, epicatechin, and caffeic acid) as a function of the pH and the pigment/copigment molar ratio. Along the pH variation, the greatest magnitude of copigmentation was obtained at pH 3.0, being significantly higher with epicatechin and caffeic acid. At high acidic pH, the main contribution of copigmentation to the total color was qual., whereas between pH 2.0 and 4.0, the main colorimetric contribution was quant. The contribution of epicatechin and caffeic acid to the color changes was more marked for the quant. characteristics. On contrast, particularly at higher pH values, the qual. contribution was more important in catechin copigmented solns. Increasing copigment concn. induced perceptible color changes at molar ratios higher than 1:2, consisting in a bluish and darkening effect of the anthocyanin solns. Among the different CIELAB attributes, hue difference was the best correlated parameter with the increase of copigment concn., proving the relevance of this physicochem. phenomenon on the qual. changes of anthocyanin color.
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Gonnet, J.-F. Colour Effects of Co-Pigmentation of Anthocyanins revisited—2.A Colorimetric Look at the Solutions of Cyanin Co-Pigmented Byrutin Using the CIELAB Scale Food Chem. 1999, 66 (3) 387– 394 DOI: 10.1016/S0308-8146(99)00088-6
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Xu, H.; Liu, X.; Yan, Q.; Yuan, F.; Gao, Y. A Novel Copigment of Quercetagetin for Stabilization of Grape Skin Anthocyanins Food Chem. 2015, 166, 50– 55 DOI: 10.1016/j.foodchem.2014.05.125
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A novel copigment of quercetagetin for stabilization of grape skin anthocyanins
Xu, Honggao; Liu, Xuan; Yan, Qiuli; Yuan, Fang; Gao, Yanxiang
Food Chemistry (2015), 166 (), 50-55CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
The thermal and light stability of grape skin anthocyanins combined with quercetagetin was investigated at designed pH values of 3, 4 and 5. The molar ratios of anthocyanins to quercetagetin were 1:10, 1:20 and 1:40 for thermally treatment at 70 °C, 80 °C and 90 °C, resp., and the ratios were tested at 5:1, 1:1, 1:5 and 1:10 in the light exposure expts. The degrdn. reaction of anthocyanins in the presence of quercetagetin followed the first-order kinetic model. The half-life (t1/2) of anthocyanins was extended significantly with the increase of quercetagetin concn. (p < 0.05). The total color difference values (ΔE*) for the anthocyanin solns. with quercetagetin were smaller than those without copigment under the same exptl. conditions (pH and light exposure time). Compared with epigallocatechin gallate (EGCG), tea polyphenols (TP), myricitrin and rutin, quercetagetin was the most effective copigment to stabilize grape skin anthocyanins.
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Shao, P.; Zhang, J.; Fang, Z.; Sun, P. Complexing of Chlorogenic Acid with B-Cyclodextrins: Inclusion Effects, Antioxidative Properties and Potential Application in Grape Juice Food Hydrocolloids 2014, 41, 132– 139 DOI: 10.1016/j.foodhyd.2014.04.003
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126
Mistry, T. V.; Cai, Y.; Lilley, T. H.; Haslam, E. Polyphenol Interactions. Part 5. Anthocyanin Co-Pigmentation J. Chem. Soc., Perkin Trans. 2 1991, 8) 1287– 1296 DOI: 10.1039/p29910001287
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Polyphenol interactions. Part 5. Anthocyanin copigmentation
Mistry, Tarankumar V.; Cai, Ya; Lilley, Terence H.; Haslam, Edwin
Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1972-1999) (1991), (8), 1287-96CODEN: JCPKBH; ISSN:0300-9580.
In aq. media, anthocyanins undergo several structural transformations and exist in a series of equil. between carbinol-base, flavylium cation, quinonoidal anhydro-base and chalcone forms. A detailed interpretation of the 1H-NMR (400 MHz) spectra of malvin in D2O is given for the first time in the context of these equil. The phenomenon of copigmentation is reviewed and the efficacy of various phenolic flavonoids, galloyl and hexahydroxycinnamyl esters as natural copigments is detd. quant. DNA, RNA and ATP also act as effective copigments for malvin in the form the flavylium ion but both caffeine and theophylline preferentially stabilize the quinonoidal-base forms of the anthocyanin. At pH 3.5 to 7.0, they give rise to stable violet through to blue and finally green colors. 1H-NMR studies of all these intermol. copigmentation reactions are reported and the phenomenon is provisionally interpreted in terms of hydrophobically reinforced π-π stacking of anthocyanin and copigment mols. in the aq. environment.
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Son, T.-D.; Chachaty, C. Nucleoside Conformations: XIV. Conformation of Adenosine Monophosphates in Aqueous Solution by Proton Magnetic Resonance Spectroscopy Biochim. Biophys. Acta, Nucleic Acids Protein Synth. 1974, 335 (1) 1– 13 DOI: 10.1016/0005-2787(74)90234-2
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128
Leydet, Y.; Gavara, R.; Petrov, V.; Diniz, A. M.; Jorge Parola, A.; Lima, J. C.; Pina, F. The Effect of Self-Aggregation on the Determination of the Kinetic and Thermodynamic Constants of the Network of Chemical Reactions in 3-Glucoside Anthocyanins Phytochemistry 2012, 83, 125– 135 DOI: 10.1016/j.phytochem.2012.06.022
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The effect of self-aggregation on the determination of the kinetic and thermodynamic constants of the network of chemical reactions in 3-glucoside anthocyanins
Leydet, Yoann; Gavara, Raquel; Petrov, Vesselin; Diniz, Ana M.; Parola, A. Jorge; Lima, Joao C.; Pina, Fernando
Phytochemistry (Elsevier) (2012), 83 (), 125-135CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Ltd.)
The six most common 3-glucoside anthocyanins, pelargonidin-3-glucoside, peonidin-3-glucoside, delphinidin-3-glucoside, malvidin-3-glucoside, cyanidin-3-glucoside and petunidin-3-glucoside were studied in great detail by NMR, UV-vis absorption and stopped flow. For each anthocyanin, the thermodn. and kinetic consts. of the network of chem. reactions were calcd. at different anthocyanin concn., from 6 × 10-6 M up to 8 × 10-4 M; an increasing of the flavylium cation acidity const. to give quinoidal base and a decreasing of the flavylium cation hydration const. to give hemiketal were obsd. by increasing the anthocyanin concn. These effects are attributed to the self-aggregation of the flavylium cation and quinoidal base, which is stronger in the last case. The UV-vis and 1H NMR spectral variations resulting from the increasing of the anthocyanin concn. were discussed in terms of two aggregation models; monomer-dimer and isodesmic, the last one considering the formation of higher order aggregates possessing the same aggregation const. of the dimer. The self-aggregation const. of flavylium cation at pH = 1.0, calcd. by both models increases by increasing the no. of methoxy (-OCH3) or hydroxy (-OH) substituents following the order: myrtillin (2 -OH), oenin (2 -OCH3), 3-OGl-petunidin (1 -OH, 1 -OCH3), kuromanin (1 -OH), 3-OGl-peonidin (1 -OCH3) and callistephin (none). Evidence for flavylium aggregates possessing a shape between J and H was achieved, as well as for the formation of higher order aggregates.
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Dimicoli, J. L.; Hélène, C. Complex Formation between Purine and Indole Derivatives in Aqueous Solutions. Proton Magnetic Resonance Studies J. Am. Chem. Soc. 1973, 95 (4) 1036– 1044 DOI: 10.1021/ja00785a008
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130
Alluis, B.; Pérol, N.; El Hajji, H.; Dangles, O. Water-Soluble Flavonol (=3Hydroxy2-Phenyl-4H-1-Benzopyran-4-One) Derivatives: Chemical Synthesis, Colouring, and Antioxidant Properties Helv. Chim. Acta 2000, 83 (2) 428– 443 DOI: 10.1002/(SICI)1522-2675(20000216)83:2<428::AID-HLCA428>3.3.CO;2-A
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131
Hondo, T.; Yoshida, K.; Nakagawa, A.; Kawai, T.; Tamura, H.; Goto, T. Structural Basis of Blue-Colour Development in Flower Petals from Commelina Communis Nature 1992, 358 (6386) 515– 518 DOI: 10.1038/358515a0
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Shiono, M.; Matsugaki, N.; Takeda, K. Phytochemistry: Structure of the Blue Cornflower Pigment Nature 2005, 436 (7052) 791– 791 DOI: 10.1038/436791a
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133
Dufour, C.; Sauvaitre, I. Interactions between Anthocyanins and Aroma Substances in a Model System. Effect on the Flavor of Grape-Derived Beverages J. Agric. Food Chem. 2000, 48 (5) 1784– 1788 DOI: 10.1021/jf990877l
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133
Interactions between anthocyanins and aroma substances in a model system. Effect on the flavor of grape-derived beverages
Dufour, Claire; Sauvaitre, Isabelle
Journal of Agricultural and Food Chemistry (2000), 48 (5), 1784-1788CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
Evaluation of the sensory quality of wine or grape-derived beverages led the authors to study the interactions between flavors and anthocyanins, the colored family of polyphenols. The flavylium cation-ligand complexation, resulting in copigmentation (rise in pigment visible absorption with a concomitant bathochromic shift), was investigated using visible absorption spectroscopy. Sole volatile phenols were found to markedly interact with malvidin-3,5-O-diglucoside. With series of guaiacyl-derived aroma substances, acyl-substituted ligands proved to be better copigments than alkyl-substituted ones. Assocn. consts. and 1:1 complex stoichiometry were further detd. for several substrates. Decreasing binding to malvin was obsd. for acetosyringone, syringaldehyde, acetovanillone, vanillin, 3,5-dimethoxyphenol, and 4-ethylguaiacol. Addn. of 10% ethanol lowered by one-third the assocn. consts. for malvin-ligand couples and for malvidin-3-O-glucoside with acetosyringone and syringaldehyde. The main driving force was ascribed to hydrophobicity, although this study evidenced an influence of the ligand substitution pattern on copigmentation.
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Tuominen, A.; Sinkkonen, J.; Karonen, M.; Salminen, J.-P. Sylvatiins, Acetylglucosylated Hydrolysable Tannins from the Petals of Geranium Sylvaticum Show Co-Pigment Effect Phytochemistry 2015, 115, 239– 251 DOI: 10.1016/j.phytochem.2015.01.005
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Sylvatiins, acetylglucosylated hydrolysable tannins from the petals of Geranium sylvaticum show co-pigment effect
Tuominen, Anu; Sinkkonen, Jari; Karonen, Maarit; Salminen, Juha-Pekka
Phytochemistry (Elsevier) (2015), 115 (), 239-251CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Ltd.)
Four hydrolysable tannins, named as sylvatiins A (1), B (2), C (3) and D (4), were isolated from the petals of Geranium sylvaticum. On the basis of spectrometric evidence of NMR anal. (1H NMR, 13C NMR, DQF-COSY, TOCSY, NOESY, HSQC and HMBC), CD and ESI-MS/MS, sylvatiins A, B and C were characterized as galloyl glucoses contg. one or two acetylglucoses attached to the 3-OH of the galloyl group, whereas sylvatiin D was found to have a chebulinic acid core contg. acetylglucose attached in a similar way. The potential of these compds. to act as defensive compds. against herbivores was evaluated using the radial diffusion assay that measures the protein pptn. capacity. In addn., the capacity of sylvatiins to act as co-pigments with anthocyanins of G. sylvaticum petals was measured in vitro at different pH values. Sylvatiins A and D maintained efficiently the purple flower color near the natural pH of petal cells. The amt. of sylvatiins was changed according to the flower color; deep purple petals with higher amt. of anthocyanin contained more sylvatiins A and C than whiter petals. It was concluded that G. sylvaticum petal cells may accumulate sylvatiins for intermol. co-pigmentation purposes.
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Dangles, O.; Saito, N.; Brouillard, R. Kinetic and Thermodynamic Control of Flavylium Hydration in the Pelargonidin-Cinnamic Acid Complexation. Origin of the Extraordinary Flower Color Diversity of Pharbitis Nil J. Am. Chem. Soc. 1993, 115 (8) 3125– 3132 DOI: 10.1021/ja00061a011
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Eiro, M. J.; Heinonen, M. Anthocyanin Color Behavior and Stability during Storage: Effect of Intermolecular Copigmentation J. Agric. Food Chem. 2002, 50 (25) 7461– 7466 DOI: 10.1021/jf0258306
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Anthocyanin Color Behavior and Stability during Storage: Effect of Intermolecular Copigmentation
Eiro, Maarit J.; Heinonen, Marina
Journal of Agricultural and Food Chemistry (2002), 50 (25), 7461-7466CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
Intermol. copigmentation reactions are significantly responsible for the manifold color expression of fruits, berries, and their products. These reactions were investigated with 5 anthocyanins and 5 phenolic acids acting as copigments. The stability of the pigment-copigment complexes formed was studied during a storage period of 6 mo. The study was conducted using a UV-visible spectrophotometer to monitor the hyperchromic effect and the bathochromic shift of the complexes. The greatest copigmentation reactions took place in malvidin 3-glucoside solns. The strongest copigments for all anthocyanins were ferulic and rosmarinic acids. The immediate reaction of rosmarinic acid with malvidin 3-glucoside resulted in the biggest bathochromic shift (19 nm) and the strongest hyperchromic effect, increasing the color intensity by 260%. The color induced by rosmarinic acid was not very stable. The color intensity of pelargonidin 3-glucoside increased greatly throughout the storage period with the addn. of ferulic and caffeic acids.
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Houbiers, C.; Lima, J. C.; Maçanita, A. L.; Santos, H. Color Stabilization of Malvidin 3-Glucoside: Self-Aggregation of the Flavylium Cation and Copigmentation with the Z-Chalcone Form J. Phys. Chem. B 1998, 102 (18) 3578– 3585 DOI: 10.1021/jp972320j
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138
Elhabiri, M.; Figueiredo, P.; Toki, K.; Figueiredo, P.; Toki, K.; Saito, N.; Brouillard, R.; Figueiredo, P.; Toki, K. Anthocyanin–aluminium and – gallium Complexes in Aqueoussolution J. Chem. Soc., Perkin Trans. 2 1997, 2) 355– 362 DOI: 10.1039/a603851d
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Anthocyanin-aluminum and -gallium complexes in aqueous solution
Elhabiri, M.; Figueiredo, P.; Toki, K.; Saito, N.; Brouillard, R.
Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1997), (2), 355-362CODEN: JCPKBH; ISSN:0300-9580. (Royal Society of Chemistry)
Complexation of aluminum and gallium ions with synthetic anthocyanin models and natural anthocyanins extd. from the blue flowers of Evolvulus pilosus cv 'Blue Daze' and the violet flowers of Matthiola incana has been thoroughly investigated in aq. soln. From UV-VIS spectroscopic data collected at pH 2-5, the presence of complexes, involving not only the colored forms but also the colorless forms of the pigments is demonstrated. A theor. treatment is developed for the calcn. of the corresponding stability consts. The pigments studied throughout this work can be divided into two series, one sharing a cyanidin chromophore and the other a delphinidin one. Within both series, individual pigments are distinguished according to the degree and type of glycosidation and/or acylation. Intramol. effects such as copigmentation of anthocyanin-aluminum complexes and the effect of the presence of a malonyl group on the formation of those complexes are discussed. These results are important to plant pigmentation and, for instance, a narrow pH domain in which color amplification due to complexation is at a max. has been found.
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Al Bittar, S.; Mora, N.; Loonis, M.; Dangles, O. Chemically Synthesized Glycosides of Hydroxylated Flavylium Ions as Suitable Models of Anthocyanins: Binding to Iron Ions and Human Serum Albumin, Antioxidant Activity in Model Gastric Conditions Molecules 2014, 19 (12) 20709– 20730 DOI: 10.3390/molecules191220709
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Kasha, M.; Rawls, H. R.; Ashraf El-Bayoumi, M. The Exciton Model in Molecular Spectroscopy Pure Appl. Chem. 1965, 11 (3–4) 371– 392 DOI: 10.1351/pac196511030371
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Exciton model in molecular spectroscopy
Kasha, Michael; Rawls, Henry R.; El-Bayoumi, M. Ashraf
Pure and Applied Chemistry (1965), 11 (3-4), 371-92CODEN: PACHAS; ISSN:0033-4545.
A summary is presented of the application of the mol. exciton model to dimers, trimers, and double and triple mols. In those cases where no significant exciton effect is observable in the singlet-singlet absorption spectrum for the composite mol., the enhancement of lowest triplet state excitation may still be conspicuous and significant.
141
Yoshida, K.; Toyama, Y.; Kameda, K.; Kondo, T. Contribution of Each Caffeoyl Residue of the Pigment Molecule of Gentiodelphin to Blue Color Development Phytochemistry 2000, 54 (1) 85– 92 DOI: 10.1016/S0031-9422(00)00049-2
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Yoshida, K.; Kondo, T.; Goto, T. Intramolecular Stacking Conformation of Gentiodelphin, a Diacylated Anthocyanin from Gentiana Makinoi Tetrahedron 1992, 48 (21) 4313– 4326 DOI: 10.1016/S0040-4020(01)80442-7
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Nerdal, W.; Andersen, Ø. M. Evidence for Self-Association of the Anthocyanin Petanin in Acidified, Methanolic Solution Using Two-Dimensional Nuclear Overhauser Enhancement NMR Experiments and Distance Geometry Calculations Phytochem. Anal. 1991, 2 (6) 263– 270 DOI: 10.1002/pca.2800020606
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Evidence for self-association of the anthocyanin petanin in acidified, methanolic solution using two-dimensional nuclear Overhauser enhancement NMR experiments and distance geometry calculations
Nerdal, Willy; Andersen, Oeyvind M.
Phytochemical Analysis (1991), 2 (6), 263-70CODEN: PHANEL; ISSN:0958-0344.
A new mechanism is described for self-assocn. of anthocyanins in soln. Petanin [petunidin 3-O-[6-O-(4-O-E-p-coumaroyl-α-L-rhamnopyranosyl)-β-D-glucopyranoside]-5-O-β-D-glucopuranoside] was studied in acidified methanolic soln. using the nuclear Overhauser enhancement (NOESY) NMR technique. Intra- and inter-mol. NOESY cross-peaks were obsd., and the corresponding proton-proton distance bounds were used in distance geometry calcns. to det. the stacking of the petanin aglycons. The orientation of two self-assocd. petanin aglycons was found to be head-to-tail along both the long and the short aglycon axis. Lack of obsd. NOESY cross-peaks between protons of the coumaroyl group and the aglycon indicated absence of intramol. stacking of the stable petanin mols. Non-coplanarity between the planes of the benzopyrylium and the Ph rings was also indicated.
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Nerdal, W.; Andersen, Ø. M. Intermolecular Aromatic Acid Association of an Anthocyanin (petanin) Evidenced by Two-Dimensional Nuclear Overhauser Enhancement Nuclear Magnetic Resonance Experiments and Distance Geometry Calculations Phytochem. Anal. 1992, 3 (4) 182– 189 DOI: 10.1002/pca.2800030408
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144
Intermolecular aromatic acid association of an anthocyanin (petanin) evidence by two-dimensional nuclear Overhauser enhancement nuclear magnetic resonance experiments and distance geometry calculations
Nerdal, Willy; Andersen, Oeyvind M.
Phytochemical Analysis (1992), 3 (4), 182-9CODEN: PHANEL; ISSN:0958-0344.
A new mechanism for the mol. assocn. of the arom acid of an anthocyanin using two-dimensional 1H NOESY expts., is described.
145
Yoshida, K.; Kondo, T.; Goto, T. Unusually Stable Monoacylated Anthocyanin from Purple Yam Dioscorea Alata Tetrahedron Lett. 1991, 32 (40) 5579– 5580 DOI: 10.1016/0040-4039(91)80088-N
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Mori, M.; Miki, N.; Ito, D.; Kondo, T.; Yoshida, K. Structure of Tecophilin, a Tri-Caffeoylanthocyanin from the Blue Petals of Tecophilaea Cyanocrocus, and the Mechanism of Blue Color Development Tetrahedron 2014, 70 (45) 8657– 8664 DOI: 10.1016/j.tet.2014.09.046
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Structure of tecophilin, a tri-caffeoylanthocyanin from the blue petals of Tecophilaea cyanocrocus, and the mechanism of blue color development
Mori, Mihoko; Miki, Naoko; Ito, Daisuke; Kondo, Tadao; Yoshida, Kumi
Tetrahedron (2014), 70 (45), 8657-8664CODEN: TETRAB; ISSN:0040-4020. (Elsevier Ltd.)
The pigment, tecophilin, in blue flowers of Tecophilaea cyanocrocus was isolated and the structure was detd. to be 3-O-(6-O-α-L-rhamnopyranosyl-β-D-glucopyranosyl)-7-O-(6-O-(4-O-(2-O-(4-O-β-D-glucopyranosyl-(E)-caffeoyl)-6-O-(4-O-β-D-glucopyranosyl-(E)-caffeoyl)-β-D-glucopyranosyl)-(E)-caffeoyl)-β-D-glucopyranosyl)delphinidin. The reprodn. expt. of the same color as petals according to the results of chem. anal. and measurement of vacuolar pH of blue cells clarified that the blue color solely develops by tecophilin without interaction of metal ions nor co-pigments. 1H NMR anal. and CD spectrum indicate the co-existence of clockwise intermol. self-assocn. of the delphinidin nuclei and intramol. π-π stacking between the chromophore and caffeoyl residues to derive bathochromic shift of the absorption spectrum and stabilize the color by preventing hydration reaction.
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Terahara, N.; Callebaut, A.; Ohba, R.; Nagata, T.; Ohnishi-Kameyama, M.; Suzuki, M. Triacylated Anthocyanins from Ajuga Reptans Flowers and Cell Cultures Phytochemistry 1996, 42 (1) 199– 203 DOI: 10.1016/0031-9422(95)00838-1
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Terahara, N.; Toki, K.; Saito, N.; Honda, T.; Matsui, T.; Osajima, Y. Eight New Anthocyanins, Ternatins C1-C5 and D3 and Preternatins A3 and C4 from Young Clitoria Ternatea Flowers J. Nat. Prod. 1998, 61 (11) 1361– 1367 DOI: 10.1021/np980160c
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Escribano-Bailón, T.; Dangles, O.; Brouillard, R. Coupling Reactions between Flavylium Ions and Catechin Phytochemistry 1996, 41 (6) 1583– 1592 DOI: 10.1016/0031-9422(95)00811-X
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Coupling reactions between flavylium ions and catechin
Escribano-Bailon, Teresa; Dangles, Olivier; Brouillard, Raymond
Phytochemistry (1996), 41 (6), 1583-92CODEN: PYTCAS; ISSN:0031-9422. (Elsevier)
In order to model natural polymeric pigments present in old red wines, new covalent adducts have been synthesized upon condensation of synthetic flavylium ions (models of anthocyanins) with catechin (model of tannins) in the presence and in the absence of acetaldehyde. These new pigments have been investigated by 1D and 2D NMR, HPLC, FAB-mass and UV-visible spectroscopies and mol. modeling. The two flavylium salts used in this work (3,4'-dimethoxy-7-hydroxyflavylium chloride and 5,7-dihydroxy-3,4'-dimethoxyflavylium chloride) display quite different reactivities toward catechin. The electronic donating effect of the catechin moiety and the formation of noncovalent dimers in acidic aq. or methanolic soln. should be mainly responsible for the improved stability of the flavylium chromophore in the new pigments.
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Dueñas, M.; Fulcrand, H.; Cheynier, V. Formation of Anthocyanin–flavanol Adducts in Model Solutions Anal. Chim. Acta 2006, 563 (1–2) 15– 25 DOI: 10.1016/j.aca.2005.10.062
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151
Dueñas, M.; Salas, E.; Cheynier, V.; Dangles, O.; Fulcrand, H. UV–Visible Spectroscopic Investigation of the 8,8-Methylmethine Catechin-Malvidin 3-Glucoside Pigments in Aqueous Solution: Structural Transformations and Molecular Complexation with Chlorogenic Acid J. Agric. Food Chem. 2006, 54 (1) 189– 196 DOI: 10.1021/jf0516989
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Chassaing, S.; Lefeuvre, D.; Jacquet, R.; Jourdes, M.; Ducasse, L.; Galland, S.; Grelard, A.; Saucier, C.; Teissedre, P.-L.; Dangles, O. Physicochemical Studies of New Anthocyano-Ellagitannin Hybrid Pigments: About the Origin of the Influence of Oak C-Glycosidic Ellagitannins on Wine Color Eur. J. Org. Chem. 2010, 2010 (1) 55– 63 DOI: 10.1002/ejoc.200901133
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Bloor, S. J. Overview of Methods for Analysis and Identification of Flavonoids Methods Enzymol. 2001, 335, 3– 14 DOI: 10.1016/S0076-6879(01)35227-8
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Dangles, O.; Saito, N.; Brouillard, R. Anthocyanin Intramolecular Copigment Effect Phytochemistry 1993, 34 (1) 119– 124 DOI: 10.1016/S0031-9422(00)90792-1
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Figueiredo, P.; George, F.; Tatsuzawa, F.; Toki, K.; Saito, N.; Brouillard, R. New Features of Intramolecular Copigmentation by Acylated Anthocyanins Phytochemistry 1999, 51, 125– 132 DOI: 10.1016/S0031-9422(98)00685-2
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New features of intramolecular copigmentation by acylated anthocyanins
Figueiredo, Paulo; George, Florian; Tatsuzawa, Fumi; Toki, Kenjiro; Saito, Norio; Brouillard, Raymond
Phytochemistry (1999), 51 (1), 125-132CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Science Ltd.)
Three series of structurally related anthocyanins, extd. from the red-purple flowers of Dendrobium "Pramot", xLaeliocattleya cv. Mini Purple, Bletilla striata and Phalaenopsis all belonging to the Orchidaceae family and another series extd. from the pink flowers of Senecio cruentus (Compositae) allowed the confirmation of the existence of strong intramol. copigmentation effects. These interactions confer stability to the colored forms of the mols., in a wide range of slightly acidic to neutral aq. media. Moreover, the existence of structural relationships among the four series stressed the different influences exerted by the diverse substituent groups. The existence of a malonylglucoside attached to position 3 of all but three of the mols. put forward a new role for the malonyl residue, in this particular position.
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Fleschhut, J.; Kratzer, F.; Rechkemmer, G.; Kulling, S. E. Stability and Biotransformation of Various Dietary Anthocyanins in Vitro Eur. J. Nutr. 2006, 45 (1) 7– 18 DOI: 10.1007/s00394-005-0557-8
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Stability and biotransformation of various dietary anthocyanins in vitro
Fleschhut, Jens; Kratzer, Frank; Rechkemmer, Gerhard; Kulling, Sabine E.
European Journal of Nutrition (2006), 45 (1), 7-18CODEN: EJNUFZ; ISSN:1436-6207. (Steinkopff Verlag)
Background Anthocyanins, which are found in high concns. in fruit and vegetable, may play a beneficial role in retarding or reversing the course of chronic degenerative diseases. However, little is known about the biotransformation and the metab. of anthocyanins so far. Aim of the study The aim of the study was to investigate possible transformation pathways of anthocyanins by human fecal microflora and by rat liver microsomes as a source of cytochrome P 450 enzymes as well as of glucuronyltransferases. Methods Pure anthocyanins, an aq. ext. of red radish as well as the assumed degrdn. products were incubated with human fecal suspension. The incubation mixts. were purified by solid-phase extn. and analyzed by HPLC/DAD/MS and GC/MS. Quantification was done by the external std. method. Furthermore the biotransformation of anthocyanins by incubation with rat liver microsomes in the presence of the cofactor NADPH (as a model for the phase I oxidn.) and in the presence of activated glucuronic acid (as a model for the phase II glucuronidation) was investigated. Results Glycosylated and acylated anthocyanins were rapidly degraded by the intestinal microflora after anaerobic incubation with a human fecal suspension. The major stable products of anthocyanin degrdn. are the corresponding phenolic acids derived from the B-ring of the anthocyanin skeleton. Anthocyanins were not metabolized by cytochrome P 450 enzymes, neither hydroxylated nor demethylated. However they were glucuronidated by rat liver microsomes to several products. Conclusions The gut microflora seem to play an important role in the biotransformation of anthocyanins. A rapid degrdn. could be one major reason for the poor bioavailability of anthocyanins in pharmacokinetic studies described so far in the literature. The formation of phenolic acids as the major stable degrdn. products gives an important hint to the fate of anthocyanins in vivo.
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Lopes, P.; Richard, T.; Saucier, C.; Teissedre, P.-L.; Monti, J.-P.; Glories, Y. Anthocyanone A: A Quinone Methide Derivative Resulting from Malvidin 3- O -Glucoside Degradation J. Agric. Food Chem. 2007, 55 (7) 2698– 2704 DOI: 10.1021/jf062875o
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Sadilova, E.; Carle, R.; Stintzing, F. C. Thermal Degradation of Anthocyanins and Its Impact on Color Andin Vitro Antioxidant Capacity Mol. Nutr. Food Res. 2007, 51 (12) 1461– 1471 DOI: 10.1002/mnfr.200700179
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Thermal degradation of anthocyanins and its impact on color and in vitro antioxidant capacity
Sadilova, Eva; Carle, Reinhold; Stintzing, Florian C.
Molecular Nutrition & Food Research (2007), 51 (12), 1461-1471CODEN: MNFRCV; ISSN:1613-4125. (Wiley-VCH Verlag GmbH & Co. KGaA)
The aim of the current study was to thoroughly investigate the structural changes of anthocyanins at pH 3.5 in purified fractions from black carrot, elderberry and strawberry heated over 6 h at 95°C. Degrdn. products were monitored by HPLC-DAD-MS3 to elucidate the prevailing degrdn. pathways. In addn., alterations of color and antioxidant properties obsd. upon heating were scrutinized. Most interestingly, the degrdn. pathways at pH 3.5 were found to differ from those at pH 1. Among others, chalcone glycosides were detected at 320 nm in heat-treated elderberry and strawberry pigment isolates, and opening of the pyrylium ring initiated anthocyanin degrdn. In the case of acylated anthocyanins, acyl-glycoside moieties were split off from the flavylium backbone, first. Finally, for all pigment isolates, phenolic acids and phloroglucinaldehyde were the terminal degrdn. products as remainders of the B- and A-ring, resp. Maximum and min. antioxidant stabilizing capacities were found in black carrot and strawberry, resp., which was explained by the high degree of acylation in the former. After heating, decline of trolox equiv. antioxidant capacity (TEAC) was obsd. in all samples, which was attributed to both anthocyanins and their colorless degrdn. products following thermal exposure. As deduced from the ratio of TEAC value and anthocyanin content, the loss of anthocyanin bioactivity could not be compensated by the antioxidant capacity of newly formed colorless phenolics upon heating.
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Yang, J.; Hu, W.; Usvyat, D.; Matthews, D.; Schütz, M.; Chan, G. K.-L. Ab Initio Determination of the Crystalline Benzene Lattice Energy to Sub-Kilojoule/mol Accuracy Science 2014, 345 (6197) 640– 643 DOI: 10.1126/science.1254419
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Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy
Yang, Jun; Hu, Weifeng; Usvyat, Denis; Matthews, Devin; Schuetz, Martin; Chan, Garnet Kin-Lic
Science (Washington, DC, United States) (2014), 345 (6197), 640-643CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
Computation of lattice energies to an accuracy sufficient to distinguish polymorphs is a fundamental bottleneck in crystal structure prediction. For the lattice energy of the prototypical benzene crystal, we combined the quantum chem. advances of the last decade to attain sub-kilojoule per mol accuracy, an order-of-magnitude improvement in certainty over prior calcns. that necessitates revision of the exptl. extrapolation to 0 K. Our computations reveal the nature of binding by improving on previously inaccessible or inaccurate multibody and many-electron contributions and provide revised ests. of the effects of temp., vibrations, and relaxation. Our demonstration raises prospects for definitive first-principles resoln. of competing polymorphs in mol. crystal structure prediction.
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Cavalcanti, R. N.; Santos, D. T.; Meireles, M. A. A. Non-Thermal Stabilization Mechanisms of Anthocyanins in Model and Food systems—An Overview Food Res. Int. 2011, 44 (2) 499– 509 DOI: 10.1016/j.foodres.2010.12.007
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Non-thermal stabilization mechanisms of anthocyanins in model and food systems-An overview
Cavalcanti, Rodrigo N.; Santos, Diego T.; Meireles, Maria Angela A.
Food Research International (2011), 44 (2), 499-509CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
A review. Phenolic compds. are part of the secondary metab. of plants and are of great importance for their survival in unfavorable environment. A class of phenolic compds. easily found in the Plant Kingdom, is anthocyanins, a flavonoid category. They are water-sol. pigments that confer the bright red, blue, and purple colors of fruits and vegetables and promote several health benefits due to their diverse biol. activities. Different factors affect the color and stability of these compds. including pH, temp., light, presence of copigments, self-assocn., metallic ions, enzymes, oxygen, ascorbic acid, sugar, among others. For this reason many studies have been conducted with the aim to increase the stability of these substances. Therefore, the present review highlights studies on the stabilization of anthocyanins and presents latent anthocyanin stabilization mechanisms and demonstrates the potentiality of the main techniques used: assocn. and encapsulation.
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Rodrigues, R. F.; Ferreira da Silva, P.; Shimizu, K.; Freitas, A. A.; Kovalenko, S. A.; Ernsting, N. P.; Quina, F. H.; Maçanita, A. Ultrafast Internal Conversion in a Model Anthocyanin-Polyphenol Complex: Implications for the Biological Role of Anthocyanins in Vegetative Tissues of Plants Chem. - Eur. J. 2009, 15 (6) 1397– 1402 DOI: 10.1002/chem.200801207
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Ultrafast internal conversion in a model anthocyanin-polyphenol complex: implications for the biological role of anthocyanins in vegetative tissues of plants
Rodrigues, Rita Franca; Ferreira da Silva, Palmira; Shimizu, Karina; Freitas, Adilson A.; Kovalenko, Sergey A.; Ernsting, Nikolaus P.; Quina, Frank H.; Macanita, Antonio
Chemistry - A European Journal (2009), 15 (6), 1397-1402CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
The red flavylium cations of anthocyanins form ground-state charge-transfer complexes with several naturally occurring electron-donor copigments, such as hydroxylated flavones and hydroxycinnamic or benzoic acids. Excitation of the 7-methoxy-4-methyl-flavylium-protocatechuic acid complex results in ultrafast (240 fs) internal conversion to the ground state of the complex by way of a low-lying charge-transfer state. Thus, both uncomplexed anthocyanins, whose excited state decays by fast (5-20 ps) excited-state proton transfer, and anthocyanin-copigment complexes have highly efficient mechanisms of deactivation that are consistent with the proposed protective role of anthocyanins against excess solar radiation in the vegetative tissues of plants.
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Ferreira da Silva, P.; Paulo, L.; Barbafina, A.; Elisei, F.; Quina, F. H.; Maçanita, A. L. Photoprotection and the Photophysics of Acylated Anthocyanins Chem. - Eur. J. 2012, 18 (12) 3736– 3744 DOI: 10.1002/chem.201102247
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Photoprotection and the Photophysics of Acylated Anthocyanins
Ferreira da Silva, Palmira; Paulo, Luisa; Barbafina, Adrianna; Eisei, Fausto; Quina, Frank H.; Macanita, Antonio L.
Chemistry - A European Journal (2012), 18 (12), 3736-3744CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
The proposed role of anthocyanins in protecting plants against excess solar radiation is consistent with the occurrence of ultrafast (5-25 ps) excited-state proton transfer as the major deexcitation pathway of these mols. However, because natural anthocyanins absorb mainly in the visible region of the spectra, with only a narrow absorption band in the UV-B region, this highly efficient deactivation mechanism would essentially only protect the plant from visible light. On the other hand, ground-state charge-transfer complexes of anthocyanins with naturally occurring electron-donor copigments, such as hydroxylated flavones, flavonoids, and hydroxycinnamic or benzoic acids, do exhibit high UV-B absorptivities that complement that of the anthocyanins. In this work, we report a comparative study of the photophysics of the naturally occurring anthocyanin cyanin, intermol. cyanin-coumaric acid complexes, and an acylated anthocyanin, i.e., cyanin with a pendant coumaric ester copigment. Both inter- and intramol. anthocyanin-copigment complexes are shown to have ultrafast energy dissipation pathways comparable to those of model flavylium cation-copigment complexes. However, from the standpoint of photoprotection, the results indicate that the covalent attachment of copigment mols. to the anthocyanin represents a much more efficient strategy by providing the plant with significant UV-B absorption capacity and at the same time coupling this absorption to efficient energy dissipation pathways (ultrafast internal conversion of the complexed form and fast energy transfer from the excited copigment to the anthocyanin followed by adiabatic proton transfer) that avoid net photochem. damage.
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Song, B. J.; Sapper, T. N.; Burtch, C. E.; Brimmer, K.; Goldschmidt, M.; Ferruzzi, M. G. Photo- and Thermodegradation of Anthocyanins from Grape and Purple Sweet Potato in Model Beverage Systems J. Agric. Food Chem. 2013, 61 (6) 1364– 1372 DOI: 10.1021/jf3044007
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Malien-Aubert, C.; Dangles, O.; Amiot, M. J. Color Stability of Commercial Anthocyanin-Based Extracts in Relation to the Phenolic Composition. Protective Effects by Intra- and Intermolecular Copigmentation J. Agric. Food Chem. 2001, 49 (1) 170– 176 DOI: 10.1021/jf000791o
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There is no corresponding record for this reference.
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Cabrita, L.; Petrov, V.; Pina, F. On the Thermal Degradation of Anthocyanidins: Cyanidin RSC Adv. 2014, 4 (36) 18939 DOI: 10.1039/c3ra47809b
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On the thermal degradation of anthocyanidins: cyanidin
Cabrita, Luis; Petrov, Vesselin; Pina, Fernando
RSC Advances (2014), 4 (36), 18939-18944CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
Cyanidin was studied by direct pH jumps (from equilibrated solns. at very low pH values to higher pH values) and reverse pH jumps (from equilibrated or not equilibrated solns. at higher pH values to very low ones). The kinetic steps of the direct and reverse pH jumps were followed by stopped flow, absorption spectroscopy and HPLC, at different timescales. The pH dependent rate const. of the slower kinetic process to reach the equil. follows a bell shaped curve as described for many synthetic flavylium compds. Unlike anthocyanins, it was proved that there is no pH dependent reversibility in the system, since the chalcone suffers an irreversible degrdn. process. The math. expression to describe the bell shaped behavior was deduced. These results contribute to explain why in plants glycosylation is crucial for the stabilization of the anthocyanins.
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Schneider, H.-J. Dispersive Interactions in Solution Complexes Acc. Chem. Res. 2015, 48 (7) 1815– 1822 DOI: 10.1021/acs.accounts.5b00111
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Dispersive Interactions in Solution Complexes
Schneider, Hans-Joerg
Accounts of Chemical Research (2015), 48 (7), 1815-1822CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
Dispersive interactions are known to play a major role in mol. assocns. in the gas phase and in the solid state. In soln., however, their significance has been disputed in recent years on the basis of several arguments. A major problem until now has been the sepn. of dispersive and hydrophobic effects, which are both maximized in water due the low polarizability of this most important medium. Analyses of complexes between porphyrins and systematically varied substrates in water have allowed us to discriminate dispersive from hydrophobic effects, as the latter turned out to be negligible for complexations with flat surfaces such as porphyrins. Also, for the first time, it has become possible to obtain binding free energy increments ΔΔG for a multitude of org. residues including halogen, amide, amino, ether, carbonyl, ester, nitro, sulfur, unsatured, and cyclopropane groups, which turned out to be additive. Binding contributions for satd. residues are unmeasurably small, with ΔΔG > 1 kJ/mol, but they increase to, e.g., ΔΔG = 5 kJ/mol for a nitro group, a value not far from, e.g., that of a stacking pyridine ring. Stacking interactions of heteroarenes with porphyrins depend essentially on the size of the arenes, in line with polarizabilities, and seem to be rather independent of the position of nitrogen within the rings. Measurements of halogen derivs. indicate that complexes with porphyrins, cyclodextrins, and pillarenes as hosts in different media consistently show increasing stability from fluorine to iodine as the substituent. This, and the obsd. sequence with other substrates, is in line with the expected increase in dispersive forces with increasing polarizability. Induced dipoles, which also would increase with polarizability, can be ruled out as providing the driving source in view of the data with halides: the obsd. stability sequence is opposite the change of electronegativity from fluorine to iodine. The same holds for the solvent effect obsd. in ethanol-water mixts. Dispersive contributions vary not only with the polarizability of the used media but also with the interacting receptor sites; it has been shown that for cucurbiturils the polarizability inside the cavity is extremely low, which also explains why hydrophobic effects are maximized with these hosts. Complexations with other known host compds., however, such as those between cryptands or cavitands with, e.g., noble gases, bear the signature of dominating dispersive forces. Some recent examples illustrate that such van der Waals forces can also play an important role in complexations with proteins. Again, a clue for this is the increase in ΔG for inhibitor binding by 7 kJ/mol for, e.g., a bromine in comparison to a fluorine deriv.
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Hunter, C. A.; Sanders, J. K. M. The Nature of.pi.-.pi. Interactions J. Am. Chem. Soc. 1990, 112 (14) 5525– 5534 DOI: 10.1021/ja00170a016
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The nature of π-π interactions
Hunter, Christopher A.; Sanders, Jeremy K. M.
Journal of the American Chemical Society (1990), 112 (14), 5525-34CODEN: JACSAT; ISSN:0002-7863.
A simple model of the charge distribution in a π-system is used to explain the strong geometrical requirements for interactions between arom. mols. The key feature of the model is that it considers the σ-framework and the π-electrons sep. and demonstrates that net favorable π-π interactions are actually the result of π-σ attractions that overcome π-π repulsions. The calcns. correlate with observations made on porphyrin π-π interactions both in soln. and in the cryst. state. By using an idealized π-atom, some general rules for predicting the geometry of favorable π-π interactions are derived. In particular a favorable offset or slipped geometry is predicted. These rules successfully predict the geometry of intermol. interactions in the crystal structures of arom. mols. and rationalize a range of host-guest phenomena. The theory demonstrates that the electron donor-acceptor concept can be misleading: it is the properties of the atoms at the points of intermol. contact rather than the overall mol. properties which are important.
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Hwang, J.; Li, P.; Carroll, W. R.; Smith, M. D.; Pellechia, P. J.; Shimizu, K. D. Additivity of Substituent Effects in Aromatic Stacking Interactions J. Am. Chem. Soc. 2014, 136 (40) 14060– 14067 DOI: 10.1021/ja504378p
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Additivity of Substituent Effects in Aromatic Stacking Interactions
Hwang, Jungwun; Li, Ping; Carroll, William R.; Smith, Mark D.; Pellechia, Perry J.; Shimizu, Ken D.
Journal of the American Chemical Society (2014), 136 (40), 14060-14067CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The goal of this study was to exptl. test the additivity of the electrostatic substituent effects (SEs) for the arom. stacking interaction. The additivity of the SEs was assessed using a small mol. model system that could adopt an offset face-to-face arom. stacking geometry. The intramol. interactions of these mol. torsional balances were quant. measured via the changes in a folded/unfolded conformational equil. Five different types of substituents were examd. (CH3, OCH3, Cl, CN, and NO2) that ranged from electron-donating to electron-withdrawing. The strength of the intramol. stacking interactions was measured for 21 substituted arom. stacking balances and 21 control balances in chloroform soln. The obsd. stability trends were consistent with additive SEs. Specifically, additive SE models could predict SEs with an accuracy from ±0.01 to ±0.02 kcal/mol. The additive SEs were consistent with Wheeler and Houk's direct SE model. However, the indirect or polarization SE model cannot be ruled out as it shows similar levels of additivity for two to three substituent systems, which were the no. of substituents in our model system. SE additivity also has practical utility as the SEs can be accurately predicted. This should aid in the rational design and optimization of systems that utilize arom. stacking interactions.
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Cockroft, S. L.; Hunter, C. A.; Lawson, K. R.; Perkins, J.; Urch, C. J. Electrostatic Control of Aromatic Stacking Interactions J. Am. Chem. Soc. 2005, 127 (24) 8594– 8595 DOI: 10.1021/ja050880n
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Electrostatic Control of Aromatic Stacking Interactions
Cockroft, Scott L.; Hunter, Christopher A.; Lawson, Kevin R.; Perkins, Julie; Urch, Christopher J.
Journal of the American Chemical Society (2005), 127 (24), 8594-8595CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
A supramol. approach has been used to investigate the free energies of intermol. arom. stacking interactions. Chem. double mutant cycles have been used to measure the effect of a range of substituents on face-to-face stacking interactions with Ph and pentafluorophenyl rings. Electrostatic effects dominate the trends in interaction energy.
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Meyer, E. A.; Castellano, R. K.; Diederich, F. Interactions with Aromatic Rings in Chemical and Biological Recognition Angew. Chem., Int. Ed. 2003, 42 (11) 1210– 1250 DOI: 10.1002/anie.200390319
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Interactions with aromatic rings in chemical and biological recognition
Meyer, Emmanuel A.; Castellano, Ronald K.; Diederich, Francois
Angewandte Chemie, International Edition (2003), 42 (11), 1210-1250CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Intermol. interactions involving arom. rings are key processes in both chem. and biol. recognition. Their understanding is essential for rational drug design and lead optimization in medicinal chem. Different approaches-biol. studies, mol. recognition studies with artificial receptors, crystallog. database mining, gas-phase studies, and theor. calcns. - are pursued to generate a profound understanding of the structural and energetic parameters of individual recognition modes involving arom. rings. This review attempts to combine and summarize the knowledge gained from these investigations. The review focuses mainly on examples with biol. relevance since one of its aims it to enhance the knowledge of mol. recognition forces that is essential for drug development.
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Salonen, L. M.; Ellermann, M.; Diederich, F. Aromatic Rings in Chemical and Biological Recognition: Energetics and Structures Angew. Chem., Int. Ed. 2011, 50 (21) 4808– 4842 DOI: 10.1002/anie.201007560
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Aromatic rings in chemical and biological recognition: energetics and structures
Salonen, Laura M.; Ellermann, Manuel; Diederich, Francois
Angewandte Chemie, International Edition (2011), 50 (21), 4808-4842CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. This review describes a multidimensional treatment of mol. recognition phenomena involving arom. rings in chem. and biol. systems. It summarizes new results reported since the appearance of an earlier review in 2003 in host-guest chem., biol. affinity assays and biostructural anal., data base mining in the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB), and advanced computational studies. Topics addressed are arene-arene, perfluoroarene-arene, S···arom., cation-π, and anion-π interactions, as well as hydrogen bonding to π systems. The generated knowledge benefits, in particular, structure-based hit-to-lead development and lead optimization both in the pharmaceutical and in the crop protection industry. It equally facilitates the development of new advanced materials and supramol. systems, and should inspire further utilization of interactions with arom. rings to control the stereochem. outcome of synthetic transformations.
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Hunter, C. A. Quantifying Intermolecular Interactions: Guidelines for the Molecular Recognition Toolbox Angew. Chem., Int. Ed. 2004, 43 (40) 5310– 5324 DOI: 10.1002/anie.200301739
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Quantifying intermolecular interactions: Guidelines for the molecular recognition toolbox
Hunter, Christopher A.
Angewandte Chemie, International Edition (2004), 43 (40), 5310-5324CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Mol. recognition events in soln. are affected by many different factors that have hampered the development of an understanding of intermol. interactions at a quant. level. Tendency is to partition these effects into discrete phenomenol. fields that are classified, named, and divorced: arom. interactions, cation-T interactions, CH-O hydrogen bonds, short strong hydrogen bonds, and hydrophobic interactions to name a few. To progress in the field, the authors need to develop an integrated quant. appreciation of the relative magnitudes of all of the different effects that might influence the mol. recognition behavior of a given system. In an effort to navigate undergraduates through the vast and sometimes contradictory literature on the subject, I have developed an approach that treats theor. ideas and exptl. observations about intermol. interactions in the gas phase, the solid state, and soln. from a single simplistic viewpoint. The key features are outlined here, and although many of the ideas will be familiar, the aim is to provide a semiquant. thermodn. ranking of these effects in soln. at room temp.
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Trouillas, P.; Di Meo, F.; Gierschner, J.; Linares, M.; Sancho-García, J. C.; Otyepka, M. Optical Properties of Wine Pigments: Theoretical Guidelines with New Methodological Perspectives Tetrahedron 2015, 71 (20) 3079– 3088 DOI: 10.1016/j.tet.2014.10.046
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London, F. The General Theory of Molecular Forces Trans. Faraday Soc. 1937, 33 (0) 8b– 26 DOI: 10.1039/tf937330008b
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Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly Nature 2005, 437 (7059) 640– 647 DOI: 10.1038/nature04162
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Interfaces and the driving force of hydrophobic assembly
Chandler, David
Nature (London, United Kingdom) (2005), 437 (7059), 640-647CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
A review. The hydrophobic effect - the tendency for oil and water to segregate - is important in diverse phenomena, from the cleaning of laundry, to the creation of micro-emulsions to make new materials, to the assembly of proteins into functional complexes. This effect is multifaceted depending on whether hydrophobic mols. are individually hydrated or driven to assemble into larger structures. Despite the basic principles underlying the hydrophobic effect being qual. well understood, only recently have theor. developments begun to explain and quantify many features of this ubiquitous phenomenon.
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Biedermann, F.; Nau, W. M.; Schneider, H.-J. The Hydrophobic Effect Revisited—Studies with Supramolecular Complexes Imply High-Energy Water as a Noncovalent Driving Force Angew. Chem., Int. Ed. 2014, 53 (42) 11158– 11171 DOI: 10.1002/anie.201310958
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The Hydrophobic Effect Revisited-Studies with Supramolecular Complexes Imply High-Energy Water as a Noncovalent Driving Force
Biedermann, Frank; Nau, Werner M.; Schneider, Hans-Joerg
Angewandte Chemie, International Edition (2014), 53 (42), 11158-11171CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Traditional descriptions of the hydrophobic effect from entropic arguments or the calcn. of solvent-occupied surfaces must be questioned in view of new results obtained with supramol. complexes. In these studies, it was possible to sep. hydrophobic from dispersive interactions, which are strongest in aq. systems. Even very hydrophobic alkanes assoc. significantly only in cavities contg. water mols. with an insufficient no. of possible hydrogen bonds. The replacement of high-energy water in cavities by guest mols. is the essential enthalpic driving force for complexation, as borne out by data for complexes of cyclodextrins, cyclophanes, and cucurbiturils, for which complexation enthalpies of up to -100 kJ mol-1 were reached for encapsulated alkyl residues. Water-box simulations were used to characterize the different contributions from high-energy water and enabled the calcn. of the assocn. free enthalpies for selected cucurbituril complexes to within a 10% deviation from exptl. values. Cavities in artificial receptors are more apt to show the enthalpic effect of high-energy water than those in proteins or nucleic acids, because they bear fewer or no functional groups in the inner cavity to stabilize interior water mols.
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Waters, M. L. Aromatic Interactions Acc. Chem. Res. 2013, 46 (4) 873– 873 DOI: 10.1021/ar4000828
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Aromatic Interactions
Waters, Marcey L.
Accounts of Chemical Research (2013), 46 (4), 873CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
There is no expanded citation for this reference.
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Yang, L.; Adam, C.; Nichol, G. S.; Cockroft, S. L. How Much Do van Der Waals Dispersion Forces Contribute to Molecular Recognition in Solution? Nat. Chem. 2013, 5 (12) 1006– 1010 DOI: 10.1038/nchem.1779
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How much do van der Waals dispersion forces contribute to molecular recognition in solution?
Yang, Lixu; Adam, Catherine; Nichol, Gary S.; Cockroft, Scott L.
Nature Chemistry (2013), 5 (12), 1006-1010CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
The emergent properties that arise from self-assembly and mol. recognition phenomena are a direct consequence of noncovalent interactions. Gas-phase measurements and computational methods point to the dominance of dispersion forces in mol. assocn., but solvent effects complicate the unambiguous quantification of these forces in soln. Here, the authors used synthetic mol. balances to measure interactions between apolar alkyl chains in 31 org., fluorous and aq. solvent environments. The exptl. interaction energies are an order of magnitude smaller than ests. of dispersion forces between alkyl chains that were derived from vaporization enthalpies and dispersion-cor. calcns. Instead, cohesive solvent-solvent interactions are the major driving force behind apolar assocn. in soln. Probably theor. models that implicate important roles for dispersion forces in mol. recognition events should be interpreted with caution in solvent-accessible systems.
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Mackerell, A. D. Empirical Force Fields for Biological Macromolecules: Overview and Issues J. Comput. Chem. 2004, 25 (13) 1584– 1604 DOI: 10.1002/jcc.20082
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Empirical force fields for biological macromolecules: Overview and issues
MacKerell, Alexander D., Jr.
Journal of Computational Chemistry (2004), 25 (13), 1584-1604CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A review. Empirical force field-based studies of biol. macromols. are becoming a common tool for investigating their structure-activity relationships at an at. level of detail. Such studies facilitate interpretation of exptl. data and allow for information not readily accessible to exptl. methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reprodn. of exptl. observables. Presented is an overview of the issues assocd. with the development and application of empirical force fields to biomol. systems. This is followed by a summary of the force fields commonly applied to the different classes of biomols.; proteins, nucleic acids, lipids, and carbohydrates. In addn., issues assocd. with computational studies on "heterogeneous" biomol. systems and the transferability of force fields to a wide range of org. mols. of pharmacol. interest are discussed.
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Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field J. Comput. Chem. 2004, 25 (9) 1157– 1174 DOI: 10.1002/jcc.20035
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Development and testing of a general Amber force field
Wang, Junmei; Wolf, Romain M.; Caldwell, James W.; Kollman, Peter A.; Case, David A.
Journal of Computational Chemistry (2004), 25 (9), 1157-1174CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
We describe here a general Amber force field (GAFF) for org. mols. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most org. and pharmaceutical mols. that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited no. of atom types, but incorporates both empirical and heuristic models to est. force consts. and partial at. charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallog. structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, resp.). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermol. energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, resp. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, resp.), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to expt.) is about 0.5 kcal/mol. GAFF can be applied to wide range of mols. in an automatic fashion, making it suitable for rational drug design and database searching.
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Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules J. Am. Chem. Soc. 1996, 118 (9) 2309– 2309 DOI: 10.1021/ja955032e
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A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules [ Erratum for J. Am. Chem. Soc. 1995, 117, 5179-5197 ]
Cornell, Wendy D.; Cieplak, Piotr; Bayly, Christopher I.; Gould, Ian R.; Merz, Kenneth M. Jr.; Ferguson, David M.; Spellmeyer, David C.; Fox, Thomas; Caldwell, James W.; Kollman, Peter A.
Journal of the American Chemical Society (1996), 118 (9), 2309CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
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Zgarbová, M.; Otyepka, M.; Sponer, J.; Hobza, P.; Jurecka, P. Large-Scale Compensation of Errors in Pairwise-Additive Empirical Force Fields: Comparison of AMBER Intermolecular Terms with Rigorous DFT-SAPT Calculations Phys. Chem. Chem. Phys. 2010, 12 (35) 10476– 10493 DOI: 10.1039/c002656e
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Šponer, J.; Banáš, P.; Jurečka, P.; Zgarbová, M.; Kührová, P.; Havrila, M.; Krepl, M.; Stadlbauer, P.; Otyepka, M. Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome J. Phys. Chem. Lett. 2014, 5 (10) 1771– 1782 DOI: 10.1021/jz500557y
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Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome
Sponer, Jiri; Banas, Pavel; Jurecka, Petr; Zgarbova, Marie; Kuhrova, Petra; Havrila, Marek; Krepl, Miroslav; Stadlbauer, Petr; Otyepka, Michal
Journal of Physical Chemistry Letters (2014), 5 (10), 1771-1782CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
A review. We present a brief overview of explicit solvent mol. dynamics (MD) simulations of nucleic acids. We explain phys. chem. limitations of the simulations, namely, the mol. mechanics (MM) force field (FF) approxn. and limited time scale. Further, we discuss relations and differences between simulations and expts., compare std. and enhanced sampling simulations, discuss the role of starting structures, comment on different versions of nucleic acid FFs, and relate MM computations with contemporary quantum chem. Despite its limitations, we show that MD is a powerful technique for studying the structural dynamics of nucleic acids with a fast growing potential that substantially complements exptl. results and aids their interpretation.
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Adcock, S. A.; McCammon, J. A. Molecular Dynamics: Survey of Methods for Simulating the Activity of Proteins Chem. Rev. 2006, 106 (5) 1589– 1615 DOI: 10.1021/cr040426m
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Molecular dynamics: Survey of methods for simulating the activity of proteins
Adcock, Stewart A.; McCammon, J. Andrew
Chemical Reviews (Washington, DC, United States) (2006), 106 (5), 1589-1615CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. Mol. dynamics simulations (MDS) of proteins have provided many insights into the internal motions of these biomols. Simulation of in silico models aids in the interpretation and reconciliation of exptl. data. With ongoing advances in both methodol. and computational resources, MDS are being extended to larger systems and longer time scales. This enables the investigation of motions and conformational changes that have functional implications and yields information that is not available though any other means. Today's results suggest that (subject to the continuing utilization of synergies between expt. and simulation) the applications of MDS will command an increasingly crit. role in the understanding of biol. systems.
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Case, D. A.; Cheatham, T. E.; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber Biomolecular Simulation Programs J. Comput. Chem. 2005, 26 (16) 1668– 1688 DOI: 10.1002/jcc.20290
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The amber biomolecular simulation programs
Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
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Brooks, B. R.; Brooks, C. L.; MacKerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S. CHARMM: The Biomolecular Simulation Program J. Comput. Chem. 2009, 30 (10) 1545– 1614 DOI: 10.1002/jcc.21287
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CHARMM: The biomolecular simulation program
Brooks, B. R.; Brooks, C. L., III; Mackerell, A. D., Jr.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A. R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R. W.; Post, C. B.; Pu, J. Z.; Schaefer, M.; Tidor, B.; Venable, R. M.; Woodcock, H. L.; Wu, X.; Yang, W.; York, D. M.; Karplus, M.
Journal of Computational Chemistry (2009), 30 (10), 1545-1614CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A review. CHARMM (Chem. at HARvard Mol. Mechanics) is a highly versatile and widely used mol. simulation program. It has been developed over the last three decades with a primary focus on mols. of biol. interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small mol. ligands, as they occur in soln., crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, mol. minimization, dynamics, and anal. techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calcns. with CHARMM can be performed using a no. of different energy functions and models, from mixed quantum mech.-mol. mech. force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009.
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Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable Molecular Dynamics with NAMD J. Comput. Chem. 2005, 26 (16) 1781– 1802 DOI: 10.1002/jcc.20289
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Scalable molecular dynamics with NAMD
Phillips, James C.; Braun, Rosemary; Wang, Wei; Gumbart, James; Tajkhorshid, Emad; Villa, Elizabeth; Chipot, Christophe; Skeel, Robert D.; Kale, Laxmikant; Schulten, Klaus
Journal of Computational Chemistry (2005), 26 (16), 1781-1802CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
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Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free J. Comput. Chem. 2005, 26 (16) 1701– 1718 DOI: 10.1002/jcc.20291
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GROMACS: Fast, flexible, and free
Van Der Spoel, David; Lindahl, Erik; Hess, Berk; Groenhof, Gerrit; Mark, Alan E.; Berendsen, Herman J. C.
Journal of Computational Chemistry (2005), 26 (16), 1701-1718CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
This article describes the software suite GROMACS (Groningen MAchine for Chem. Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for mol. dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addn., it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequil. dynamics and free energy detns. are incorporated. Interfaces with popular quantum-chem. packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and anal. programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.
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Leach, A. R. Molecular Modelling: Principles and Applications; Pearson, 2001.
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Vashisth, H.; Skiniotis, G.; Brooks, C. L. Collective Variable Approaches for Single Molecule Flexible Fitting and Enhanced Sampling Chem. Rev. 2014, 114 (6) 3353– 3365 DOI: 10.1021/cr4005988
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Bruccoleri, R. E.; Karplus, M. Conformational Sampling Using High-Temperature Molecular Dynamics Biopolymers 1990, 29 (14) 1847– 1862 DOI: 10.1002/bip.360291415
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Chocholoušová, J.; Vacek, J.; Hobza, P. Acetic Acid Dimer in the Gas Phase, Nonpolar Solvent, Microhydrated Environment, and Dilute and Concentrated Acetic Acid: Ab Initio Quantum Chemical and Molecular Dynamics Simulations J. Phys. Chem. A 2003, 107 (17) 3086– 3092 DOI: 10.1021/jp027637k
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Acetic Acid Dimer in the Gas Phase, Nonpolar Solvent, Microhydrated Environment, and Dilute and Concentrated Acetic Acid: Ab Initio Quantum Chemical and Molecular Dynamics Simulations
Chocholousova, Jana; Vacek, Jaroslav; Hobza, Pavel
Journal of Physical Chemistry A (2003), 107 (17), 3086-3092CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Theor. study of the acetic acid dimer, its microhydration and its behavior in water and chloroform soln. was performed. To characterize the system, the authors adopted ab initio methods at the DFT and RI MP2 (the resoln. of the identity approxn. MP2) levels for the gas-phase calcns., PCM (polarizable continuum model) approxn. using the polarizable conductor calcn. model (COSMO) for description of solvent, and const. energy (NVE) and const. temp. (NVT) mol. dynamics simulations for gas phase and explicit solvent calcns., resp. The cyclic structure of the acetic acid dimer is the most stable in the gas phase only. During microhydration, the water mols. are incorporated in the dimer leading to water-sepd. structures. This conclusion is based on ab initio quantum chem. calcns., as well as on mol. dynamics simulations. The fact that the cyclic structure does not appear in water soln. is in agreement with previous theor. and exptl. results. Extending the search also on other acetic acid dimer structures, acetic acid does not form any dimer structure in water soln. The cyclic structure also probably is stable in chloroform soln.
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Zelený, T.; Hobza, P.; Kabelác, M. Microhydration of Guanine···cytosine Base Pairs, a Theoretical Study on the Role of Water in Stability, Structure and Tautomeric Equilibrium Phys. Chem. Chem. Phys. 2009, 11 (18) 3430– 3435 DOI: 10.1039/b819350a
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Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding Chem. Phys. Lett. 1999, 314 (1–2) 141– 151 DOI: 10.1016/S0009-2614(99)01123-9
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Replica-exchange molecular dynamics method for protein folding
Sugita, Y.; Okamoto, Y.
Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
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Beck, D. A. C.; White, G. W. N.; Daggett, V. Exploring the Energy Landscape of Protein Folding Using Replica-Exchange and Conventional Molecular Dynamics Simulations J. Struct. Biol. 2007, 157 (3) 514– 523 DOI: 10.1016/j.jsb.2006.10.002
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Laio, A.; Parrinello, M. Escaping Free-Energy Minima Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (20) 12562– 12566 DOI: 10.1073/pnas.202427399
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Escaping free-energy minima
Laio, Alessandro; Parrinello, Michele
Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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Barducci, A.; Bonomi, M.; Parrinello, M. Metadynamics Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1 (5) 826– 843 DOI: 10.1002/wcms.31
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Metadynamics
Barducci, Alessandro; Bonomi, Massimiliano; Parrinello, Michele
Wiley Interdisciplinary Reviews: Computational Molecular Science (2011), 1 (5), 826-843CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. Metadynamics is a powerful technique for enhancing sampling in mol. dynamics simulations and reconstructing the free-energy surface as a function of few selected degrees of freedom, often referred to as collective variables (CVs). In metadynamics, sampling is accelerated by a history-dependent bias potential, which is adaptively constructed in the space of the CVs. Since its first appearance, significant improvements have been made to the original algorithm, leading to an efficient, flexible, and accurate method that has found many successful applications in several domains of science. Here, we discuss first the theory underlying metadynamics and its recent developments. In particular, we focus on the crucial issue of choosing an appropriate set of CVs and on the possible strategies to alleviate this difficulty. Later in the second part, we present a few recent representative applications, which we have classified into three main classes: solid-state physics, chem. reactions, and biomols.
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Brás, N. F.; Cruz, L.; Fernandes, P. A.; De Freitas, V.; Ramos, M. J. Conformational Study of Two Diasteroisomers of Vinylcatechin Dimers in a Methanol Solution Int. J. Quantum Chem. 2011, 111 (7–8) 1498– 1510 DOI: 10.1002/qua.22631
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Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W. Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models Acc. Chem. Res. 2000, 33 (12) 889– 897 DOI: 10.1021/ar000033j
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Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models
Kollman, Peter A.; Massova, Irina; Reyes, Carolina; Kuhn, Bernd; Huo, Shuanghong; Chong, Lillian; Lee, Matthew; Lee, Taisung; Duan, Yong; Wang, Wei; Donini, Oreola; Cieplak, Piotr; Srinivasan, Jaysharee; Case, David A.; Cheatham, Thomas E., III
Accounts of Chemical Research (2000), 33 (12), 889-897CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
A review, with 63 refs. A historical perspective on the application of mol. dynamics (MD) to biol. macromols. is presented. Recent developments combining state-of-the-art force fields with continuum solvation calcns. have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from mol. dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.
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Bahar, I.; Lezon, T. R.; Bakan, A.; Shrivastava, I. H. Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins Chem. Rev. 2010, 110 (3) 1463– 1497 DOI: 10.1021/cr900095e
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Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins
Bahar, Ivet; Lezon, Timothy R.; Bakan, Ahmet; Shrivastava, Indira H.
Chemical Reviews (Washington, DC, United States) (2010), 110 (3), 1463-1497CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. Structural dynamics and function of membrane proteins are discussed in relation to principal component anal. of exptl. resolved conformations, normal mode anal. and elastic network models.
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Andricioaei, I.; Karplus, M. On the Calculation of Entropy from Covariance Matrices of the Atomic Fluctuations J. Chem. Phys. 2001, 115 (14) 6289– 6292 DOI: 10.1063/1.1401821
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On the calculation of entropy from covariance matrices of the atomic fluctuations
Andricioaei, Ioan; Karplus, Martin
Journal of Chemical Physics (2001), 115 (14), 6289-6292CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An ad hoc method for calcg. the entropy of a biomol. system from the covariance matrix of the at. fluctuations is analyzed. It is shown that its essential assumption can be eliminated by a quasiharmonic anal. The computer time required for use of the latter is of the same order as that of the former.
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Tsui, V.; Case, D. A. Theory and Applications of the Generalized Born Solvation Model in Macromolecular Simulations Biopolymers 2000, 56 (4) 275– 291 DOI: 10.1002/1097-0282(2000)56:4<275::AID-BIP10024>3.0.CO;2-E
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Theory and applications of the generalized Born solvation model in macromolecular simulations
Tsui V; Case D A
Biopolymers (2000-2001), 56 (4), 275-91 ISSN:0006-3525.
Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface-area based "hydrophobic" term) to explicit solvent simulations for a 10 base-pair DNA oligomer, and for the 108-residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NH [bond] O and NH [bond] N internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.
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Rocchia, W.; Alexov, E.; Honig, B. Extending the Applicability of the Nonlinear Poisson–Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions J. Phys. Chem. B 2001, 105 (28) 6507– 6514 DOI: 10.1021/jp010454y
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Extending the applicability of the nonlinear Poisson-Boltzmann equation: multiple dielectric constants and multivalent ions
Rocchia, W.; Alexov, E.; Honig, B.
Journal of Physical Chemistry B (2001), 105 (28), 6507-6514CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
A new version of the DelPhi program, which provides numerical solns. to the nonlinear Poisson-Boltzmann (PB) equation, is reported. The program can divide space into multiple regions contg. different dielec. consts. and can treat systems contg. mixed salt solns. where the valence and concn. of each ion is different. The electrostatic free energy is calcd. by decompg. the various energy terms into Coulombic interactions so that that the calcd. free energies are independent of the lattice used to solve the PB equation. This, together with algorithms that optimally position polarization charges on the mol. surface, leads to a significant decrease in the dependence of the electrostatic free energy on the resoln. of the lattice used to solve the PB equation and, hence, to a remarkable improvement in the precision of the calcd. values. The Gauss-Seidel algorithm used in the current version of DelPhi is retained so that the new program retains many of the optimization features of the old one. The program uses dynamic memory allocation and can easily handle systems requiring large grid dimensions - for example, a 3003 system can be conveniently treated on a single SGI R12000 processor. An algorithm that ests. the best relaxation parameter to solve the nonlinear equation for a given system is described, and is implemented in the program at run time. A no. of applications of the program are presented.
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Baker, C. M.; Lopes, P. E. M.; Zhu, X.; Roux, B.; MacKerell, A. D. Accurate Calculation of Hydration Free Energies Using Pair-Specific Lennard-Jones Parameters in the CHARMM Drude Polarizable Force Field J. Chem. Theory Comput. 2010, 6 (4) 1181– 1198 DOI: 10.1021/ct9005773
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Accurate Calculation of Hydration Free Energies using Pair-Specific Lennard-Jones Parameters in the CHARMM Drude Polarizable Force Field
Baker, Christopher M.; Lopes, Pedro E. M.; Zhu, Xiao; Roux, Benoit; MacKerell, Alexander D.
Journal of Chemical Theory and Computation (2010), 6 (4), 1181-1198CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Lennard-Jones (LJ) parameters for a variety of model compds. have previously been optimized within the CHARMM Drude polarizable force field to reproduce accurately pure liq. phase thermodn. properties as well as addnl. target data. While the polarizable force field resulting from this optimization procedure has been shown to satisfactorily reproduce a wide range of exptl. ref. data across numerous series of small mols., a slight but systematic overestimate of the hydration free energies has also been noted. Here, the reprodn. of exptl. hydration free energies is greatly improved by the introduction of pair-specific LJ parameters between solute heavy atoms and water oxygen atoms that override the std. LJ parameters obtained from combining rules. The changes are small and a systematic protocol is developed for the optimization of pair-specific LJ parameters and applied to the development of pair-specific LJ parameters for alkanes, alcs., and ethers. The resulting parameters not only yield hydration free energies in good agreement with exptl. values, but also provide a framework upon which other pair-specific LJ parameters can be added as new compds. are parametrized within the CHARMM Drude polarizable force field. Detailed anal. of the contributions to the hydration free energies reveals that the dispersion interaction is the main source of the systematic errors in the hydration free energies. This information suggests that the systematic error may result from problems with the LJ combining rules and is combined with anal. of the pair-specific LJ parameters obtained in this work to identify a preliminary improved combining rule.
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Allinger, N. L. Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms J. Am. Chem. Soc. 1977, 99 (25) 8127– 8134 DOI: 10.1021/ja00467a001
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Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms
Allinger, Norman L.
Journal of the American Chemical Society (1977), 99 (25), 8127-34CODEN: JACSAT; ISSN:0002-7863.
An improved force field for mol.-mechanics calcns. of the structures and energies of hydrocarbons is presented. The problem of simultaneously obtaining a sufficiently large gauche butane interaction energy while keeping the H atoms small enough for good structural predictions was solved with 1- and 2-fold rotational barriers. For 42 selected diverse types of hydrocarbons, the std. deviation between the calcd. and exptl. heats of formation is 0.42 kcal/mol, compared with an av. reported exptl. error for the same group of compds. of 0.40 kcal/mol.
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Charlton, A. J.; Davis, A. L.; Jones, D. P.; Lewis, J. R.; Davies, A. P.; Haslam, E.; Williamson, M. P. The Self-Association of the Black Tea Polyphenol Theaflavin and Its Complexation with Caffeine J. Chem. Soc. Perkin Trans. 2 2000, 2) 317– 322 DOI: 10.1039/a906380c
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207
Kunsági-Máté, S.; Szabó, K.; Nikfardjam, M. P.; Kollár, L. Determination of the Thermodynamic Parameters of the Complex Formation between Malvidin-3-O-Glucoside and Polyphenols. Copigmentation Effect in Red Wines J. Biochem. Biophys. Methods 2006, 69 (1–2) 113– 119 DOI: 10.1016/j.jbbm.2006.03.014
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Determination of the thermodynamic parameters of the complex formation between malvidin-3-O-glucoside and polyphenols. Copigmentation effect in red wines
Kunsagi-Mate, Sandor; Szabo, Kornelia; Nikfardjam, Martin P.; Kollar, Laszlo
Journal of Biochemical and Biophysical Methods (2006), 69 (1-2), 113-119CODEN: JBBMDG; ISSN:0165-022X. (Elsevier Ltd.)
The thermodn. of the mol. assocn. process between the malvidin-3-O-glucoside and a series of polyphenol derivs. (called copigmentation' in food chem.) were studied in aq. media. The Gibbs free energy, enthalpy and entropy values were detd. by the fluorometric method. A combination of the Job's method with the van't Hoff theory was applied for data evaluation. The results show the exothermic character of the copigmentation process. The change of the enthalpy seems to be the same in every complexation step. However, the decreasing of the entropy term is higher at higher stoichiometries. As a result, the Gibbs free energy changes and, thus, the complex stability decreases quickly with increasing stoichiometry. Quantum-chem. investigation reveals the complexity of mol. interactions between malvidin and polyphenols, which is preferably based on π-π and OH-π interaction moderated by repulsive Coulomb-type interactions.
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Kalisz, S.; Oszmiański, J.; Hładyszowski, J.; Mitek, M. Stabilization of Anthocyanin and Skullcap Flavone Complexes – Investigations with Computer Simulation and Experimental Methods Food Chem. 2013, 138 (1) 491– 500 DOI: 10.1016/j.foodchem.2012.10.146
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Kunsági-Máté, S.; Ortmann, E.; Kollár, L.; Nikfardjam, M. P. Effect of the Solvatation Shell Exchange on the Formation of Malvidin- 3- O -Glucoside–Ellagic Acid Complexes J. Phys. Chem. B 2007, 111 (40) 11750– 11755 DOI: 10.1021/jp0740144
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Sousa, A.; Araújo, P.; Cruz, L.; Brás, N. F.; Mateus, N.; De Freitas, V. Evidence for Copigmentation Interactions between Deoxyanthocyanidin Derivatives (Oaklins) and Common Copigments in Wine Model Solutions J. Agric. Food Chem. 2014, 62 (29) 6995– 7001 DOI: 10.1021/jf404640m
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Košinová, P.; Berka, K.; Wykes, M.; Otyepka, M.; Trouillas, P. Positioning of Antioxidant Quercetin and Its Metabolites in Lipid Bilayer Membranes: Implication for Their Lipid-Peroxidation Inhibition J. Phys. Chem. B 2012, 116 (4) 1309– 1318 DOI: 10.1021/jp208731g
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Positioning of Antioxidant Quercetin and Its Metabolites in Lipid Bilayer Membranes: Implication for Their Lipid-Peroxidation Inhibition
Kosinova, Pavlina; Berka, Karel; Wykes, Michael; Otyepka, Michal; Trouillas, Patrick
Journal of Physical Chemistry B (2012), 116 (4), 1309-1318CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
Among numerous biol. activities, natural polyphenols are antioxidants widely distributed in plants capable of inhibiting lipid peroxidn., which belongs to the most serious degenerative cell processes. Positioning of antioxidants in lipid bilayers can provide an insight to the lipid-peroxidn. inhibition at the mol. level. This work aims at detg. the location and orientation of quercetin and its most representative (glucuronidated, methylated, and sulfated) metabolites in lipid bilayer via mol. dynamic simulations. We show that quercetin derivs. penetrate the lipid bilayer and that the depths of penetration depend on mol. charge and substitutional variations. In the presence of charged substituents (sulfates and glucuronidates), the mol. is pulled toward the lipid bilayer surface. The orientation also depends on substitution as H-bonds are formed between the polar head groups of the bilayer and the (i) OH groups, (ii) sugar, and (iii) sulfate moieties of the antioxidants. As flavonoids and their derivs. are preferentially localized in the lipid bilayer membrane or on the bilayer/water interface, they readily conc. in a relatively narrow membrane region. Despite the low concns. of flavonoids in food, their spatial confinement in the membrane greatly enhances their local concn. in this vital region, thus increasing their importance for in vivo biol. activities including oxidative stress defense.
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Sirk, T. W.; Brown, E. F.; Sum, A. K.; Friedman, M. Molecular Dynamics Study on the Biophysical Interactions of Seven Green Tea Catechins with Lipid Bilayers of Cell Membranes J. Agric. Food Chem. 2008, 56 (17) 7750– 7758 DOI: 10.1021/jf8013298
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Molecular Dynamics Study on the Biophysical Interactions of Seven Green Tea Catechins with Lipid Bilayers of Cell Membranes
Sirk, Timothy W.; Brown, Eugene F.; Sum, Amadeu K.; Friedman, Mendel
Journal of Agricultural and Food Chemistry (2008), 56 (17), 7750-7758CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
Mol. dynamics simulations were performed to study the interactions of bioactive catechins (flavonoids) commonly found in green tea with lipid bilayers, as a model for cell membranes. Previously, multiple exptl. studies rationalized catechin's anticarcinogenic, antibacterial, and other beneficial effects in terms of physicochem. mol. interactions with the cell membranes. To contribute toward understanding the mol. role of catechins on the structure of cell membranes, we present simulation results for seven green tea catechins in lipid bilayer systems representative of HepG2 cancer cells. Our simulations show that the seven tea catechins evaluated have a strong affinity for the lipid bilayer via hydrogen bonding to the bilayer surface, with some of the smaller catechins able to penetrate underneath the surface. Epigallocatechin-gallate (EGCG) showed the strongest interaction with the lipid bilayer based on the no. of hydrogen bonds formed with lipid headgroups. The simulations also provide insight into the functional characteristics of the catechins that distinguish them as effective compds. to potentially alter the lipid bilayer properties. The results on the hydrogen-bonding effects, described here for the first time, may contribute to a better understanding of proposed multiple mol. mechanisms of the action of catechins in microorganisms, cancer cells, and tissues.
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Paloncýová, M.; Fabre, G.; DeVane, R. H.; Trouillas, P.; Berka, K.; Otyepka, M. Benchmarking of Force Fields for Molecule–Membrane Interactions J. Chem. Theory Comput. 2014, 10 (9) 4143– 4151 DOI: 10.1021/ct500419b
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Benchmarking of Force Fields for Molecule-Membrane Interactions
Paloncyova, Marketa; Fabre, Gabin; DeVane, Russell H.; Trouillas, Patrick; Berka, Karel; Otyepka, Michal
Journal of Chemical Theory and Computation (2014), 10 (9), 4143-4151CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Free energy profiles of eleven compds. with a model dimyristoylphosphatidylcholine (DMPC) membrane bilayer have been calcd. using five force fields, namely Berger, Slipids, CHARMM36, GAFFlipids, and GROMOS 43A1-S3 via mol. dynamics simulations. For the sake of comparison, the semicontinuous tool COSMOmic was also used. High correlation was obsd. between theor. and exptl. partition coeffs. (log K). Partition coeffs. calcd. by all-at. force fields (Slipids, CHARMM36, and GAFFlipids) and COSMOmic differed by less than 0.75 log units from the expt. and Slipids emerged as the best performing force field. This work provides the following recommendations (i) for a global, systematic and high throughput thermodn. evaluations (e.g., log K) of drugs COSMOmic is a tool of choice due to low computational costs; (ii) for studies of the hydrophilic mols. CHARMM36 should be considered; and (iii) for studies of more complex systems, taking into account all pros and cons, Slipids is the force field of choice.
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Podloucká, P.; Berka, K.; Fabre, G.; Paloncýová, M.; Duroux, J.-L.; Otyepka, M.; Trouillas, P. Lipid Bilayer Membrane Affinity Rationalizes Inhibition of Lipid Peroxidation by a Natural Lignan Antioxidant J. Phys. Chem. B 2013, 117 (17) 5043– 5049 DOI: 10.1021/jp3127829
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215
Zhou, H.-X.; Gilson, M. K. Theory of Free Energy and Entropy in Noncovalent Binding Chem. Rev. 2009, 109 (9) 4092– 4107 DOI: 10.1021/cr800551w
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Theory of Free Energy and Entropy in Noncovalent Binding
Zhou, Huan-Xiang; Gilson, Michael K.
Chemical Reviews (Washington, DC, United States) (2009), 109 (9), 4092-4107CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. Theory of free energy and entropy in noncovalent binding aims to support the development of well-founded models of binding and meaningful interpretation of exptl. data. Discussion includes the statistical thermodn. of binding., changes in translational and other entropy components on binding.
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Černỳ, J.; Hobza, P. Non-Covalent Interactions in Biomacromolecules Phys. Chem. Chem. Phys. 2007, 9 (39) 5291– 5303 DOI: 10.1039/b704781a
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Grimme, S.; Antony, J.; Schwabe, T.; Mück-Lichtenfeld, C. Density Functional Theory with Dispersion Corrections for Supramolecular Structures, Aggregates, and Complexes of (bio) Organic Molecules Org. Biomol. Chem. 2007, 5 (5) 741– 758 DOI: 10.1039/b615319b
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Sherrill, C. D. Computations of Noncovalent N Interactions Rev. Comput. Chem. 2008, 26, 1 DOI: 10.1002/9780470399545.ch1
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Tschumper, G. S. Computations for Weak Noncovalent Rev. Comput. Chem. 2008, 26, 39 DOI: 10.1002/9780470399545.ch2
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Foster, M. E.; Sohlberg, K. Empirically Corrected DFT and Semi-Empirical Methods for Non-Bonding Interactions Phys. Chem. Chem. Phys. 2010, 12 (2) 307– 322 DOI: 10.1039/B912859J
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Riley, K. E.; Pitoňák, M.; Jurečka, P.; Hobza, P. Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories Chem. Rev. 2010, 110 (9) 5023– 5063 DOI: 10.1021/cr1000173
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Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories
Riley, Kevin E.; Pitonak, Michal; Jurecka, Petr; Hobza, Pavel
Chemical Reviews (Washington, DC, United States) (2010), 110 (9), 5023-5063CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. Topics covered include: wave function theory; MP2; methods from MP3 to CCSD; d. functional theories; empirical dispersion corrections; plane wave codes and nonlocal pseudopotentials; symmetry-adapted perturbation theory; and semiempirical quantum chem. theories.
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Hobza, P. The Calculation of Intermolecular Interaction Energies Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2011, 107, 148– 168 DOI: 10.1039/c1pc90005f
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The calculation of intermolecular interaction energies
Hobza, Pavel
Annual Reports on the Progress of Chemistry, Section C: Physical Chemistry (2011), 107 (), 148-168CODEN: ACPCDW; ISSN:0260-1826. (Royal Society of Chemistry)
All life on our earth can be viewed as an application of supramol. chem., with noncovalent interactions playing a central role. The knowledge of total interaction energies as well as their components is topical for understanding the nature of these interactions and, in a broader sense, also for understanding the nature of stabilization of noncovalent systems like biomacromols. Accurate data on interaction energies can only be obtained from coupled-cluster with single and double and perturbative triple excitations (CCSD(T)) calcns. performed with extended basis sets. The CCSDD(T) calcns. thus provide benchmark data which can be used for testing and/or parameterizing other, computationally economical techniques. In the present review the applicability and performance of various recently introduced wavefunction and d. functional methods are examd. in detail.
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Grimme, S. Density Functional Theory with London Dispersion Corrections Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1 (2) 211– 228 DOI: 10.1002/wcms.30
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Density functional theory with london dispersion corrections
Grimme, Stefan
Wiley Interdisciplinary Reviews: Computational Molecular Science (2011), 1 (2), 211-228CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. Dispersion corrections to std. Kohn-Sham d. functional theory (DFT) are reviewed. The focus is on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on sepd. fragments. The recommended approaches (van der Waals d. functional and DFT-D) are asymptotically correct and can be used in combination with std. or slightly modified (short-range) exchange-correlation functionals. The importance of the dispersion energy in intramol. cases (conformational problems and thermochem.) is highlighted.
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Klimeš, J.; Michaelides, A. Perspective: Advances and Challenges in Treating van Der Waals Dispersion Forces in Density Functional Theory J. Chem. Phys. 2012, 137 (12) 120901 DOI: 10.1063/1.4754130
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Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
Klimes, Jiri; Michaelides, Angelos
Journal of Chemical Physics (2012), 137 (12), 120901/1-120901/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A review. Electron dispersion forces play a crucial role in detg. the structure and properties of biomols., mol. crystals, and many other systems. However, an accurate description of dispersion is highly challenging, with the most widely used electronic structure technique, d. functional theory (DFT), failing to describe them with std. approxns. Therefore, applications of DFT to systems where dispersion is important have traditionally been of questionable accuracy. However, the last decade has seen a surge of enthusiasm in the DFT community to tackle this problem and in so-doing to extend the applicability of DFT-based methods. Here we discuss, classify, and evaluate some of the promising schemes to emerge in recent years. A brief perspective on the outstanding issues that remain to be resolved and some directions for future research are also provided. (c) 2012 American Institute of Physics.
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Ehrlich, S.; Moellmann, J.; Grimme, S. Dispersion-Corrected Density Functional Theory for Aromatic Interactions in Complex Systems Acc. Chem. Res. 2013, 46 (4) 916– 926 DOI: 10.1021/ar3000844
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Dispersion-Corrected Density Functional Theory for Aromatic Interactions in Complex Systems
Ehrlich, Stephan; Moellmann, Jonas; Grimme, Stefan
Accounts of Chemical Research (2013), 46 (4), 916-926CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
Arom. interactions play a key role in many chem. and biol. systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with std. wave function theory (WFT). Although d. functional theory (DFT) can easily treat systems of more than 200 atoms, std. semilocal (hybrid) d. functional approxns. fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramol. noncovalent interactions. Therefore dispersion-cor. DFT provides a unique tool for the investigation and anal. of a wide range of complex arom. systems. In this Account, we start with an anal. of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The min. for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of satd. and arom. model complexes, we show that increased dispersion coeffs. for sp2-hybridized carbon atoms play a major role in arom. stacking. Modern dispersion-cor. DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate ref. data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, d.-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramol. interactions that arise in the mol. crystals of arom. mols. In studies of hexahelicene, dispersion-cor. DFT yields "the right answer for the right reason". By comparison, std. DFT calcns. reproduce intramol. distances quite accurately in single-mol. calcns. while inter- and intramol. distances become too large when dispersion-uncorrected solid-state calcns. are carried out. Dispersion-cor. DFT can fix this problem, and these results are in excellent agreement with exptl. structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calcns. for the formation of a cationic, quadruply charged dimer of a porphyrin deriv., a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-cor. DFT with an adequate continuum solvation model can accurately reproduce exptl. free assocn. enthalpies in soln. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qual. or quant. correct picture of the interactions of this complex.
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DiStasio, R. A., Jr.; Gobre, V. V.; Tkatchenko, A. Many-Body van Der Waals Interactions in Molecules and Condensed Matter J. Phys.: Condens. Matter 2014, 26 (21) 213202 DOI: 10.1088/0953-8984/26/21/213202
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Many-body van der Waals interactions in molecules and condensed matter
DiStasio, Robert A.; Gobre, Vivekanand V.; Tkatchenko, Alexandre
Journal of Physics: Condensed Matter (2014), 26 (21), 213202/1-213202/16, 16 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
A review. This work reviews the increasing evidence that many-body van der Waals (vdW) or dispersion interactions play a crucial role in the structure, stability and function of a wide variety of systems in biol., chem. and physics. Starting with the exact expression for the electron correlation energy provided by the adiabatic connection fluctuation-dissipation theorem, we derive both pairwise and many-body interat. methods for computing the long-range dispersion energy by considering a model system of coupled quantum harmonic oscillators within the RPA. By coupling this approach to d. functional theory, the resulting many-body dispersion (MBD) method provides an accurate and efficient scheme for computing the frequency-dependent polarizability and many-body vdW energy in mols. and materials with a finite electronic gap. A select collection of applications are presented that ascertain the fundamental importance of these non-bonded interactions across the spectrum of intermol. (the S22 and S66 benchmark databases), intramol. (conformational energies of alanine tetrapeptide) and supramol. (binding energy of the 'buckyball catcher') complexes, as well as mol. crystals (cohesive energies in oligoacenes). These applications demonstrate that electrodynamic response screening and beyond-pairwise many-body vdW interactions - both captured at the MBD level of theory - play a quant., and sometimes even qual., role in describing the properties considered herein. This work is then concluded with an in-depth discussion of the challenges that remain in the future development of reliable (accurate and efficient) methods for treating many-body vdW interactions in complex materials and provides a road-map for navigating many of the research avenues that are yet to be explored.
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Casimir, H.; Polder, D. The Influence of Retardation on the London-van Der Waals Forces Phys. Rev. 1948, 73 (4) 360 DOI: 10.1103/PhysRev.73.360
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The influence of retardation on the London-van der Waals forces
Casimir, H. B. G.; Polder, D.
Physical Review (1948), 73 (), 360-72CODEN: PHRVAO; ISSN:0031-899X.
cf. C.A. 41, 1899i. Math.theoretical. The influence of retardation on the energy of interaction between two neutral atoms is investigated by means of quantum electrodynamics. In the interactions between a neutral atom and a perfectly conducting plane, and between two atoms, it is found that the influence of radiation is described by a monotonically decreasing correction factor which is equal to unity for small distances, R, compared with the wave lengths corresponding to the at. frequencies, and proportional to 1/R when R is large compared with these wave lengths.
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Starkschall, G.; Gordon, R. G. Calculation of Coefficients in the Power Series Expansion of the Long-Range Dispersion Force between Atoms J. Chem. Phys. 1972, 56 (6) 2801– 2806 DOI: 10.1063/1.1677610
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229
Tang, K.; Toennies, J. P. An Improved Simple Model for the van Der Waals Potential Based on Universal Damping Functions for the Dispersion Coefficients J. Chem. Phys. 1984, 80 (8) 3726– 3741 DOI: 10.1063/1.447150
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An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients
Tang, K. T.; Toennies, J. Peter
Journal of Chemical Physics (1984), 80 (8), 3726-41CODEN: JCPSA6; ISSN:0021-9606.
By using the earlier model (K.T.T. and J.P.T., 1977), a simple expression was derived for the radial-dependent damping functions for the individual dispersion coeffs. C2n for arbitrary even orders 2n. The damping functions are only a function of the Born-Mayer range parameter b, and thus can be applied to all systems for which this is known or can be estd. For H(1S)-H(1S), the results agree with the ab-initio damping functions of A. Koide, et al., (1981). Comparisons with less accurate previous calcns. for other systems also show agreement. By adding a Born-Mayer repulsive term [A exp(-bR)] to the damped dispersion potential, a simple universal expression was obtained for the well region of the atom-atom van der Waals potential with only 5 essential parameters A, b, C6, C8, and C10. The model was tested for the systems: H23Σ, He2, Ar2, NaK3Σ, and LiHg, for which either very precise theor. or exptl. data are available. For each system, the ab-initio dispersion coeffs. together with the parameters ε and Rm were used to det. A and b from the model potential. With these values, the reduced potentials were calcd., and found to agree with the exptl. potentials to better than 1%, and always less than the exptl. uncertainties.
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Thakkar, A. J.; Hettema, H.; Wormer, P. E. Abinitio Dispersion Coefficients for Interactions Involving Rare-Gas Atoms J. Chem. Phys. 1992, 97 (5) 3252– 3257 DOI: 10.1063/1.463012
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Lein, M.; Dobson, J. F.; Gross, E. K. Toward the Description of van Der Waals Interactions within Density Functional Theory J. Comput. Chem. 1999, 20 (1) 12– 22 DOI: 10.1002/(SICI)1096-987X(19990115)20:1<12::AID-JCC4>3.0.CO;2-U
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Kamal, C.; Ghanty, T.; Banerjee, A.; Chakrabarti, A. The van Der Waals Coefficients between Carbon Nanostructures and Small Molecules: A Time-Dependent Density Functional Theory Study J. Chem. Phys. 2009, 131 (16) 164708 DOI: 10.1063/1.3256238
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233
Johnson, E. R.; Becke, A. D. A Post-Hartree–Fock Model of Intermolecular Interactions J. Chem. Phys. 2005, 123 (2) 024101 DOI: 10.1063/1.1949201
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A post-Hartree-Fock model of intermolecular interactions
Johnson, Erin R.; Becke, Axel D.
Journal of Chemical Physics (2005), 123 (2), 024101/1-024101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Intermol. interactions are of great importance in chem. but are difficult to model accurately with computational methods. In particular, Hartree-Fock and std. d.-functional approxns. do not include the physics necessary to properly describe dispersion. These methods are sometimes cor. to account for dispersion by adding a pairwise C6/R6 term, with C6 dispersion coeffs. dependent on the atoms involved. We present a post-Hartree-Fock model in which C6 coeffs. are generated by the instantaneous dipole moment of the exchange hole. This model relies on occupied orbitals only, and involves only one, universal, empirical parameter to limit the dispersion energy at small interat. sepns. The model is extensively tested on isotropic C6 coeffs. of 178 intermol. pairs. It is also applied to the calcn. of the geometries and binding energies of 20 intermol. complexes involving dispersion, dipole-induced dipole, dipole-dipole, and hydrogen-bonding interactions, with remarkably good results.
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Becke, A. D.; Johnson, E. R. Exchange-Hole Dipole Moment and the Dispersion Interaction J. Chem. Phys. 2005, 122 (15) 154104 DOI: 10.1063/1.1884601
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Exchange-hole dipole moment and the dispersion interaction
Becke, Axel D.; Johnson, Erin R.
Journal of Chemical Physics (2005), 122 (15), 154104/1-154104/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A simple model is presented in which the instantaneous dipole moment of the exchange hole is used to generate a dispersion interaction between nonoverlapping systems. The model is easy to implement, requiring no electron correlation (in the usual sense) or time dependence, and has been tested on various at. and mol. pairs. The resulting C6 dispersion coeffs. are remarkably accurate.
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Johnson, E. R. Dependence of Dispersion Coefficients on Atomic Environment J. Chem. Phys. 2011, 135 (23) 234109 DOI: 10.1063/1.3670015
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Misquitta, A. J. Intermolecular Interactions. In Handbook of Computational Chemistry; Springer, 2012; pp 157– 193.
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237
Wen, S.; Nanda, K.; Huang, Y.; Beran, G. J. Practical Quantum Mechanics-Based Fragment Methods for Predicting Molecular Crystal Properties Phys. Chem. Chem. Phys. 2012, 14 (21) 7578– 7590 DOI: 10.1039/c2cp23949c
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Practical quantum mechanics-based fragment methods for predicting molecular crystal properties
Wen, Shuhao; Nanda, Kaushik; Huang, Yuanhang; Beran, Gregory J. O.
Physical Chemistry Chemical Physics (2012), 14 (21), 7578-7590CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
A review. Significant advances in fragment-based electronic structure methods have created a real alternative to force-field and d. functional techniques in condensed-phase problems such as mol. crystals. This perspective article highlights some of the important challenges in modeling mol. crystals and discusses techniques for addressing them. First, we survey recent developments in fragment-based methods for mol. crystals. Second, we use examples from our own recent research on a fragment-based QM/MM method, the hybrid many-body interaction (HMBI) model, to analyze the phys. requirements for a practical and effective mol. crystal model chem. We demonstrate that it is possible to predict mol. crystal lattice energies to within a couple kJ mol-1 and lattice parameters to within a few percent in small-mol. crystals. Fragment methods provide a systematically improvable approach to making predictions in the condensed phase, which is crit. to making robust predictions regarding the subtle energy differences found in mol. crystals.
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Wu, Q.; Yang, W. Empirical Correction to Density Functional Theory for van Der Waals Interactions J. Chem. Phys. 2002, 116 (2) 515– 524 DOI: 10.1063/1.1424928
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Empirical correction to density functional theory for van der Waals interactions
Wu, Qin; Yang, Weitao
Journal of Chemical Physics (2002), 116 (2), 515-524CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An empirical method has been designed to account for the van der Waals interactions in practical mol. calcns. with d. functional theory. For each atom pair sepd. at a distance R, the method adds to the d. functional electronic structure calcns. an addnl. attraction energy EvdW = -fd(R)C6R-6, where fd(R) is the damping function which equals to one at large value of R and zero at small value of R. The coeffs. C6 for pair interactions between hydrogen, carbon, nitrogen, and oxygen atoms have been developed in this work by a least-square fitting to the mol. C6 coeffs. obtained from the dipole oscillator strength distribution method by Meath and co-workers. Two forms of the damping functions have been studied, with one dropping to zero at short distances much faster than the other. Four d. functionals have been examd.: Becke's three parameter hybrid functional with the Lee-Yang-Parr correlation functional, Becke's 1988 exchange functional with the LYP correlation functional, Becke's 1988 exchange functional with Perdew and Wang's 1991 (PW91) correlation functional, and PW91 exchange and correlation functional. The method has been applied to three systems where the van der Waals attractions are known to be important: rare-gas diat. mols., stacking of base pairs, and polyalanines' conformation stabilities. The results show that this empirical method, with the damping function dropping to zero smoothly, provides a significant correction to both of the Becke's hybrid functional and the PW91 exchange and correlation functional. Results are comparable with the corresponding second-order Moller-Plesset calcns. in many cases.
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Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections Phys. Chem. Chem. Phys. 2008, 10 (44) 6615– 6620 DOI: 10.1039/b810189b
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Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
Chai, Jeng-Da; Head-Gordon, Martin
Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
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Liu, Y.; Goddard, W. A. I. A Universal Damping Function for Empirical Dispersion Correction on Density Functional Theory Mater. Trans. 2009, 50 (7) 1664– 1670 DOI: 10.2320/matertrans.MF200911
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A universal damping function for empirical dispersion correction on density functional theory
Liu, Yi; Goddard, William A., III
Materials Transactions (2009), 50 (7), 1664-1670CODEN: MTARCE; ISSN:1345-9678. (Japan Institute of Metals)
A damped London dispersion interaction is generally adopted in empirical dispersion corrections on d. functional theory (DFT), where dispersion parameters are detd. empirically to reproduce correct dispersive interactions after assuming a damping function. The key to a successful dispersion correction is choosing an appropriate damping function. In this work we propose a single universal damping function that can represent several damping functions used in literatures with a few adjustable parameters. This universal damping function provides a unified formula that allows convenient comparison and flexible optimization in dispersion cor. DFT methods. Using the optimized universal damping functions and dispersion parameters, we develop dispersion correction methods for HF, B3LYP and PBE theories. We calc. the dispersive energies accurately for rare gas diat. mols. and benzene dimers with an averaged error <4.1%.
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Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu J. Chem. Phys. 2010, 132 (15) 154104 DOI: 10.1063/1.3382344
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A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory J. Comput. Chem. 2011, 32 (7) 1456– 1465 DOI: 10.1002/jcc.21759
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Effect of the damping function in dispersion corrected density functional theory
Grimme, Stefan; Ehrlich, Stephan; Goerigk, Lars
Journal of Computational Chemistry (2011), 32 (7), 1456-1465CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
It is shown by an extensive benchmark on mol. energy data that the math. form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a std. "zero-damping" formula and rational damping to finite values for small interat. distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coeffs. is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interat. forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramol. dispersion in four representative mol. structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermol. distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of cor. GGAs for non-covalent interactions. According to the thermodn. benchmarks BJ-damping is more accurate esp. for medium-range electron correlation problems and only small and practically insignificant double-counting effects are obsd. It seems to provide a phys. correct short-range behavior of correlation/dispersion even with unmodified std. functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying d. functional. © 2011 Wiley Periodicals, Inc.; J. Comput. Chem., 2011.
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Johnson, E. R.; Becke, A. D. A Post-Hartree-Fock Model of Intermolecular Interactions: Inclusion of Higher-Order Corrections J. Chem. Phys. 2006, 124 (17) 174104 DOI: 10.1063/1.2190220
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A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections
Johnson, Erin R.; Becke, Axel D.
Journal of Chemical Physics (2006), 124 (17), 174104/1-174104/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermol. C6 dispersion coeffs. [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermol. interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coeffs. C8 and C10. The extended model performs very well for prediction of intermonomer sepns. and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.
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Grimme, S. Accurate Description of van Der Waals Complexes by Density Functional Theory Including Empirical Corrections J. Comput. Chem. 2004, 25 (12) 1463– 1473 DOI: 10.1002/jcc.20078
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244
Accurate description of van der Waals complexes by density functional theory including empirical corrections
Grimme, Stefan
Journal of Computational Chemistry (2004), 25 (12), 1463-1473CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
An empirical method to account for van der Waals interactions in practical calcns. in the framework of the d. functional theory (termed DFT-D) was tested for a wide variety of mol. complexes. As in previous schemes, the dispersive energy was described by damped interat. potentials of the form C6R-6. The use of pure, gradient-cor. d. functionals (BLYP and PBE), together with the resoln.-of-the-identity (RI) approxn. for the Coulomb operator, allows very efficient computations for large systems. In contrast to the previous work, extended AO basis sets of polarized TZV or QZV quality were employed, which reduced the basis set superposition error to a negligible extend. By using a global scaling factor for the at. C6 coeffs., the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes was found to be insignificant if steep damping functions were employed. The method was applied to a total of 29 complexes of atoms and small mols. (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene·H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theor. or exptl. results for binding energies and intermol. distances is obtained. For stacked arom. systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to std. MP2 treatments that systematically over-bind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chem. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calcns. of the interaction energies.
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Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction J. Comput. Chem. 2006, 27 (15) 1787– 1799 DOI: 10.1002/jcc.20495
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Semiempirical GGA-type density functional constructed with a long-range dispersion correction
Grimme, Stefan
Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
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Jurečka, P.; Černỳ, J.; Hobza, P.; Salahub, D. R. Density Functional Theory Augmented with an Empirical Dispersion Term. Interaction Energies and Geometries of 80 Noncovalent Complexes Compared with Ab Initio Quantum Mechanics Calculations J. Comput. Chem. 2007, 28 (2) 555– 569 DOI: 10.1002/jcc.20570
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247
Tkatchenko, A.; Scheffler, M. Accurate Molecular van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data Phys. Rev. Lett. 2009, 102 (7) 073005 DOI: 10.1103/PhysRevLett.102.073005
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Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data
Tkatchenko, Alexandre; Scheffler, Matthias
Physical Review Letters (2009), 102 (7), 073005/1-073005/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
We present a parameter-free method for an accurate detn. of long-range van der Waals interactions from mean-field electronic structure calcns. Our method relies on the summation of interat. C6 coeffs., derived from the electron d. of a mol. or solid and accurate ref. data for the free atoms. The mean abs. error in the C6 coeffs. is 5.5% when compared to accurate exptl. values for 1225 intermol. pairs, irresp. of the employed exchange-correlation functional. We show that the effective at. C6 coeffs. depend strongly on the bonding environment of an atom in a mol. Finally, we analyze the van der Waals radii and the damping function in the C6R-6 correction method for d.-functional theory calcns.
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Steinmann, S. N.; Corminboeuf, C. A System-Dependent Density-Based Dispersion Correction J. Chem. Theory Comput. 2010, 6 (7) 1990– 2001 DOI: 10.1021/ct1001494
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248
A System-Dependent Density-Based Dispersion Correction
Steinmann, Stephan N.; Corminboeuf, Clemence
Journal of Chemical Theory and Computation (2010), 6 (7), 1990-2001CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
D. functional approxns. fail to provide a consistent description of weak mol. interactions arising from small electron d. overlaps. A simple remedy to correct for the missing interactions is to add a posteriori an attractive energy term summed over all atom pairs in the system. The d.-dependent energy correction, presented herein, is applicable to all elements of the periodic table and is easily combined with any electronic structure method, which lacks the accurate treatment of weak interactions. Dispersion coeffs. are computed according to Becke and Johnson's exchange-hole dipole moment (XDM) formalism, thereby depending on the chem. environment of an atom (d., oxidn. state). The long-range ∼R-6 potential is supplemented with higher-order correction terms (∼R-8 and ∼R-10) through the universal damping function of Tang and Toennies. A genuine damping factor depending on (iterative) Hirshfeld (overlap) populations, at. ionization energies, and two adjustable parameters specifically fitted to a given DFT functional is also introduced. The proposed correction, dDXDM, dramatically improves the performance of popular d. functionals. The anal. of 30 (dispersion cor.) d. functionals on 145 systems reveals that dDXDM largely reduces the errors of the parent functionals for both inter- and intramol. interactions. With mean abs. deviations (MADs) of 0.74-0.84 kcal mol-1, PBE-dDXDM, PBE0-dDXDM, and B3LYP-dDXDM outperform the computationally more demanding and most recent functionals such as M06-2X and B2PLYP-D (MAD of 1.93 and 1.06 kcal mol-1, resp.).
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Steinmann, S. N.; Corminboeuf, C. Comprehensive Benchmarking of a Density-Dependent Dispersion Correction J. Chem. Theory Comput. 2011, 7 (11) 3567– 3577 DOI: 10.1021/ct200602x
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249
Comprehensive Benchmarking of a Density-Dependent Dispersion Correction
Steinmann, Stephan N.; Corminboeuf, Clemence
Journal of Chemical Theory and Computation (2011), 7 (11), 3567-3577CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Std. d. functional approxns. cannot accurately describe interactions between nonoverlapping densities. A simple remedy consists in correcting for the missing interactions a posteriori, adding an attractive energy term summed over all atom pairs. The d.-dependent energy correction, dDsC, presented herein, is constructed from dispersion coeffs. computed on the basis of a generalized gradient approxn. to Becke and Johnson's exchange-hole dipole moment formalism. DDsC also relies on an extended Tang and Toennies damping function accounting for charge-overlap effects. The comprehensive benchmarking on 341 diverse reaction energies divided into 18 illustrative test sets validates the robust performance and general accuracy of dDsC for describing various intra- and intermol. interactions. With a total MAD of 1.3 kcal mol-1, B97-dDsC slightly improves the results of M06-2X and B2PLYP-D3 (MAD = 1.4 kcal mol-1 for both) at a lower computational cost. The d. dependence of both the dispersion coeffs. and the damping function makes the approach esp. valuable for modeling redox reactions and charged species in general.
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Steinmann, S. N.; Corminboeuf, C. A Generalized-Gradient Approximation Exchange Hole Model for Dispersion Coefficients J. Chem. Phys. 2011, 134 (4) 044117 DOI: 10.1063/1.3545985
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A generalized-gradient approximation exchange hole model for dispersion coefficients
Steinmann, Stephan N.; Corminboeuf, Clemence
Journal of Chemical Physics (2011), 134 (4), 044117/1-044117/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A simple method for computing accurate d.-dependent dispersion coeffs. is presented. The dispersion coeffs. are modeled by a generalized gradient-type approxn. to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a mol., gives mean abs. errors in the C6 coeffs. for 90 complexes below 10%. The inclusion of the missing long-range van der Waals interactions in d. functionals using the derived coeffs. in a pair wise correction leads to highly accurate typical noncovalent interaction energies. (c) 2011 American Institute of Physics.
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Liu, Y.; Goddard, W. A., III First-Principles-Based Dispersion Augmented Density Functional Theory: From Molecules to Crystals J. Phys. Chem. Lett. 2010, 1 (17) 2550– 2555 DOI: 10.1021/jz100615g
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251
First-Principles-Based Dispersion Augmented Density Functional Theory: From Molecules to Crystals
Liu, Yi; Goddard, William A., III
Journal of Physical Chemistry Letters (2010), 1 (17), 2550-2555CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Std. implementations of d. functional theory (DFT) describe well strongly bound mols. and solids but fail to describe long-range van der Waals attractions. We propose here first-principles-based augmentation to DFT that leads to the proper long-range 1/R6 attraction of the London dispersion while leading to low gradients (small forces) at normal valence distances so that it preserves the accurate geometries and thermochem. of std. DFT methods. The DFT-low gradient (DFT-lg) formula differs from previous DFT-D methods by using a purely attractive dispersion correction while not affecting valence bond distances. We demonstrate here that the DFT-lg model leads to good descriptions for graphite, benzene, naphthalene, and anthracene crystals, using just three parameters fitted to reproduce the full potential curves of high-level ab initio quantum mechanics [CCSD(T)] on gas-phase benzene dimers. The addnl. computational costs for this DFT-lg formalism are negligible.
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Kim, H.; Choi, J.-M.; Goddard, W. A., III Universal Correction of Density Functional Theory to Include London Dispersion (up to Lr, Element 103) J. Phys. Chem. Lett. 2012, 3 (3) 360– 363 DOI: 10.1021/jz2016395
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Universal Correction of Density Functional Theory to Include London Dispersion (up to Lr, Element 103)
Kim, Hyungjun; Choi, Jeong-Mo; Goddard, William A., III
Journal of Physical Chemistry Letters (2012), 3 (3), 360-363CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Conventional d. functional theory (DFT) fails to describe accurately the London dispersion essential for describing mol. interactions in soft matter (biol. systems, polymers, nucleic acids) and mol. crystals. This has led to several methods in which atom-dependent potentials are added into the Kohn-Sham DFT energy. Some of these corrections were fitted to accurate quantum mech. results, but it will be tedious to det. the appropriate parameters to describe all of the atoms of the periodic table. We propose an alternative approach in which a single parameter in the low-gradient (lg) functional form is combined with the rule-based UFF (universal force-field) nonbond parameters developed for the entire periodic table (up to Lr, Z = 103), named as a DFT-ulg method. We show that DFT-ulg method leads to a very accurate description of the properties for mol. complexes and mol. crystals, providing the means for predicting more accurate weak interactions across the periodic table.
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Román-Pérez, G.; Soler, J. M. Efficient Implementation of a van Der Waals Density Functional: Application to Double-Wall Carbon Nanotubes Phys. Rev. Lett. 2009, 103 (9) 096102 DOI: 10.1103/PhysRevLett.103.096102
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253
Efficient Implementation of a van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes
Roman-Perez, Guillermo; Soler, Jose M.
Physical Review Letters (2009), 103 (9), 096102/1-096102/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
We present an efficient implementation of the van der Waals d. functional of Dion et al., which expresses the nonlocal correlation energy as a double spatial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the self-consistent potential, total energy, and at. forces, in O(NlogN) operations. The resulting overhead, for medium and large systems, is a small fraction of the total computational cost, representing a dramatic speedup over the O(N2) evaluation of the double integral. This opens the realm of first-principles simulations to the large systems of interest in soft matter and biomol. problems. We apply the method to calc. the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.
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Andersson, Y.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Interactions in Density-Functional Theory Phys. Rev. Lett. 1996, 76 (1) 102– 105 DOI: 10.1103/PhysRevLett.76.102
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255
Dobson, J. F.; Dinte, B. P. Constraint Satisfaction in Local and Gradient Susceptibility Approximations: Application to a van Der Waals Density Functional Phys. Rev. Lett. 1996, 76 (11) 1780 DOI: 10.1103/PhysRevLett.76.1780
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Sato, T.; Tsuneda, T.; Hirao, K. Van Der Waals Interactions Studied by Density Functional Theory Mol. Phys. 2005, 103 (6–8) 1151– 1164 DOI: 10.1080/00268970412331333474
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Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Density Functional for General Geometries Phys. Rev. Lett. 2004, 92 (24) 246401 DOI: 10.1103/PhysRevLett.92.246401
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Van der Waals Density Functional for General Geometries
Dion, M.; Rydberg, H.; Schroeder, E.; Langreth, D. C.; Lundqvist, B. I.
Physical Review Letters (2004), 92 (24), 246401/1-246401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
A scheme within d. functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg et al., Phys. Rev. Lett. 91, 126402 (2003)]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long-range part of the correlation functional, the nonlocal correlations are expressed in terms of a d.-d. interaction formula. It contains a relatively simple parametrized kernel, with parameters detd. by the local d. and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.
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Pernal, K.; Podeszwa, R.; Patkowski, K.; Szalewicz, K. Dispersionless Density Functional Theory Phys. Rev. Lett. 2009, 103 (26) 263201 DOI: 10.1103/PhysRevLett.103.263201
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Klimeš, J.; Bowler, D. R.; Michaelides, A. Chemical Accuracy for the van Der Waals Density Functional J. Phys.: Condens. Matter 2010, 22 (2) 022201 DOI: 10.1088/0953-8984/22/2/022201
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Chemical accuracy for the van der Waals density functional
Klimes, Jiri; Bowler, David R.; Michaelides, Angelos
Journal of Physics: Condensed Matter (2010), 22 (2), 022201/1-022201/5CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
The non-local van der Waals d. functional (vdW-DF) of Dion et al is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be dramatically improved both for dispersion and hydrogen bonded complexes through the judicious selection of its underlying exchange functional. New and published exchange functionals are identified that deliver much better than chem. accuracy from vdW-DF for the S22 benchmark set of weakly interacting dimers and for water clusters. Improved performance for the adsorption of water on salt is also obtained.
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Lee, K.; Murray, É. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Higher-Accuracy van Der Waals Density Functional Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82 (8) 081101 DOI: 10.1103/PhysRevB.82.081101
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Higher-accuracy van der Waals density functional
Lee, Kyuho; Murray, Eamonn D.; Kong, Lingzhu; Lundqvist, Bengt I.; Langreth, David C.
Physical Review B: Condensed Matter and Materials Physics (2010), 82 (8), 081101/1-081101/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We propose a second version of the van der Waals d. functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in detg. the vdW kernel. The predicted binding energy, equil. sepn., and potential-energy curve shape are close to those of accurate quantum chem. calcns. on 22 duplexes. We anticipate the enabling of chem. accurate calcns. in sparse materials of importance for condensed matter, surface, chem., and biol. physics.
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Hamada, I. Van Der Waals Density Functional Made Accurate Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89 (12) 121103 DOI: 10.1103/PhysRevB.89.121103
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van der Waals density functional made accurate
Hamada, Ikutaro
Physical Review B: Condensed Matter and Materials Physics (2014), 89 (12), 121103/1-121103/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
I propose a van der Waals d. functional (vdW-DF) that improves upon the description of energetics and geometries of mols., solids, and adsorption systems over the original vdW-DF. The functional is based on the nonlocal correlation for the second version of the vdW-DF and an exchange functional that recovers the second-order gradient expansion approxn. in the slowly varying limit, while reproducing the large d. gradient behavior proposed by Becke. A systematic assessment of the proposed functional is presented, which demonstrates the applicability of the proposed vdW-DF to a wide range of systems.
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Vydrov, O. A.; Van Voorhis, T. Nonlocal van Der Waals Density Functional Made Simple Phys. Rev. Lett. 2009, 103 (6) 063004 DOI: 10.1103/PhysRevLett.103.063004
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Nonlocal van der Waals Density Functional Made Simple
Vydrov, Oleg A.; Van Voorhis, Troy
Physical Review Letters (2009), 103 (6), 063004/1-063004/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
We derive a nonlocal correlation functional that adequately describes van der Waals interactions not only in the asymptotic long-range regime but also at short range. Unlike its precursor, developed by Langreth, Lundqvist, and co-workers, the new functional has a simple analytic form, finite for all interelectron sepns., well behaved in the slowly varying d. limit, and generalized to spin-polarized systems.
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Vydrov, O. A.; Van Voorhis, T. Improving the Accuracy of the Nonlocal van Der Waals Density Functional with Minimal Empiricism J. Chem. Phys. 2009, 130 (10) 104105 DOI: 10.1063/1.3079684
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Vydrov, O. A.; Van Voorhis, T. Implementation and Assessment of a Simple Nonlocal van Der Waals Density Functional J. Chem. Phys. 2010, 132 (16) 164113 DOI: 10.1063/1.3398840
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Vydrov, O. A.; Van Voorhis, T. Nonlocal van Der Waals Density Functional: The Simpler the Better J. Chem. Phys. 2010, 133 (24) 244103 DOI: 10.1063/1.3521275
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Nonlocal van der Waals density functional: The simpler the better
Vydrov, Oleg A.; Van Voorhis, Troy
Journal of Chemical Physics (2010), 133 (24), 244103/1-244103/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron d. as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy min. but also far from equil. Our model exhibits an outstanding precision at predicting equil. intermonomer sepns. in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability. (c) 2010 American Institute of Physics.
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Sabatini, R.; Gorni, T.; de Gironcoli, S. Nonlocal van Der Waals Density Functional Made Simple and Efficient Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (4) 041108 DOI: 10.1103/PhysRevB.87.041108
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Nonlocal van der Waals density functional made simple and efficient
Sabatini, Riccardo; Gorni, Tommaso; de Gironcoli, Stefano
Physical Review B: Condensed Matter and Materials Physics (2013), 87 (4), 041108/1-041108/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We present a simple revision of the VV10 nonlocal d. functional by Vydrov and Van Voorhis for dispersion interactions. Unlike the original functional our modification allows nonlocal correlation energy and its derivs. to be efficiently evaluated in a plane wave framework along the lines pioneered by Roman-Perez and Soler. Our revised functional maintains the outstanding precision of the original VV10 in noncovalently bound complexes and performs well in representative covalent, ionic, and metallic solids.
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Hujo, W.; Grimme, S. Performance of the van Der Waals Density Functional VV10 and (hybrid) GGA Variants for Thermochemistry and Noncovalent Interactions J. Chem. Theory Comput. 2011, 7 (12) 3866– 3871 DOI: 10.1021/ct200644w
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Performance of the van der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions
Hujo, Waldemar; Grimme, Stefan
Journal of Chemical Theory and Computation (2011), 7 (12), 3866-3871CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The nonlocal van der Waals d. functional VV10 (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103) is tested for the thermochem. properties of 1200 + atoms and mols. in the GMTKN30 database in order to assess its global accuracy. Five GGA and hybrid functionals in unmodified form are augmented by the nonlocal (NL) part of the VV10 functional (one parameter adjusted). The addn. of the NL dispersion energy definitely improves the results of all tested functionals. On the basis of little empiricism and basic phys. insight, DFT-NL can be recommended as a fully electronic, robust electronic structure method.
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Aragó, J.; Ortí, E.; Sancho-García, J. C. Nonlocal van Der Waals Approach Merged with Double-Hybrid Density Functionals: Toward the Accurate Treatment of Noncovalent Interactions J. Chem. Theory Comput. 2013, 9 (8) 3437– 3443 DOI: 10.1021/ct4003527
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Nonlocal van der Waals Approach Merged with Double-Hybrid Density Functionals: Toward the Accurate Treatment of Noncovalent Interactions
Arago, Juan; Orti, Enrique; Sancho-Garcia, Juan C.
Journal of Chemical Theory and Computation (2013), 9 (8), 3437-3443CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Noncovalent interactions drive the self-assembly of weakly interacting mol. systems to form supramol. aggregates, which play a major role in nanotechnol. and biochem. In this work, we present a thorough assessment of the performance of different double-hybrid d. functionals (PBE0-DH-NL, revPBE0-DH-NL, B2PLYP-NL, and TPSS0-DH-NL), as well as their parent hybrid and (meta)GGA functionals, in combination with the most modern version of the nonlocal (NL) van der Waals correction. It is shown that this nonlocal correction can be successfully coupled with double-hybrid d. functionals thanks to the short-range attenuation parameter b, which has been optimized against ref. interaction energies of benchmarking mol. complexes (S22 and S66 databases). Among all the double-hybrid functionals evaluated, revPBE0-DH-NL and B2PLYP-NL behave remarkably accurate with mean unsigned errors (MUE) as small as 0.20 kcal/mol for the training sets and in the 0.25-0.42 kcal/mol range for an independent database (NCCE31). They can be thus seen as appropriate functionals to use in a broad no. of applications where noncovalent interactions play an important role. Overall, the nonlocal van der Waals approach combined with last-generation d. functionals is confirmed as an accurate and affordable computational tool for the modeling of weakly bonded mol. systems.
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Cooper, V. R. Van Der Waals Density Functional: An Appropriate Exchange Functional Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (16) 161104 DOI: 10.1103/PhysRevB.81.161104
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Van der Waals density functional: An appropriate exchange functional
Cooper, Valentino R.
Physical Review B: Condensed Matter and Materials Physics (2010), 81 (16), 161104/1-161104/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
In this Rapid Communication, an exchange functional which is compatible with the nonlocal Rutgers-Chalmers correlation functional [van der Waals d. functional (vdW-DF)] is presented. This functional, when employed with vdW-DF, demonstrates remarkable improvements on intermol. sepn. distances while further improving the accuracy of vdW-DF interaction energies. The key to the success of this three-parameter functional is its redn. in short-range exchange repulsion through matching to the gradient expansion approxn. in the slowly varying/high-d. limit while recovering the large reduced gradient, s, limit set in the revised Perdew-Burke-Ernzerhof (revPBE) exchange functional. This augmented exchange functional could be a soln. to long-standing issues of vdW-DF lending to further applicability of d.-functional theory to the study of relatively large, dispersion bound (van der Waals) complexes.
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Vydrov, O. A.; Van Voorhis, T. Benchmark Assessment of the Accuracy of Several van Der Waals Density Functionals J. Chem. Theory Comput. 2012, 8 (6) 1929– 1934 DOI: 10.1021/ct300081y
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Benchmark Assessment of the Accuracy of Several van der Waals Density Functionals
Vydrov, Oleg A.; Van Voorhis, Troy
Journal of Chemical Theory and Computation (2012), 8 (6), 1929-1934CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The nonlocal correlation functional VV10, developed recently in our group, describes the whole range of dispersion interactions in a seamless and general fashion using only the electron d. as input. The VV10 functional has a simple analytic form that can be adjusted for pairing with the exchange functional of choice. In this paper, we use several benchmark data sets of weakly interacting mol. complexes to test the accuracy of two VV10 variants, differing in their treatment of the exchange component. For the sake of comparison, several other d. functionals suitable for noncovalent interactions were also tested against the same benchmarks. We find that the "default" version of VV10 with semilocal exchange gives very accurate geometries and binding energies for most van der Waals complexes but systematically overbinds hydrogen-bonded complexes. The alternative variant of VV10 with long-range cor. hybrid exchange performs exceptionally well for all types of weak bonding sampled in this study, including hydrogen bonds.
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Hujo, W.; Grimme, S. Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions J. Chem. Theory Comput. 2013, 9 (1) 308– 315 DOI: 10.1021/ct300813c
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Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions
Hujo, Waldemar; Grimme, Stefan
Journal of Chemical Theory and Computation (2013), 9 (1), 308-315CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The nonlocal, electron d. dependent dispersion correction of Vydrov and Van Voorhis (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103), termed VV10 or DFT-NL, was implemented for structural optimizations of mols. It was tested in combination with the four (hybrid)GGA d. functionals TPSS, TPSS0, B3LYP, and revPBE38 for inter- and intramol. noncovalent interactions (NCI) and compared to results from atom-pairwise dispersion cor. DFT-D3. The methods were applied to a wide range of different problems, namely the S22 and S66 test sets, large transition metal complexes, water hexamer clusters, hexahelicene, and four other difficult cases of intramol. NCI. Crit. interat. distances were computed remarkably accurately by both dispersion corrections compared to theor. or exptl. ref. data and inter- and intramol. interactions were treated on equal footing. The methods can be recommended as reliable and robust tools for geometry optimizations of large systems in which long-range dispersion forces are crucial.
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Tran, F.; Hutter, J. Nonlocal van Der Waals Functionals: The Case of Rare-Gas Dimers and Solids J. Chem. Phys. 2013, 138 (20) 204103 DOI: 10.1063/1.4807332
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Gobre, V. V.; Tkatchenko, A. Scaling Laws for van Der Waals Interactions in Nanostructured Materials Nat. Commun. 2013, 4, 2341 DOI: 10.1038/ncomms3341
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Scaling laws for van der Waals interactions in nanostructured materials
Gobre Vivekanand V; Tkatchenko Alexandre
Nature communications (2013), 4 (), 2341 ISSN:.
Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.
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Ambrosetti, A.; Alfè, D.; DiStasio, R. A., Jr.; Tkatchenko, A. Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems J. Phys. Chem. Lett. 2014, 5 (5) 849– 855 DOI: 10.1021/jz402663k
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Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems
Ambrosetti, Alberto; Alfe, Dario; DiStasio, Robert A.; Tkatchenko, Alexandre
Journal of Physical Chemistry Letters (2014), 5 (5), 849-855CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Noncovalent interactions are ubiquitous in mol. and condensed-phase environments, and hence a reliable theor. description of these fundamental interactions could pave the way toward a more complete understanding of the microscopic underpinnings for a diverse set of systems in chem. and biol. In this work, we demonstrate that recent algorithmic advances coupled to the availability of large-scale computational resources make the stochastic quantum Monte Carlo approach to solving the Schrodinger equation an optimal contender for attaining "chem. accuracy" (1 kcal/mol) in the binding energies of supramol. complexes of chem. relevance. To illustrate this point, we considered a select set of seven host-guest complexes, representing the spectrum of noncovalent interactions, including dispersion or van der Waals forces, π-π stacking, hydrogen bonding, hydrophobic interactions, and electrostatic (ion-dipole) attraction. A detailed anal. of the interaction energies reveals that a complete theor. description necessitates treatment of terms well beyond the std. London and Axilrod-Teller contributions to the van der Waals dispersion energy.
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Šimová, L.; Řezáč, J.; Hobza, P. Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction J. Chem. Theory Comput. 2013, 9 (8) 3420– 3428 DOI: 10.1021/ct4002762
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Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction
Simova, Lucia; Rezac, Jan; Hobza, Pavel
Journal of Chemical Theory and Computation (2013), 9 (8), 3420-3428CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The CCSD(T) method stands out among various coupled-cluster (CC) approxns. as the golden std. in computational chem. and is widely and successfully used in the realm of covalent and noncovalent interactions. The CCSD(T) method provides reliable interaction energies, but their surprising accuracy is believed to arise partially from an error compensation. The convergence of the CC expansion has been investigated up to fully iterative pentuple excitations (CCSDTQP); for the smallest eight electron complexes, the full CI calcns. have also been performed. We conclude that the convergence of interaction energy at noncovalent accuracy (0.01 kcal/mol) for the complexes studied is reached already at CCSDTQ or CCSDT(Q) levels. When even higher accuracy (spectroscopic accuracy of 1 cm-1, or 3 cal/mol) is required, then the noniterative CCSDTQ(P) method could be used.
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Řezáč, J.; Šimová, L.; Hobza, P. CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods J. Chem. Theory Comput. 2013, 9 (1) 364– 369 DOI: 10.1021/ct3008777
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CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods
Rezac, Jan; Simova, Lucia; Hobza, Pavel
Journal of Chemical Theory and Computation (2013), 9 (1), 364-369CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The CCSD(T) method is often called the "gold std." of computational chem., because it is one of the most accurate methods applicable to reasonably large mols. It is particularly useful for the description of noncovalent interactions where the inclusion of triple excitations is necessary for achieving a satisfactory accuracy. While it is widely used as a benchmark, the accuracy of CCSD(T) interaction energies has not been reliably quantified yet against more accurate calcns. In this work, we compare the CCSD[T], CCSD(T), and CCSD(TQ) noniterative methods with full CCSDTQ and CCSDT(Q) calcns. We investigate various types of noncovalent complexes [hydrogen-bonded (water dimer, ammonia dimer, water ··· ammonia), dispersion-bound (methane dimer, methane ··· ammonia), and π-π stacked (ethene dimer)] using various coupled-clusters schemes up to CCSDTQ in 6-31G*(0.25), 6-31G**(0.25, 0.15), and aug-cc-pVDZ basis sets. We show that CCSDT(Q) reproduces the CCSDTQ results almost exactly and can thus serve as a benchmark in the cases where CCSDTQ calcns. are not feasible. Surprisingly, the CCSD[T] method provides better agreement with the benchmark values than the other noniterative analogs, CCSD(T) and CCSD(TQ), and even than the much more expensive iterative CCSDT scheme. The CCSD[T] interaction energies differ from the benchmark data by less than 5 cal/mol on av. (for all complexes and all basis sets), whereas the error of CCSD(T) is 9 cal/mol. In larger systems, the difference between these two methods can grow by as much as 0.15 kcal/mol. While this effect can be explained only as an error compensation, the CCSD[T] method certainly deserves more attention in accurate calcns. of noncovalent interactions.
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Kong, L.; Bischoff, F. A.; Valeev, E. F. Explicitly Correlated R12/F12 Methods for Electronic Structure Chem. Rev. 2012, 112 (1) 75– 107 DOI: 10.1021/cr200204r
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Explicitly Correlated R12/F12 Methods for Electronic Structure
Kong, Liguo; Bischoff, Florian A.; Valeev, Edward F.
Chemical Reviews (Washington, DC, United States) (2012), 112 (1), 75-107CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. The following topics are discussed: Electron correlation in atoms and mols.(CI wave functions and their symmetries); Explicitly correlated methods and wave functions; Core technol. of modern R12 methods; Coupled-Cluster R12 methods; Multireference R12 methods (R12-MRCI, MRMP2-F12, [2]R12, CASPT2-F12 and MRCI-F12, G-CASSCF, MR CABS Single correction, comparison of MR-R12 Methods).
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Burns, L. A.; Marshall, M. S.; Sherrill, C. D. Appointing Silver and Bronze Standards for Noncovalent Interactions: A Comparison of Spin-Component-Scaled (SCS), Explicitly Correlated (F12), and Specialized Wavefunction Approaches J. Chem. Phys. 2014, 141 (23) 234111 DOI: 10.1063/1.4903765
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Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches
Burns, Lori A.; Marshall, Michael S.; Sherrill, C. David
Journal of Chemical Physics (2014), 141 (23), 234111/1-234111/21CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A systematic examn. of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-std. quality benchmarks available for 345 interaction energies of 49 bimol. complexes. Quantum chem. techniques examd. include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examn. of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissocn. curves. Moreover, when benchmarking accuracy is desirable but gold-std. computations are unaffordable, this work recommends silver-std. [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-std. [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, resp. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys.140, 094106 (2014)] and d. functional theory [L. A. Burns, A. Vazquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys.134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance. (c) 2014 American Institute of Physics.
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Austin, B. M.; Zubarev, D. Y.; Lester, W. A., Jr. Quantum Monte Carlo and Related Approaches Chem. Rev. 2012, 112 (1) 263– 288 DOI: 10.1021/cr2001564
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Quantum Monte Carlo and Related Approaches
Austin, Brian M.; Zubarev, Dmitry Yu.; Lester, William A., Jr.
Chemical Reviews (Washington, DC, United States) (2012), 112 (1), 263-288CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. The following topics are discussed: Variational Monte Carlo, Fixed-node diffusion Monte Carlo, Self-healing diffusion Monte Carlo, Auxiliary field quantum Monte Carlo, Reptation quantum Monte Carlo, Full CI quantum Monte Carlo, Time-dependent quantum Monte Carlo; Trial electronic wave functions (antisym., backflow transformed, Jastrow), Trial wave function optimization, Effective core potentials; Computational considerations (Linear scaling quantum Monte Carlo, Parallelization and hardware acceleration, Advances in algorithms and software); Applications.
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Dubeckỳ, M.; Jurečka, P.; Derian, R.; Hobza, P.; Otyepka, M.; Mitas, L. Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy J. Chem. Theory Comput. 2013, 9 (10) 4287– 4292 DOI: 10.1021/ct4006739
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Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy
Dubecky, Matus; Jurecka, Petr; Derian, Rene; Hobza, Pavel; Otyepka, Michal; Mitas, Lubos
Journal of Chemical Theory and Computation (2013), 9 (10), 4287-4292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
An accurate description of noncovalent interaction energies is one of the most challenging tasks in computational chem. To date, nonempirical CCSD-(T)/CBS has been used as a benchmark ref. However, its practical use is limited due to the rapid growth of its computational cost with the system complexity. Here, we show that the fixed-node diffusion Monte Carlo (FN-DMC) method with a more favorable scaling is capable of reaching the CCSD-(T)/CBS within subchem. accuracy (<0.1 kcal/mol) on a testing set of six small noncovalent complexes including the water dimer. In benzene/water, benzene/methane, and the T-shape benzene dimer, FN-DMC provides interaction energies that agree within 0.25 kcal/mol with the best available CCSD-(T)/CBS ests. The demonstrated predictive power of FN-DMC therefore provides new opportunities for studies of the vast and important class of medium/large noncovalent complexes.
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Dubeckỳ, M.; Derian, R.; Jurečka, P.; Mitas, L.; Hobza, P.; Otyepka, M. Quantum Monte Carlo for Noncovalent Interactions: An Efficient Protocol Attaining Benchmark Accuracy Phys. Chem. Chem. Phys. 2014, 16 (38) 20915– 20923 DOI: 10.1039/C4CP02093F
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Neese, F.; Wennmohs, F.; Hansen, A. Efficient and Accurate Local Approximations to Coupled-Electron Pair Approaches: An Attempt to Revive the Pair Natural Orbital Method J. Chem. Phys. 2009, 130 (11) 114108 DOI: 10.1063/1.3086717
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Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method
Neese, Frank; Wennmohs, Frank; Hansen, Andreas
Journal of Chemical Physics (2009), 130 (11), 114108/1-114108/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Coupled-electron pair approxns. (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small mols. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochem., kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular d. functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient prodn. level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized mols. in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of d. fitting (or resoln. of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the av. no. of PNOs per electron pair, and the no. of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to abs. deviations from the canonical result of only a few kcal mol-1. Extended numerical test calcns. demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochem., kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chem. applications. (c) 2009 American Institute of Physics.
283
Neese, F.; Hansen, A.; Liakos, D. G. Efficient and Accurate Approximations to the Local Coupled Cluster Singles Doubles Method Using a Truncated Pair Natural Orbital Basis J. Chem. Phys. 2009, 131 (6) 064103 DOI: 10.1063/1.3173827
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283
Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
Neese, Frank; Hansen, Andreas; Liakos, Dimitrios G.
Journal of Chemical Physics (2009), 131 (6), 064103/1-064103/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A prodn. level implementation of the closed-shell local quadratic CI and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals (local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approxn. (LNPO-CEPA) method and makes extended use of the resoln. of the identity (RI) or d. fitting (DF) approxn. Two variants of each method are compared. The less accurate approxns. (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indexes to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (TCutPNO) has been studied. Extended numerical tests have been performed on abs. and relative correlation energies as function of basis set size and TCutPNO as well as on reaction energies, isomerization energies, and weak intermol. interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calcns. on larger mols. are reported (ranging from 40-86 atoms) and it is shown that for medium sized mols. the total wall clock time required to complete the LPNO-CCSD calcns. is only two to four times that of the preceding SCF. Thus these methods are highly suitable for large-scale computational chem. applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts. (c) 2009 American Institute of Physics.
284
Huntington, L. M.; Nooijen, M. pCCSD: Parameterized Coupled-Cluster Theory with Single and Double Excitations J. Chem. Phys. 2010, 133 (18) 184109 DOI: 10.1063/1.3494113
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285
Huntington, L. M. J.; Hansen, A.; Neese, F.; Nooijen, M. Accurate Thermochemistry from a Parameterized Coupled-Cluster Singles and Doubles Model and a Local Pair Natural Orbital Based Implementation for Applications to Larger Systems J. Chem. Phys. 2012, 136 (6) 064101 DOI: 10.1063/1.3682325
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286
Hansen, A.; Liakos, D. G.; Neese, F. Efficient and Accurate Local Single Reference Correlation Methods for High-Spin Open-Shell Molecules Using Pair Natural Orbitals J. Chem. Phys. 2011, 135 (21) 214102 DOI: 10.1063/1.3663855
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286
Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals
Hansen, Andreas; Liakos, Dimitrios G.; Neese, Frank
Journal of Chemical Physics (2011), 135 (21), 214102/1-214102/20CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A prodn. level implementation of the high-spin open-shell (spin unrestricted) single ref. coupled pair, quadratic CI and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier. The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation assocd. with the large no. of PNOs becomes feasible through the extensive use of d. fitting (resoln. of the identity (RI)) techniques. Tech. complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the ref. determinant are discussed in detail. As in the closed-shell case, only three cutoff parameters control the av. no. of PNOs per electron pair, the size of the significant pair list, and the no. of contributing auxiliary basis functions per PNO. The chosen threshold default values ensure robustness and the results of the parent canonical methods are reproduced to high accuracy. Comprehensive numerical tests on abs. and relative energies as well as timings consistently show that the outstanding performance of the LPNO methods carries over to the open-shell case with minor modifications. Finally, hyperfine couplings calcd. with the variational LPNO-CEPA/1 method, for which a well-defined expectation value type d. exists, indicate the great potential of the LPNO approach for the efficient calcn. of mol. properties. (c) 2011 American Institute of Physics.
287
Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. Natural Triple Excitations in Local Coupled Cluster Calculations with Pair Natural Orbitals J. Chem. Phys. 2013, 139 (13) 134101 DOI: 10.1063/1.4821834
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287
Natural triple excitations in local coupled cluster calculations with pair natural orbitals
Riplinger, Christoph; Sandhoefer, Barbara; Hansen, Andreas; Neese, Frank
Journal of Chemical Physics (2013), 139 (13), 134101/1-134101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calcn. of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calcns. on alkane chains. The accuracy of the DLPNO-CCSD(T) approxn. relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an av. error of approx. 0.5 kcal/mol for a challenging test set of medium sized org. mols. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addn. to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calcn. on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.
288
Sparta, M.; Neese, F. Chemical Applications Carried out by Local Pair Natural Orbital Based Coupled-Cluster Methods Chem. Soc. Rev. 2014, 43 (14) 5032– 5041 DOI: 10.1039/c4cs00050a
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289
Liakos, D. G.; Hansen, A.; Neese, F. Weak Molecular Interactions Studied with Parallel Implementations of the Local Pair Natural Orbital Coupled Pair and Coupled Cluster Methods J. Chem. Theory Comput. 2011, 7 (1) 76– 87 DOI: 10.1021/ct100445s
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289
Weak molecular interactions studied with parallel implementations of the local pair natural orbital coupled pair and coupled cluster methods
Liakos, Dimitrios G.; Hansen, Andreas; Neese, Frank
Journal of Chemical Theory and Computation (2011), 7 (1), 76-87CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
A parallel implementation of the recently developed local pair natural orbital CEPA (LPNO-CEPA/n, n = Version 1, 2, or 3) and the corresponding LPNO coupled cluster method with single- and double excitations (LPNO-CCSD) is described. A detailed anal. alongside pseudocode is presented for the most important computational steps. The scaling with respect to the no. of processors is reasonable and speedups of about 10 with 14 processors have been found in benchmark calcns. (wall-clock time). The most important factor limiting the efficiency of the scaling with respect to the no. of processors is probably the limited bandwidth of the presently prevailing multicore machines. The parallel LPNO methods were applied to study weak intermol. interactions. Initially, the well-established S22 set of mols. was studied. The mean abs. error resulting from the use of the LPNO-CEPA/1 method relative to the most recent CCSD(T) ref. data is found to be 0.24 kcal/mol. Thus, LPNO-CEPA/1 holds great promise for the efficient ab initio treatment of weak intermol. interactions. In order to demonstrate the applicability of the methods to real systems, a two-dimensional potential energy surface for a trimer of 2,4-dihydroxy-3-acetyl-6-Me acetophenone [C11H12O4] (81 atoms, 1296 basis functions, 133 single points) has been calcd. with the LPNO-CEPA/1 method. In this system, a clear distinction can be made between hydrogen bonding and π-π interactions. The global min. on the PES obtained from the calcns. agrees excellently with the exptl. detd. crystal structure. By contrast, popular d. functional methods show no discernible min.
290
Liakos, D. G.; Neese, F. Improved Correlation Energy Extrapolation Schemes Based on Local Pair Natural Orbital Methods J. Phys. Chem. A 2012, 116 (19) 4801– 4816 DOI: 10.1021/jp302096v
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290
Improved Correlation Energy Extrapolation Schemes Based on Local Pair Natural Orbital Methods
Liakos, Dimitrios G.; Neese, Frank
Journal of Physical Chemistry A (2012), 116 (19), 4801-4816CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
It is well-known that the basis set limit is difficult to reach in correlated post Hartree-Fock ab initio calcns. One possible route forward is to employ basis set extrapolation schemes. In order to avoid prohibitively expensive calcns., the highest level calcn. (typically based on the "gold std." coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T)) is only performed with the smallest basis set, and the remaining basis set incompleteness is estd. at a lower level of theory, typically second-order Moeller-Plesset perturbation theory (MP2). In this work, we provide a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approxn., version 1 (CEPA/1) or the local pair natural orbital version of this method (LPNO-CEPA/1). It is shown that the MP2 method achieves apparent accuracy only due to error cancellation. Systematically more accurate results at small addnl. computational cost are obtained if the MP2 step is replaced by LPNO-CEPA/1. The errors of LPNO-CEPA/1 relative to canonical CEPA/1 are negligible. Owing to the highly systematic nature of the deviations between canonical and LPNO methods, basis set extrapolation reduces the LPNO errors in the total energies by 1 order of magnitude (∼0.2 kcal/mol) and errors in energy differences to essentially zero. Using the CCSD(T)/LPNO-CEPA/1-based extrapolation scheme, new ref. values are proposed for the recently published S66 set of interaction energies. The deviations between the new values and the original interactions energies are mostly very small but reach values up to 0.3 kcal/mol.
291
Schwabe, T. Accurate and Fast Treatment of Large Molecular Systems: Assessment of CEPA and pCCSD within the Local Pair Natural Orbital Approximation J. Comput. Chem. 2012, 33 (26) 2067– 2072 DOI: 10.1002/jcc.23042
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292
Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method J. Chem. Phys. 2013, 138 (3) 034106 DOI: 10.1063/1.4773581
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292
An efficient and near linear scaling pair natural orbital based local coupled cluster method
Riplinger, Christoph; Neese, Frank
Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
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Sancho-García, J. C.; Aragó, J.; Ortí, E.; Olivier, Y. Obtaining the Lattice Energy of the Anthracene Crystal by Modern yet Affordable First-Principles Methods J. Chem. Phys. 2013, 138 (20) 204304 DOI: 10.1063/1.4806436
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294
Grimme, S. Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory Chem. - Eur. J. 2012, 18 (32) 9955– 9964 DOI: 10.1002/chem.201200497
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Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory
Grimme, Stefan
Chemistry - A European Journal (2012), 18 (32), 9955-9964, S9955/1-S9955/53CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
The equil. assocn. free enthalpies ΔGa for typical supramol. complexes in soln. are calcd. by ab initio quantum chem. methods. Ten neutral and three pos. charged complexes with exptl. ΔGa values in the range 0 to -21 kcal mol-1 (on av. -6 kcal mol-1) are investigated. The theor. approach employs a (non-dynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion cor. d. functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to det. structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calcns. Low-lying vibrational modes are treated by a free-rotor approxn. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60 kcal mol-1 (up to 200% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semi-local (TPSS) and a hybrid d. functional (PW6B95) have been tested. Although the ΔGa values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔGa values with errors of only 2 kcal mol-1 on av. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramol. chem. and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.
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Calbo, J.; Ortí, E.; Sancho-García, J. C.; Aragó, J. Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van Der Waals Corrections J. Chem. Theory Comput. 2015, 11 (3) 932– 939 DOI: 10.1021/acs.jctc.5b00002
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295
Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections
Calbo, Joaquin; Orti, Enrique; Sancho-Garcia, Juan C.; Arago, Juan
Journal of Chemical Theory and Computation (2015), 11 (3), 932-939CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We present a thorough assessment of the performance of some representative double-hybrid d. functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting mol. systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of ref. interaction energies was computed for the supramol. complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the d. functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate assocn. energies very close to the chem. accuracy. Overall, the NL van der Waals approach combined with proper d. functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramol. systems.
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Pitoňák, M.; Řezáč, J.; Hobza, P. Spin-Component Scaled Coupled-Clusters Singles and Doubles Optimized towards Calculation of Noncovalent Interactions Phys. Chem. Chem. Phys. 2010, 12 (33) 9611– 9614 DOI: 10.1039/c0cp00158a
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297
Grimme, S. Improved Second-Order Møller–Plesset Perturbation Theory by Separate Scaling of Parallel-and Antiparallel-Spin Pair Correlation Energies J. Chem. Phys. 2003, 118 (20) 9095– 9102 DOI: 10.1063/1.1569242
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298
Szabados, Á. Theoretical Interpretation of Grimme’s Spin-Component-Scaled Second Order Møller-Plesset Theory J. Chem. Phys. 2006, 125 (21) 214105 DOI: 10.1063/1.2404660
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298
Theoretical interpretation of Grimme's spin-component-scaled second order Moller-Plesset theory
Szabados, Agnes
Journal of Chemical Physics (2006), 125 (21), 214105/1-214105/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
It is shown that spin-component-scaled second order Moller-Plesset theory proposed by Grimme [J. Chem. Phys. 118, 9095 (2003)] can be interpreted as a two-parameter scaling of the zero order Hamiltonian, a generalization of the approach reported by Feenberg [Phys. Rev. 103, 1116 (1956)].
299
Fink, R. F. Spin-Component-Scaled Møller–Plesset (SCS-MP) Perturbation Theory: A Generalization of the MP Approach with Improved Properties J. Chem. Phys. 2010, 133 (17) 174113 DOI: 10.1063/1.3503041
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300
Hill, J. G.; Platts, J. A. Spin-Component Scaling Methods for Weak and Stacking Interactions J. Chem. Theory Comput. 2007, 3 (1) 80– 85 DOI: 10.1021/ct6002737
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300
Spin-Component Scaling Methods for Weak and Stacking Interactions
Hill, J. Grant; Platts, James A.
Journal of Chemical Theory and Computation (2007), 3 (1), 80-85CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
New scaling parameters are presented for use in the spin-component scaled (SCS) variant of d. fitted local second-order Moller-Plesset perturbation theory (DF-LMP2) that have been optimized for use in evaluating the interaction energy between nucleic acid base pairs. The optimal set of parameters completely neglects the contribution from antiparallel-spin electron pairs to the MP2 energy while scaling the parallel contribution by 1.76. These spin-component scaled for nucleobases (SCSN) parameters are obtained by minimizing, with respect to SCS parameters, the rms interaction energy error relative to the best available literature values, over a set of ten stacked nucleic acid base pairs. The applicability of this scaling to a wide variety of noncovalent interactions is verified through evaluation of a larger set of model complexes, including those dominated by dispersion and electrostatics.
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Hill, J. G.; Platts, J. A. Calculating Stacking Interactions in Nucleic Acid Base-Pair Steps Using Spin-Component Scaling and Local Second Order Møller–Plesset Perturbation Theory Phys. Chem. Chem. Phys. 2008, 10 (19) 2785– 2791 DOI: 10.1039/b718691f
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302
Karton, A.; Tarnopolsky, A.; Lamere, J.-F.; Schatz, G. C.; Martin, J. M. Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics J. Phys. Chem. A 2008, 112 (50) 12868– 12886 DOI: 10.1021/jp801805p
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302
Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics
Karton, Amir; Tarnopolsky, Alex; Lamere, Jean-Francois; Schatz, George C.; Martin, Jan M. L.
Journal of Physical Chemistry A (2008), 112 (50), 12868-12886CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
We present a no. of near-exact, nonrelativistic, Born-Oppenheimer ref. data sets for the parametrization of more approx. methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochem. protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small mols. that cover varying degrees of non-dynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calcd. DFT values with exptl. atomization energies is hampered by comparatively large exptl. uncertainties in many exptl. values and compds. errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. The optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimol. and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x,y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochem. and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochem. and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochem., B2GP-PLYP appears to be the more robust toward non-dynamical correlation and strongly polar character. We addnl. find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.
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Distasio, R. A., Jr.; Head-Gordon, M. Optimized Spin-Component Scaled Second-Order Møller-Plesset Perturbation Theory for Intermolecular Interaction Energies Mol. Phys. 2007, 105 (8) 1073– 1083 DOI: 10.1080/00268970701283781
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Marchetti, O.; Werner, H.-J. Accurate Calculations of Intermolecular Interaction Energies Using Explicitly Correlated Coupled Cluster Wave Functions and a Dispersion-Weighted MP2 Method J. Phys. Chem. A 2009, 113 (43) 11580– 11585 DOI: 10.1021/jp9059467
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Riley, K. E.; Platts, J. A.; Řezáč, J.; Hobza, P.; Hill, J. G. Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions J. Phys. Chem. A 2012, 116 (16) 4159– 4169 DOI: 10.1021/jp211997b
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306
Takatani, T.; Hohenstein, E. G.; Sherrill, C. D. Improvement of the Coupled-Cluster Singles and Doubles Method via Scaling Same-and Opposite-Spin Components of the Double Excitation Correlation Energy J. Chem. Phys. 2008, 128 (12) 124111 DOI: 10.1063/1.2883974
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Jung, Y.; Lochan, R. C.; Dutoi, A. D.; Head-Gordon, M. Scaled Opposite-Spin Second Order Møller–Plesset Correlation Energy: An Economical Electronic Structure Method J. Chem. Phys. 2004, 121 (20) 9793– 9802 DOI: 10.1063/1.1809602
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Lochan, R. C.; Jung, Y.; Head-Gordon, M. Scaled Opposite Spin Second Order Møller-Plesset Theory with Improved Physical Description of Long-Range Dispersion Interactions J. Phys. Chem. A 2005, 109 (33) 7598– 7605 DOI: 10.1021/jp0514426
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Takatani, T.; Sherrill, C. D. Performance of Spin-Component-Scaled Møller–Plesset Theory (SCS-MP2) for Potential Energy Curves of Noncovalent Interactions Phys. Chem. Chem. Phys. 2007, 9 (46) 6106– 6114 DOI: 10.1039/b709669k
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Antony, J.; Grimme, S. Is Spin-Component Scaled Second-Order Møller-Plesset Perturbation Theory an Appropriate Method for the Study of Noncovalent Interactions in Molecules? J. Phys. Chem. A 2007, 111 (22) 4862– 4868 DOI: 10.1021/jp070589p
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Bachorz, R. A.; Bischoff, F. A.; Höfener, S.; Klopper, W.; Ottiger, P.; Leist, R.; Frey, J. A.; Leutwyler, S. Scope and Limitations of the SCS-MP2 Method for Stacking and Hydrogen Bonding Interactions Phys. Chem. Chem. Phys. 2008, 10 (19) 2758– 2766 DOI: 10.1039/b718494h
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King, R. A. On the Accuracy of Spin-Component-Scaled Perturbation Theory (SCS-MP2) for the Potential Energy Surface of the Ethylene Dimer Mol. Phys. 2009, 107 (8–12) 789– 795 DOI: 10.1080/00268970802641242
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Grabowski, I.; Fabiano, E.; Sala, F. D. A Simple Non-Empirical Procedure for Spin-Component-Scaled MP2 Methods Applied to the Calculation of the Dissociation Energy Curve of Noncovalently-Interacting Systems Phys. Chem. Chem. Phys. 2013, 15 (37) 15485– 15493 DOI: 10.1039/c3cp51431e
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314
Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van Der Waals Complexes Chem. Rev. 1994, 94 (7) 1887– 1930 DOI: 10.1021/cr00031a008
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Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes
Jeziorski, Bogumil; Moszynski, Robert; Szalewicz, Krzysztof
Chemical Reviews (Washington, DC, United States) (1994), 94 (7), 1887-930CODEN: CHREAY; ISSN:0009-2665.
The topics reviewed with 445 refs. include: polarization theory; exchange effects; multipole expansion of the interaction energy; charge-overlap effects and bipolar expansion of polarization energies; the intramonomer electron correlation problem and many-body formulation of symmetry-adapted perturbation theory; and applications.
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Misquitta, A. J.; Podeszwa, R.; Jeziorski, B.; Szalewicz, K. Intermolecular Potentials Based on Symmetry-Adapted Perturbation Theory with Dispersion Energies from Time-Dependent Density-Functional Calculations J. Chem. Phys. 2005, 123 (21) 214103 DOI: 10.1063/1.2135288
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Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations
Misquitta, Alston J.; Podeszwa, Rafal; Jeziorski, Bogumil; Szalewicz, Krzysztof
Journal of Chemical Physics (2005), 123 (21), 214103/1-214103/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calcn. of the dispersion energy utilizing frequency-dependent d. susceptibilities of monomers obtained from time-dependent d.-functional theory (DFT). In the present paper, we report numerical calcns. for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer sepns., including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the min. and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calcg. the dispersion and other interaction energy components at this level of accuracy.
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Hesselmann, A.; Jansen, G.; Schütz, M. Interaction Energy Contributions of H-Bonded and Stacked Structures of the AT and GC DNA Base Pairs from the Combined Density Functional Theory and Intermolecular Perturbation Theory Approach J. Am. Chem. Soc. 2006, 128 (36) 11730– 11731 DOI: 10.1021/ja0633363
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Rezáč, J.; Riley, K. E.; Hobza, P. S66: A Well-Balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures J. Chem. Theory Comput. 2011, 7 (8) 2427– 2438 DOI: 10.1021/ct2002946
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S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures
Rezac, Jan; Riley, Kevin E.; Hobza, Pavel
Journal of Chemical Theory and Computation (2011), 7 (8), 2427-2438CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
With numerous new quantum chem. methods being developed in recent years and the promise of even more new methods to be developed in the near future, it is clearly crit. that highly accurate, well-balanced, ref. data for many different at. and mol. properties be available for the parametrization and validation of these methods. One area of research that is of particular importance in many areas of chem., biol., and material science is the study of noncovalent interactions. Because these interactions are often strongly influenced by correlation effects, it is necessary to use computationally expensive high-order wave function methods to describe them accurately. Here, the authors present a large new database of interaction energies calcd. using an accurate CCSD(T)/CBS scheme. Data are presented for 66 mol. complexes, at their ref. equil. geometries and at 8 points systematically exploring their dissocn. curves; in total, the database contains 594 points: 66 at equil. geometries, and 528 in dissocn. curves. The data set is designed to cover the most common types of noncovalent interactions in biomols., while keeping a balanced representation of dispersion and electrostatic contributions. The data set is therefore well suited for testing and development of methods applicable to bioorg. systems. In addn. to the benchmark CCSD(T) results, the authors also provide decompns. of the interaction energies by DFT-SAPT calcns. The data set was used to test several correlated QM methods, including those parametrized specifically for noncovalent interactions. Among these, the SCS-MI-CCSD method outperforms all other tested methods, with a root-mean-square error of 0.08 kcal/mol for the S66 data set.
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Sinnokrot, M. O.; Sherrill, C. D. Substituent Effects in Π–π Interactions: Sandwich and T-Shaped Configurations J. Am. Chem. Soc. 2004, 126 (24) 7690– 7697 DOI: 10.1021/ja049434a
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Substituent Effects in π-π Interactions: Sandwich and T-Shaped Configurations
Sinnokrot, Mutasem Omar; Sherrill, C. David
Journal of the American Chemical Society (2004), 126 (24), 7690-7697CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Sandwich and T-shaped configurations of benzene dimer, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile are studied by coupled-cluster theory to elucidate how substituents tune π-π interactions. All substituted sandwich dimers bind more strongly than benzene dimer, whereas the T-shaped configurations bind more or less favorably depending on the substituent. Symmetry-adapted perturbation theory (SAPT) indicates that electrostatic, dispersion, induction, and exchange-repulsion contributions are all significant to the overall binding energies, and all but induction are important in detg. relative energies. Models of π-π interactions based solely on electrostatics, such as the Hunter-Sanders rules, do not seem capable of explaining the energetic ordering of the dimers considered.
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Sure, R.; Grimme, S. Corrected Small Basis Set Hartree-Fock Method for Large Systems J. Comput. Chem. 2013, 34 (19) 1672– 1685 DOI: 10.1002/jcc.23317
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Corrected small basis set Hartree-Fock method for large systems
Sure, Rebecca; Grimme, Stefan
Journal of Computational Chemistry (2013), 34 (19), 1672-1685CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
A quantum chem. method based on a Hartree-Fock calcn. with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge mol. systems. The method is suggested as a partial replacement of semiempirical approaches or d. functional theory (DFT) in particular when self-interaction errors are acute. In order to get accurate results three phys. plausible atom pair-wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short-ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so-called Hartee-Fock-3c (HF-3c) method is tested for geometries of small org. mols., interaction energies and geometries of noncovalently bound complexes, for supramol. systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost. © 2013 Wiley Periodicals, Inc.
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Goerigk, L.; Collyer, C. A.; Reimers, J. R. Recommending Hartree–Fock Theory with London-Dispersion and Basis-Set-Superposition Corrections for the Optimization or Quantum Refinement of Protein Structures J. Phys. Chem. B 2014, 118 (50) 14612– 14626 DOI: 10.1021/jp510148h
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Brandenburg, J.; Grimme, S. Dispersion Corrected Hartree-Fock and Density Functional Theory for Organic Crystal Structure Prediction Top. Curr. Chem. 2013, 345, 1 DOI: 10.1007/128_2013_488
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Brandenburg, J. G.; Hochheim, M.; Bredow, T.; Grimme, S. Low-Cost Quantum Chemical Methods for Noncovalent Interactions J. Phys. Chem. Lett. 2014, 5 (24) 4275– 4284 DOI: 10.1021/jz5021313
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Low-Cost Quantum Chemical Methods for Noncovalent Interactions
Brandenburg, Jan Gerit; Hochheim, Manuel; Bredow, Thomas; Grimme, Stefan
Journal of Physical Chemistry Letters (2014), 5 (24), 4275-4284CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
A review. The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chem., ranging from supramol. host-guest complexes and biomol. applications to the challenging task of crystal structure prediction. While London dispersion inclusive d. functional theory (DFT-D) can be applied, faster "low-cost" methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical mol.-orbital-based methods. Various levels of approxns. are discussed based either on canonical Hartree-Fock or on semilocal d. functionals. The performance for intermol. interactions is examd. on various small to large mol. complexes and org. solids covering many different chem. groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle d. functional theory results. The mean unsigned deviations of binding energies from ref. data are typically 10-30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.
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Grimme, S.; Brandenburg, J. G.; Bannwarth, C.; Hansen, A. Consistent Structures and Interactions by Density Functional Theory with Small Atomic Orbital Basis Sets J. Chem. Phys. 2015, 143 (5) 054107 DOI: 10.1063/1.4927476
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Consistent structures and interactions by density functional theory with small atomic orbital basis sets
Grimme, Stefan; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
Journal of Chemical Physics (2015), 143 (5), 054107/1-054107/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A d. functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chem. systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approxn. in a modified global hybrid functional with a relatively large amt. of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta AO Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold cor. (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a phys. sound and asymptotically correct manner. PBEh-3c yields good results for thermochem. properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equil. structures, a new compilation of std. test sets is suggested. These consist of small (light) mols., partially flexible, medium-sized org. mols., mols. comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate ref. data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calcns. conducted for mol. crystals to test structures (including cell vols.) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calcns. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theor. chem. and physics. (c) 2015 American Institute of Physics.
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Stewart, J. J. Optimization of Parameters for Semiempirical Methods I. Method J. Comput. Chem. 1989, 10 (2) 209– 220 DOI: 10.1002/jcc.540100208
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Optimization of parameters for semiempirical methods. I. Method
Stewart, James J. P.
Journal of Computational Chemistry (1989), 10 (2), 209-20CODEN: JCCHDD; ISSN:0192-8651.
A new method for obtaining optimized parameters for semiempirical methods is developed and applied to the MNDO method. The method uses derivs. of calcd. values for properties with respect to adjustable parameters to obtain the optimized values of parameters. The large increase in speed is a result of using a simple series expression for calcd. values of properties rather than employing full semiempirical calcns. With this optimization procedure, the rate-detg. step for parameterizing elements changes from the mechanics of parameterization to the assembling of exptl. ref. data.
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Weber, W.; Thiel, W. Orthogonalization Corrections for Semiempirical Methods Theor. Chem. Acc. 2000, 103 (6) 495– 506 DOI: 10.1007/s002149900083
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Orthogonalization corrections for semiempirical methods
Weber, Wolfgang; Thiel, Walter
Theoretical Chemistry Accounts (2000), 103 (6), 495-506CODEN: TCACFW; ISSN:1432-881X. (Springer-Verlag)
Based on a general discussion of orthogonalization effects, two new one-electron orthogonalization corrections are derived to improve existing semiempirical models at the NDDO level. The first one accounts for valence-shell orthogonalization effects on the resonance integrals, while the second one includes the dominant repulsive core-valence interactions through an effective core potential. The corrections for the resonance integrals consist of three-center terms which incorporate stereodiscriminating properties into the two-center matrix elements of the core Hamiltonian. They provide a better description of conformational properties, which is rationalized qual. and demonstrated through numerical calcns. on small model systems. The proposed corrections are part of a new general-purpose semiempirical method which will be described elsewhere.
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Stewart, J. J. Optimization of Parameters for Semiempirical Methods VI: More Modifications to the NDDO Approximations and Re-Optimization of Parameters J. Mol. Model. 2013, 19 (1) 1– 32 DOI: 10.1007/s00894-012-1667-x
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Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters
Stewart, James J. P.
Journal of Molecular Modeling (2013), 19 (1), 1-32CODEN: JMMOFK; ISSN:0948-5023. (Springer)
Modern semiempirical methods are of sufficient accuracy when used in the modeling of mols. of the same type as used as ref. data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using exptl. and high-level ab initio ref. data, augmented by a new type of ref. data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approxns.: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Av. unsigned errors (AUEs) in geometry and ΔH f for PM7 were reduced relative to PM6; for simple gas-phase org. systems, the AUE in bond lengths decreased by about 5 % and the AUE in ΔH f decreased by about 10 %; for org. solids, the AUE in ΔH f dropped by 60 % and the redn. was 33.3 % for geometries. A two-step process (PM7-TS) for calcg. the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple org. reactions was decreased from values of 12.6 kcal/mol-1 in PM6 and 10.8 kcal/mol-1 in PM7 to 3.8 kcal/mol-1. The origins of the errors in NDDO methods have been examd., and were found to be attributable to inadequate and inaccurate ref. data. This conclusion provides insight into how these methods can be improved.
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Tuttle, T.; Thiel, W. OM X-D: Semiempirical Methods with Orthogonalization and Dispersion Corrections. Implementation and Biochemical Application Phys. Chem. Chem. Phys. 2008, 10 (16) 2159– 2166 DOI: 10.1039/b718795e
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Thiel, W. Semiempirical Quantum–chemical Methods Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4 (2) 145– 157 DOI: 10.1002/wcms.1161
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Semiempirical quantum-chemical methods
Thiel, Walter
Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (2), 145-157CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
The semiempirical methods of quantum chem. are reviewed, with emphasis on established NDDO-based methods (MNDO, AM1, PM3) and on the more recent orthogonalization-cor. methods (OM1, OM2, OM3). After a brief historical overview, the methodol. is presented in nontech. terms, covering the underlying concepts, parameterization strategies, and computational aspects, as well as linear scaling and hybrid approaches. The application section addresses selected recent benchmarks and surveys ground-state and excited-state studies, including recent OM2-based excited-state dynamics investigations.
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Řezáč, J.; Fanfrlík, J.; Salahub, D.; Hobza, P. Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes J. Chem. Theory Comput. 2009, 5 (7) 1749– 1760 DOI: 10.1021/ct9000922
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Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes
Rezac, Jan; Fanfrlik, Jindrich; Salahub, Dennis; Hobza, Pavel
Journal of Chemical Theory and Computation (2009), 5 (7), 1749-1760CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Because of its construction and parametrization for more than 80 elements, the semiempirical quantum chem. PM6 method is superior to other similar methods. Despite its advantages, however, the PM6 method fails for the description of noncovalent interactions, specifically the dispersion energy and H-bonding. Upon inclusion of correction terms for dispersion and H-bonding, the performance of the method was found to be dramatically improved. The former correction included two parameters in the damping function that were parametrized to reproduce the benchmark interaction energies [CCSD(T)/complete basis set (CBS) limit] of the dispersion-bonded complexes from the S22 data set. The latter correction was parametrized on an extended set of H-bonded stabilization energies detd. at the MP2/cc-pVTZ level. The resulting PM6-DH method was tested on the S22 data set, for which chem. accuracy (error < 1 kcal/mol) was achieved, and also on the JSCH2005 set, for which significant improvement over the original PM6 method was also obtained. Implementation of anal. gradients allows very efficient geometry optimization, which, for all complexes, provides better agreement with the benchmark data. Excellent results were also achieved for small peptides, and here again, chem. accuracy was obtained (i.e., the error with respect to CCSD(T)/CBS results was smaller than 1 kcal/mol). The performance of the technique was finally demonstrated on extended complexes, namely, the porphine dimer and various graphene models with DNA bases and base pairs, where the PM6-DH stabilization energies agree very well with available benchmark data obtained with DFT-D, SCS-MP2, and MP2.5 methods. The PM6-DH calcns. are very efficient and can be routinely applied for systems of up to 1000 atoms. For nonarom. systems, the use of a linear scaling version of the SCF procedure based on localized orbitals speeds up the method significantly and allows one to investigate systems with several thousand atoms. The method can thus replace force fields, which face basic problems for the description of quantum effects, in many applications.
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Korth, M.; Pitoňák, M.; Řezáč, J.; Hobza, P. A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods J. Chem. Theory Comput. 2010, 6 (1) 344– 352 DOI: 10.1021/ct900541n
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A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods
Korth, Martin; Pitonak, Michal; Rezac, Jan; Hobza, Pavel
Journal of Chemical Theory and Computation (2010), 6 (1), 344-352CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Semiempirical methods could offer a feasible compromise between ab initio and empirical approaches for the calcn. of large mols. with biol. relevance. A key problem for attempts in this direction is the rather bad performance of current semiempirical methods for noncovalent interactions, esp. hydrogen-bonding. On the basis of the recently introduced PM6-DH method, which includes empirical corrections for dispersion (D) and hydrogen-bond (H) interactions, we have developed an improved and transferable H-bonding correction for semiempirical quantum chem. methods. The performance of the improved correction is evaluated for PM6, AM1, OM3, and SCC-DFTB (enhanced by std. empirical dispersion corrections) with several test sets for noncovalent interactions and is shown to reach the quality of current DFT-D approaches for these types of problems.
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Porezag, D.; Frauenheim, T.; Köhler, T.; Seifert, G.; Kaschner, R. Construction of Tight-Binding-like Potentials on the Basis of Density-Functional Theory: Application to Carbon Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51 (19) 12947 DOI: 10.1103/PhysRevB.51.12947
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Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon
Porezag, D.; Frauenheim, Th.; Koehler, Th.; Seifert, G.; Kaschner, R.
Physical Review B: Condensed Matter (1995), 51 (19), 12947-57CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The authors present a d.-functional-based scheme for detg. the necessary parameters of common nonorthogonal tight-binding (TB) models within the framework of the LCAO formalism using the local-d. approxn. (LDA). By only considering two-center integrals the Hamiltonian and overlap matrix elements are calcd. out of suitable input densities and potentials rather than fitted to exptl. data. Anal. functions can be derived for the C-C, C-H, and H-H Hamiltonians and overlap matrix elements. The usual short-range repulsive potential appearing in most TB models is fitted to self-consistent calcns. performed within the LDA. The calcn. of forces is easy and allows an application of the method to mol.-dynamics simulations. Despite its extreme simplicity, the method is transferable to complex carbon and hydrocarbon systems. The detn. of equil. geometries, total energies, and vibrational modes of carbon clusters, hydrocarbon mols., and solid-state modifications of carbon yield results showing an overall good agreement with more sophisticated methods.
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Seifert, G.; Porezag, D.; Frauenheim, T. Calculations of Molecules, Clusters, and Solids with a Simplified LCAO-DFT-LDA Scheme Int. J. Quantum Chem. 1996, 58 (2) 185– 192 DOI: 10.1002/(SICI)1097-461X(1996)58:2<185::AID-QUA7>3.3.CO;2-B
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333
Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen Bonding and Stacking Interactions of Nucleic Acid Base Pairs: A Density-Functional-Theory Based Treatment J. Chem. Phys. 2001, 114 (12) 5149– 5155 DOI: 10.1063/1.1329889
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Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment
Elstner, Marcus; Hobza, Pavel; Frauenheim, Thomas; Suhai, Sandor; Kaxiras, Efthimios
Journal of Chemical Physics (2001), 114 (12), 5149-5155CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We extend an approx. d. functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irresp. of the correlation function applied. An empirical formula, consisting of an R-6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coeff., which is calcd. from exptl. at. polarizabilities, can be consistently added to the total energy expression of the method. We apply this approx. DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.
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Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Materials Properties Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58 (11) 7260 DOI: 10.1103/PhysRevB.58.7260
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Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties
Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.
Physical Review B: Condensed Matter and Materials Physics (1998), 58 (11), 7260-7268CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
We outline details about an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability. The method is based on a second-order expansion of the Kohn-Sham total energy in d.-functional theory (DFT) with respect to charge-d. fluctuations. The zeroth-order approach is equiv. to a common std. non-self-consistent (TB) scheme, while at second-order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual "band structure" and short-range repulsive terms the final approx. Kohn-Sham energy addnl. includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approx. includes self-interaction contributions of a given atom if the charges are located at one and the same atom. We apply the new SCC scheme to problems where deficiencies within the non-SCC std. TB approach become obvious. We thus considerably improve transferability.
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Kunsági-Máté, S.; Ortmann, E.; Kollár, L.; Szabó, K.; Nikfardjam, M. P. Effect of Ferrous and Ferric Ions on Copigmentation in Model Solutions J. Mol. Struct. 2008, 891 (1–3) 471– 474 DOI: 10.1016/j.molstruc.2008.04.036
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Bondi, A. J. Van Der Waals Volumes and Radii J. Phys. Chem. 1964, 68 (3) 441– 451 DOI: 10.1021/j100785a001
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van der Waals volumes and radii
Bondi, A.
Journal of Physical Chemistry (1964), 68 (3), 441-51CODEN: JPCHAX; ISSN:0022-3654.
Intermol. van der Waals radii of the nonmetallic elements were assembled into a list of recommended values for vol. calcns. These values were arrived at by selecting from the most reliable x-ray diffraction data those which could be reconciled with crystal d. at 0°K. (to give reasonable packing d.), gas kinetic collision cross section, crit. d., and with liquid state properties. A qual. understanding of the nature of van der Waals radii is provided by correlation with the de Broglie wavelength of the outermost valence electron. Tentative values for the van der Waals radii of metallic elements in organometallic compds. are proposed. A list of increments for the vol. of mols. impenetrable to thermal collision, the so-called van der Waals vol., and of the corresponding increments in area per mol. is given.
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As seen in previous sections, we are aware that in principle, CCSD(T), or other methods such as QMC, are more desirable. However, such methods are currently too computationally demanding to be applied to real-world copigmentation systems.
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Freitas, A. A.; Shimizu, K.; Dias, L. G.; Quina, F. H. A Computational Study of Substituted Flavylium Salts and Their Quinonoidal Conjugate-Bases: S0→S1 Electronic Transition, Absolute pKa and Reduction Potential Calculations by DFT and Semiempirical Methods J. Braz. Chem. Soc. 2007, 18 (8) 1537– 1546 DOI: 10.1590/S0103-50532007000800014
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A computational study of substituted flavylium salts and their quinonoidal conjugate-bases: S0→S1 electronic transition, absolute pKa and reduction potential calculations by DFT and semiempirical methods
Freitas, Adilson A.; Shimizu, K.; Dias, Luis G.; Quina, Frank H.
Journal of the Brazilian Chemical Society (2007), 18 (8), 1537-1546CODEN: JOCSET; ISSN:0103-5053. (Sociedade Brasileira de Quimica)
The electronic transitions for flavylium cations and quinonoidal bases of 17 substituted flavylium salts have been studied at semiempirical and DFT (d. functional theory) levels. Solvent effect on electronic spectra was included by Polarizable Continuum Model, PCM. We assigned longest-wavelength absorption maxima to HOMO→LUMO transition. Both levels of theory gave good results for electronic transitions of flavylium cations whereas only TDDFT-PCM calcns. could be used for electronic transitions of their quinonoidal bases. We also performed abs. pKa calcns. of nine flavylium salts at DFT level. The pKa calcd. values by our PCM parameterization gave excellent results with mean abs. deviation less than a half of one pKa unit. One-electron redn. potentials were carried out for 5 flavylium cations at DFT level. The theor. results found were in good agreement with exptl. values after adjustment for a systematic deviation.
339
Sakata, K.; Saito, N.; Honda, T. Ab Initio Study of Molecular Structures and Excited States in Anthocyanidins Tetrahedron 2006, 62 (15) 3721– 3731 DOI: 10.1016/j.tet.2006.01.081
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Ab initio study of molecular structures and excited states in anthocyanidins
Sakata, Ken; Saito, Norio; Honda, Toshio
Tetrahedron (2006), 62 (15), 3721-3731CODEN: TETRAB; ISSN:0040-4020. (Elsevier B.V.)
The structural and electronic characters of four types of hydroxyl group-substituted anthocyanidins (pelargonidin, cyanidin, delphinidin, and aurantinidin) were examd. using quantum chem. calcns. For these cationic mols., both the planar and non-planar structures in the electronic ground state were detd. at the B3LYP/D95 level of theory. We revealed that the planar structure is slightly more stable than the non-planar structure for each mol. For the optimized planar structures, single excitation-CI (SE-CI) based on the RHF (RHF) wave function was evaluated and the electronic character in the low-excited states was discussed in terms of the MO theory. Symmetry adapted cluster (SAC)/SAC-CI calcns. were also carried out to est. the excitation energies precisely. The results showed that hydroxylation of the Ph group causes a change in the excitation energies without taking the solvent effects into account. The results are in agreement with spectral expts. and previous MO calcns.
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Anouar, E. H.; Gierschner, J.; Duroux, J.-L.; Trouillas, P. UV/Visible Spectra of Natural Polyphenols: A Time-Dependent Density Functional Theory Study Food Chem. 2012, 131 (1) 79– 89 DOI: 10.1016/j.foodchem.2011.08.034
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UV/Visible spectra of natural polyphenols: A time-dependent density functional theory study
Anouar, El Hassane; Gierschner, Johannes; Duroux, Jean-Luc; Trouillas, Patrick
Food Chemistry (2012), 131 (1), 79-89CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
In addn. to their numerous biol. activities, natural and hemisynthetic polyphenols contribute to the large variety of colors (from red to violet) in nature (e.g., fruit, vegetables, leaves and petals). In order to understand the color variation attributed to the multitude of chem. structures of this wide class of compds., time-dependent d. functional quantum-chem. calcns. at the B3P86/6-311+G(d,p) level of theory appears as a relevant and efficient tool. The UV/Vis properties of 33 polyphenols were systematically investigated, including mainly flavonoids, isoflavonoids and flavonolignans. On the basis of MO anal. we established the structure-property relationship, inter alia showing the role of π orbital (de-)localization, mesomeric (+M) effects of hydroxyl groups and structural modification of the mol. backbone. The results might help in the future, for example, for the prediction of novel hemisynthetic compds.
341
Millot, M.; Di Meo, F.; Tomasi, S.; Boustie, J.; Trouillas, P. Photoprotective Capacities of Lichen Metabolites: A Joint Theoretical and Experimental Study. J. Photochem. Photobiol., B 111, 17– 26. DOI: 10.1016/j.jphotobiol.2012.03.005
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Carvalho, A. R. F.; Oliveira, J.; De Freitas, V.; Mateus, N.; Melo, A. Unusual Color Change of Vinylpyranoanthocyanin–Phenolic Pigments J. Agric. Food Chem. 2010, 58 (7) 4292– 4297 DOI: 10.1021/jf904246g
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Quartarolo, A. D.; Russo, N. A Computational Study (TDDFT and RICC2) of the Electronic Spectra of Pyranoanthocyanins in the Gas Phase and Solution J. Chem. Theory Comput. 2011, 7 (4) 1073– 1081 DOI: 10.1021/ct2000974
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A Computational Study (TDDFT and RICC2) of the Electronic Spectra of Pyranoanthocyanins in the Gas Phase and Solution
Quartarolo, Angelo Domenico; Russo, Nino
Journal of Chemical Theory and Computation (2011), 7 (4), 1073-1081CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The conformational structures and UV-vis absorption electronic spectra of a class of derived anthocyanin mols. (pyranoanthocyanins) have been investigated mainly by means of d. functional (DFT) and time-dependent DFT methods. Pyranoanthocyanins are natural pigments present in aged wines and absorb at shorter wavelengths (around 500 nm) than the parent anthocyanin compds., giving an orange-brown colored soln. The investigated mols. are derived from the reaction of glycosylated malvidin, peonidin, and petunidin with enolizable mols. (acetaldehyde and pyruvic acid) and vinyl derivs. During wine storage, the concn. of pyranoanthocyanins increases with time, and anal. measurements (e.g., UV-vis spectroscopy) can characterize aged wines by color anal. The prediction of absorption electronic spectra from TDDFT results, with the inclusion of water bulk solvation effects through the conductor-like polarizable continuum model, gives an abs. mean deviation from exptl. absorption maxima of 0.1 eV and a good reprodn. of the spectra line shape over the visible range of the spectrum. TDDFT calcd. excitation energies agree with those obtained from ab initio multireference coupled cluster with the resoln. of identity approxn. (RICC2) methods, calcd. at DFT gas-phase geometries.
344
Milián-Medina, B.; Gierschner, J. Computational Design of Low Singlet–triplet Gap All-Organic Molecules for OLED Application Org. Electron. 2012, 13 (6) 985– 991 DOI: 10.1016/j.orgel.2012.02.010
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Computational design of low singlet-triplet gap all-organic molecules for OLED application
Milian-Medina, Begona; Gierschner, Johannes
Organic Electronics (2012), 13 (6), 985-991CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
It was recently reported that external quantum efficiency in org. LEDs can be substantially enhanced when triplet excitons are harvested through upconversion by E-type delayed fluorescence in materials with small singlet-triplet energy gap ΔEST, based on donor-acceptor (DA) chromophores. Furthermore, org. solar cells (OSCs) might profit from such materials in order to reduce recombination losses. However, targeted design rules for such materials are missing up to now. In this paper, we follow a facile (TD-)DFT-based computational design concept by engineering the fragment frontier orbitals in DA systems. The calcns. show that optimized systems with very small ΔEST in the range of kT can be achieved by balancing the energetic offset between fragment MOs as well as through the nature of the DA connector. Application in OLED will addnl. require small non-radiative rates, which recommends large bandgap materials. Utilization in polymeric DA systems with small ΔEST in OSCs requires the full exploration of the chain length dependence of the resp. oligomers.
345
Dreuw, A.; Weisman, J. L.; Head-Gordon, M. Long-Range Charge-Transfer Excited States in Time-Dependent Density Functional Theory Require Non-Local Exchange J. Chem. Phys. 2003, 119 (6) 2943– 2946 DOI: 10.1063/1.1590951
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Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange
Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin
Journal of Chemical Physics (2003), 119 (6), 2943-2946CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The electrostatic attraction between the sepd. charges in long-range excited charge-transfer states originates from the non-local Hartree-Fock exchange potential and is, thus, a non-local property. Present-day time-dependent d. functional theory employing local exchange-correlation functionals does not capture this effect and therefore fails to describe charge-transfer excited states correctly. A hybrid method that is qual. correct is described.
346
Dreuw, A.; Head-Gordon, M. Single-Reference Ab Initio Methods for the Calculation of Excited States of Large Molecules Chem. Rev. 2005, 105 (11) 4009– 4037 DOI: 10.1021/cr0505627
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Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules
Dreuw, Andreas; Head-Gordon, Martin
Chemical Reviews (Washington, DC, United States) (2005), 105 (11), 4009-4037CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review of single-ref. ab initio excited state methods, which are applicable to large mols. and do not explicitly include correlation through the ground-state wave function. CIS, TDHF, and TDDFT are rigorously introduced by outlining their derivations and theor. footing, where special emphasis is put on their relations to each other. Different methods for the anal. of complicated electronically excited states are reviewed and comparatively discussed. The applicability of the presented methods is outlined, their limitations are show, and out their strengths and weaknesses are pointed out.
347
Casida, M. E.; Gutierrez, F.; Guan, J.; Gadea, F.-X.; Salahub, D.; Daudey, J.-P. Charge-Transfer Correction for Improved Time-Dependent Local Density Approximation Excited-State Potential Energy Curves: Analysis within the Two-Level Model with Illustration for H2 and LiH J. Chem. Phys. 2000, 113 (17) 7062– 7071 DOI: 10.1063/1.1313558
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Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 and LiH
Casida, Mark E.; Gutierrez, Fabien; Guan, Jingang; Gadea, Florent-Xavier; Salahub, Dennis; Daudey, Jean-Pierre
Journal of Chemical Physics (2000), 113 (17), 7062-7071CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Time-dependent d.-functional theory (TDDFT) is an increasingly popular approach for calcg. mol. excitation energies. However, the TDDFT lowest triplet excitation energy, ωT, of a closed-shell mol. often falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphys. behavior occurs because ωT2 must become neg. wherever symmetry breaking lowers the energy of the ground state soln. below that of the symmetry unbroken soln. We use the fact that the ΔSCF method gives a qual. correct first triplet excited state to derive a "charge-transfer correction" (CTC) for the time-dependent local d. approxn. (TDLDA) within the two-level model and the Tamm-Dancoff approxn. (TDA). Although this correction would not be needed for the exact exchange-correlation functional, it is evidently important for a correct description of mol. excited state potential energy surfaces in the TDLDA. As a byproduct of our anal., we show why TDLDA and LDA ΔSCF excitation energies are often very similar near the equil. geometries. The reasoning given here is fairly general and it is expected that similar corrections will be needed in the case of generalized gradient approxns. and hybrid functionals.
348
Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange–correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP) Chem. Phys. Lett. 2004, 393 (1–3) 51– 57 DOI: 10.1016/j.cplett.2004.06.011
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A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
Chemical Physics Letters (2004), 393 (1-3), 51-57CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the std. error function with parameter 0.33.
349
Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–atom Dispersion Corrections Phys. Chem. Chem. Phys. 2008, 10 (44) 6615– 6620 DOI: 10.1039/b810189b
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Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
Chai, Jeng-Da; Head-Gordon, Martin
Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
350
Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Double-Hybrid Density Functionals J. Chem. Phys. 2009, 131 (17) 174105 DOI: 10.1063/1.3244209
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Long-range corrected double-hybrid density functionals
Chai, Jeng-Da; Head-Gordon, Martin
Journal of Chemical Physics (2009), 131 (17), 174105/1-174105/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We extend the range of applicability of our previous long-range cor. (LC) hybrid functional, ωB97X, with a nonlocal description of electron correlation, inspired by second-order Moller-Plesset (many-body) perturbation theory. This LC "double-hybrid" d. functional, denoted as ωB97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calcns. using triple and quadruple zeta basis sets), and also sep. using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calcns. (as well as training set results), ωB97X-2 yields high accuracy for thermochem., kinetics, and noncovalent interactions. In addn., owing to its high fraction of exact Hartree-Fock exchange, ωB97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as sym. homonuclear radical cations. (c) 2009 American Institute of Physics.
351
Caricato, M.; Trucks, G. W.; Frisch, M. J.; Wiberg, K. B. Oscillator Strength: How Does TDDFT Compare to EOM-CCSD? J. Chem. Theory Comput. 2011, 7 (2) 456– 466 DOI: 10.1021/ct100662n
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Oscillator Strength: How Does TDDFT Compare to EOM-CCSD?
Caricato, Marco; Trucks, Gary W.; Frisch, Michael J.; Wiberg, Kenneth B.
Journal of Chemical Theory and Computation (2011), 7 (2), 456-466CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We compare a large variety of d. functionals against the equation of motion coupled cluster singles and doubles (EOM-CCSD) method for the calcn. of oscillator strengths. Valence and Rydberg states are considered for a test set composed of 11 small org. mols. In our previous work, the same systems and methods were tested against exptl. results for the excitation energies. The results from this investigation confirm our previous findings, i.e., that there is a large difference between the functionals. For the oscillator strength, the av. best agreement with EOM-CCSD is provided by CAM-B3LYP followed by LC-ωPBE and, to a lesser extent, B3P86 and LC-BLYP.
352
Beyhan, S. M.; Götz, A. W.; Ariese, F.; Visscher, L.; Gooijer, C. Computational Study on the Anomalous Fluorescence Behavior of Isoflavones J. Phys. Chem. A 2011, 115 (9) 1493– 1499 DOI: 10.1021/jp109059e
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353
Malcıoğlu, O. B.; Calzolari, A.; Gebauer, R.; Varsano, D.; Baroni, S. Dielectric and Thermal Effects on the Optical Properties of Natural Dyes: A Case Study on Solvated Cyanin J. Am. Chem. Soc. 2011, 133 (39) 15425– 15433 DOI: 10.1021/ja201733v
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Petrone, A.; Cerezo, J.; Ferrer, F. J. A.; Donati, G.; Improta, R.; Rega, N.; Santoro, F. Absorption and Emission Spectral Shapes of a Prototype Dye in Water by Combining Classical/Dynamical and Quantum/Static Approaches J. Phys. Chem. A 2015, 119 (21) 5426– 5438 DOI: 10.1021/jp510838m
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355
Sinnecker, S.; Rajendran, A.; Klamt, A.; Diedenhofen, M.; Neese, F. Calculation of Solvent Shifts on Electronic G-Tensors with the Conductor-Like Screening Model (COSMO) and Its Self-Consistent Generalization to Real Solvents (Direct COSMO-RS) J. Phys. Chem. A 2006, 110, 2235– 2245 DOI: 10.1021/jp056016z
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355
Calculation of Solvent Shifts on Electronic g-Tensors with the Conductor-Like Screening Model (COSMO) and Its Self-Consistent Generalization to Real Solvents (Direct COSMO-RS)
Sinnecker, Sebastian; Rajendran, Arivazhagan; Klamt, Andreas; Diedenhofen, Michael; Neese, Frank
Journal of Physical Chemistry A (2006), 110 (6), 2235-2245CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
The conductor-like screening model (COSMO) was used to investigate the solvent influence on electronic g-values of org. radicals. The previously studied di-Ph nitric oxide and di-tert-Bu nitric oxide radicals were taken as test cases. The calcns. employed spin-unrestricted d. functional theory and the BP and B3LYP d. functionals. The g-tensors were calcd. as mixed second deriv. properties with respect to the external magnetic field and the electron magnetic moment. The first-order response of the Kohn-Sham orbitals with respect to the external magnetic field was detd. through the coupled-perturbed DFT approach. The spin-orbit coupling operator was treated using an accurate multicenter spin-orbit mean-field (SOMF) approach. Provided that important hydrogen bonds are explicitly modeled by a supermol. approach and that the basis set is sufficiently satd., the COSMO calcns. lead to accurate predictions of isotropic g-shifts with deviations of not more than 100 ppm relative to expt. Very accurate results were obtained by employing a recently developed self-consistent modification of the COSMO method to real solvents (COSMO-RS), which we briefly introduce in this paper as direct COSMO-RS (D-COSMO-RS). This model gives isotropic g-shifts of similar high accuracy for water without using the supermol. approach. This is an important result because it solves many of the problems assocd. with the supermol. approach such as local min. and the choice of a suitable model system. Thus, the self-consistent D-COSMO-RS incorporates some specific solvation effects into continuum models, in particular it appears to successfully model the effects of hydrogen bonding. Although not yet widely validated, this opens a novel approach for the calcn. of properties which so far only could be calcd. by the inclusion of explicit solvent mols. in continuum solvation methods.
356
Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models Chem. Rev. 2005, 105, 2999– 3093 DOI: 10.1021/cr9904009
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Quantum Mechanical Continuum Solvation Models
Tomasi, Jacopo; Mennucci, Benedetta; Cammi, Roberto
Chemical Reviews (Washington, DC, United States) (2005), 105 (8), 2999-3093CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review.
357
Ge, X.; Timrov, I.; Binnie, S.; Biancardi, A.; Calzolari, A.; Baroni, S. Accurate and Inexpensive Prediction of the Color Optical Properties of Anthocyanins in Solution J. Phys. Chem. A 2015, 119 (16) 3816– 3822 DOI: 10.1021/acs.jpca.5b01272
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Pedersen, M. N.; Hedegård, E. D.; Olsen, J. M. H.; Kauczor, J.; Norman, P.; Kongsted, J. Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method J. Chem. Theory Comput. 2014, 10 (3) 1164– 1171 DOI: 10.1021/ct400946k
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Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method
Pedersen, Morten N.; Hedegaard, Erik D.; Olsen, Jogvan Magnus H.; Kauczor, Joanna; Norman, Patrick; Kongsted, Jacob
Journal of Chemical Theory and Computation (2014), 10 (3), 1164-1171CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We present a combination of the polarizable embedding (PE) scheme with the complex polarization propagator (CPP) method with the aim of calcg. response properties including relaxation for large and complex systems. This new approach, termed PE-CPP, will benefit from the highly advanced description of the environmental electrostatic potential and polarization in the PE method as well as the treatment of near-resonant effects in the CPP approach. The PE-CPP model has been implemented in a Kohn-Sham d. functional theory approach, and we present pilot calcns. exemplifying the implementation for the UV/vis and carbon K-edge X-ray absorption spectra of the protein plastocyanin. Furthermore, tech. details assocd. with a PE-CPP calcn. are discussed.
359
Olsen, J. M.; Aidas, K.; Kongsted, J. Excited States in Solution through Polarizable Embedding J. Chem. Theory Comput. 2010, 6 (12) 3721– 3734 DOI: 10.1021/ct1003803
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Excited States in Solution through Polarizable Embedding
Olsen, Jogvan Magnus; Aidas, Kestutis; Kongsted, Jacob
Journal of Chemical Theory and Computation (2010), 6 (12), 3721-3734CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We present theory and implementation of an advanced quantum mechanics/mol. mechanics (QM/MM) approach using a fully self-consistent polarizable embedding (PE) scheme. It is a polarizable layered model designed for effective yet accurate inclusion of an anisotropic medium in a quantum mech. calcn. The polarizable embedding potential is described by an atomistic representation including terms up to localized octupoles and anisotropic polarizabilities. It is generally applicable to any quantum chem. description but is here implemented for the case of Kohn-Sham d. functional theory which we denote the PE-DFT method. It has been implemented in combination with time-dependent quantum mech. linear and nonlinear response techniques, thus allowing for assessment of electronic excitation processes and dynamic ground- and excited-state mol. properties using a nonequil. formulation of the environmental response. In our formulation of polarizable embedding we explicitly take into account the full self-consistent many-body environmental response from both ground and excited states. The PE-DFT method can be applied to any mol. system, e.g., proteins, nanoparticles and solute-solvent systems. Here, we present numerical examples of solvent shifts and excited-state properties related to a set of org. mols. in aq. soln.
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Sjöqvist, J.; Linares, M.; Mikkelsen, K. V.; Norman, P. QM/MM-MD Simulations of Conjugated Polyelectrolytes: A Study on Luminescent Conjugated Oligothiophenes for Use as Bio-Physical Probes J. Phys. Chem. A 2014, 118 (19) 3419– 3428 DOI: 10.1021/jp5009835
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Avila Ferrer, F. J.; Cerezo, J.; Stendardo, E.; Improta, R.; Santoro, F. Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation J. Chem. Theory Comput. 2013, 9 (4) 2072– 2082 DOI: 10.1021/ct301107m
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Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation
Avila Ferrer, Francisco J.; Cerezo, Javier; Stendardo, Emiliano; Improta, Roberto; Santoro, Fabrizio
Journal of Chemical Theory and Computation (2013), 9 (4), 2072-2082CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The authors carefully study the relation between computed data and exptl. electronic spectra. To that end, the authors compare both vertical transition energies, EV, and characteristic frequencies of the spectrum like the max., νmax, and the center of gravity, M1, taking advantage of an anal. expression of M1 in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, exptl. spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, the authors simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with exptl. data. Results indicate that the customary comparison of exptl. νmax and computational EV, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the studied systems, are ∼0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of exptl. and computed M1 and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs probably help rationalize which kind of correction 1 should expect when comparing EV, M1, and νmax.
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Avila Ferrer, F. J.; Cerezo, J.; Soto, J.; Improta, R.; Santoro, F. First-Principle Computation of Absorption and Fluorescence Spectra in Solution Accounting for Vibronic Structure, Temperature Effects and Solvent Inhomogenous Broadening Comput. Theor. Chem. 2014, 1040–1041, 328– 337 DOI: 10.1016/j.comptc.2014.03.003
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362
First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogeneous broadening
Avila Ferrer, Francisco Jose; Cerezo, Javier; Soto, Juan; Improta, Roberto; Santoro, Fabrizio
Computational & Theoretical Chemistry (2014), 1040-1041 (), 328-337CODEN: CTCOA5; ISSN:2210-271X. (Elsevier B.V.)
We compute the line shape of absorption and emission electronic spectra of two different dyes, coumarin C153 and N-methyl-6-quinolinium betaine accounting for the vibronic structure, temp. effects and polar solvent inhomogeneous broadening, without using any phenomenol. parameter. We exploit a no. of recent developments including a time-dependent (TD) approach to the computation of vibronic spectra that provides fully converged line shapes at finite temp. accounting for both Duschinsky and Herzberg-Teller effects, and the state-specific (SS) implementation of Polarizable Continuum Model (PCM). This latter is adopted to compute the solvent reorganization energy connected to inhomogeneous broadening. We compute the absorption and fluorescence spectra in the gas-phase, non-polar and polar solvents analyzing the relative importance of different sources of broadening. To this end we investigate the performance of time-dependent d. functional theory, complete active space self consistent field (CASSCF), and complete active space 2nd-order perturbation theory (CASPT2) methods in the computation of inhomogeneous broadening.

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María Oyón-Ardoiz, Elvira Manjón, María Teresa Escribano-Bailón, Ignacio García-Estévez. Potential Use of Torulaspora delbrueckii As a New Source of Mannoproteins of Oenological Interest. Journal of Agricultural and Food Chemistry 2024, 72 (20) , 11606-11616. https://doi.org/10.1021/acs.jafc.4c01001
Bárbara Torres-Rochera, Elvira Manjón, Natércia F Brás, María Teresa Escribano-Bailón, Ignacio García-Estévez. Supramolecular Study of the Interactions between Malvidin-3-O-Glucoside and Wine Phenolic Compounds: Influence on Color. Journal of Agricultural and Food Chemistry 2024, 72 (4) , 1894-1901. https://doi.org/10.1021/acs.jafc.2c08502
Tobias B. Koch, Anna M. Gabler, Florian Biener, Johanna Kreißl, Oliver Frank, Corinna Dawid, Heiko Briesen. Investigating the Role of Odorant–Polymer Interactions in the Aroma Perception of Red Wine: A Density Functional Theory-Based Approach. Journal of Agricultural and Food Chemistry 2023, 71 (50) , 20231-20242. https://doi.org/10.1021/acs.jafc.3c03443
Qianyu Zhao, Hua Zhang, Haitian Zhao, Hongwei Zhu, Jia Liu, Bin Li, Minjie Li, Xin Yang. Construction of a Biomimetic Receptor Based on Hydrophilic Multifunctional Monomer Covalent Organic Framework Molecularly Imprinted Polymers for Molecular Recognition of Cyanidin-3-O-Glucoside. Journal of Agricultural and Food Chemistry 2023, 71 (46) , 18024-18036. https://doi.org/10.1021/acs.jafc.3c04391
Judith Bijlsma, Wouter J. C. de Bruijn, Jamie Koppelaar, Mark G. Sanders, Krassimir P. Velikov, Jean-Paul Vincken. Interactions of Natural Flavones with Iron Are Affected by 7-O-Glycosylation, but Not by Additional 6″-O-Acylation. ACS Food Science & Technology 2023, 3 (6) , 1111-1121. https://doi.org/10.1021/acsfoodscitech.3c00112
Bohan Ma, Bin Dai, Xinghua Zhao, Mengge Zhao, Xingbin Yang, Langjun Cui, Hongjun Shao. Color-Stabilizing Effects and Mechanisms of Schisandra Lignans on the Anthocyanins Enriched with Petunidin-3-O-glucoside. ACS Food Science & Technology 2023, 3 (4) , 717-728. https://doi.org/10.1021/acsfoodscitech.2c00435
Rafael Grande, Riikka Räisänen, Jinze Dou, Satu Rajala, Kiia Malinen, Paula A. Nousiainen, Monika Österberg. In Situ Adsorption of Red Onion (Allium cepa) Natural Dye on Cellulose Model Films and Fabrics Exploiting Chitosan as a Natural Mordant. ACS Omega 2023, 8 (6) , 5451-5463. https://doi.org/10.1021/acsomega.2c06650
André Seco, Nuno Basílio, Natércia F. Brás, Kumi Yoshida, Tadao Kondo, Kin-ichi Oyama, Fernando Pina. Intermolecular Copigmentation Between Delphinidin 3-O-Glucoside and Chlorogenic Acid: Taking into Account the Existence of Neutral and Negatively Charged Forms of the Copigment. Journal of Agricultural and Food Chemistry 2022, 70 (36) , 11391-11400. https://doi.org/10.1021/acs.jafc.2c03879
Ambrósio Camuenho, André Seco, A. Jorge Parola, Nuno Basílio, Fernando Pina. Intermolecular Copigmentation of Malvidin-3-O-glucoside with Caffeine in Water: The Effect of the Copigment on the pH-Dependent Reversible and Irreversible Processes. ACS Omega 2022, 7 (29) , 25502-25509. https://doi.org/10.1021/acsomega.2c02571
Ellia H. La, M. Monica Giusti. Ultraviolet–Visible Excitation of cis- and trans-p-Coumaric Acylated Delphinidins and Their Resulting Photochromic Characteristics. ACS Food Science & Technology 2022, 2 (5) , 878-887. https://doi.org/10.1021/acsfoodscitech.2c00028
Rattapol Meelapsom, Waranphat Rattanakaroonjit, Akarapong Prakobkij, Nutthaporn Malahom, Saksri Supasorn, Sukhum Ruangchai, Purim Jarujamrus. Smartphone-Assisted Colorimetric Determination of Iron Ions in Water by Using Anthocyanin from Ruellia tuberosa L. as a Green Indicator and Application for Hands-on Experiment Kit. Journal of Chemical Education 2022, 99 (4) , 1660-1671. https://doi.org/10.1021/acs.jchemed.1c01120
Cláudia Novais, Adriana K. Molina, Rui M. V. Abreu, Celestino Santo-Buelga, Isabel C. F. R. Ferreira, Carla Pereira, Lillian Barros. Natural Food Colorants and Preservatives: A Review, a Demand, and a Challenge. Journal of Agricultural and Food Chemistry 2022, 70 (9) , 2789-2805. https://doi.org/10.1021/acs.jafc.1c07533
Lucia Panzella, Alessandra Napolitano. Condensed Tannins, a Viable Solution To Meet the Need for Sustainable and Effective Multifunctionality in Food Packaging: Structure, Sources, and Properties. Journal of Agricultural and Food Chemistry 2022, 70 (3) , 751-758. https://doi.org/10.1021/acs.jafc.1c07229
Luis Cruz, Nuno Basílio, Nuno Mateus, Victor de Freitas, Fernando Pina. Natural and Synthetic Flavylium-Based Dyes: The Chemistry Behind the Color. Chemical Reviews 2022, 122 (1) , 1416-1481. https://doi.org/10.1021/acs.chemrev.1c00399
Fabian Weber. Noncovalent Polyphenol–Macromolecule Interactions and Their Effects on the Sensory Properties of Foods. Journal of Agricultural and Food Chemistry 2022, 70 (1) , 72-78. https://doi.org/10.1021/acs.jafc.1c05873
Xu Zhao, Xinke Zhang, Xiaoming He, Changqing Duan, Fei He. Acetylation of Malvidin-3-O-glucoside Impedes Intermolecular Copigmentation: Experimental and Theoretical Investigations. Journal of Agricultural and Food Chemistry 2021, 69 (27) , 7733-7741. https://doi.org/10.1021/acs.jafc.1c02378
Luís Cruz, Juan Correa, Nuno Mateus, Victor de Freitas, Maun H. Tawara, Eduardo Fernandez-Megia. Dendrimers as Color-Stabilizers of Pyranoanthocyanins: The Dye Concentration Governs the Host–Guest Interaction Mechanisms. ACS Applied Polymer Materials 2021, 3 (3) , 1457-1464. https://doi.org/10.1021/acsapm.0c01321
Joana Oliveira, Joana Azevedo, Natércia Teixeira, Paula Araújo, Victor de Freitas, Nuno Basílio, Fernando Pina. On the Limits of Anthocyanins Co-Pigmentation Models and Respective Equations. Journal of Agricultural and Food Chemistry 2021, 69 (4) , 1359-1367. https://doi.org/10.1021/acs.jafc.0c05954
Laura Estévez, Marta Queizán, Ricardo A. Mosquera, Lucia Guidi, Ermes Lo Piccolo, Marco Landi. First Characterization of the Formation of Anthocyanin–Ge and Anthocyanin–B Complexes through UV–Vis Spectroscopy and Density Functional Theory Quantum Chemical Calculations. Journal of Agricultural and Food Chemistry 2021, 69 (4) , 1272-1282. https://doi.org/10.1021/acs.jafc.0c06827
Cátia I. Sampaio, Luís F. Sousa, Alice M. Dias. Separation of Anthocyaninic and Nonanthocyaninic Flavonoids by Liquid–Liquid Extraction Based on Their Acid–Base Properties: A Green Chemistry Approach. Journal of Chemical Education 2020, 97 (12) , 4533-4539. https://doi.org/10.1021/acs.jchemed.0c00139
Savanah G. Reeves, Arpad Somogyi, Wayne E. Zeller, Theresa A. Ramelot, Kelly C. Wrighton, Ann E. Hagerman. Proanthocyanidin Structural Details Revealed by Ultrahigh Resolution FT-ICR MALDI-Mass Spectrometry, 1H–13C HSQC NMR, and Thiolysis-HPLC–DAD. Journal of Agricultural and Food Chemistry 2020, 68 (47) , 14038-14048. https://doi.org/10.1021/acs.jafc.0c04877
Daisuke Kajiya. Demonstrating Purple Color Development to Students by Showing the Highly Visual Effects of Aluminum Ions and pH on Aqueous Anthocyanin Solutions. Journal of Chemical Education 2020, 97 (11) , 4084-4090. https://doi.org/10.1021/acs.jchemed.0c00476
Hiléia K. S. Souza, Nuno Mateus, Victor de Freitas, Maria Pilar Gonçalves, Luís Cruz. Chemical/Color Stability and Rheological Properties of Cyanidin-3-Glucoside in Deep Eutectic Solvents as a Gateway to Design Task-Specific Bioactive Compounds. ACS Sustainable Chemistry & Engineering 2020, 8 (43) , 16184-16196. https://doi.org/10.1021/acssuschemeng.0c04839
Michal Langer, Markéta Paloncýová, Miroslav Medved’, Michal Otyepka. Molecular Fluorophores Self-Organize into C-Dot Seeds and Incorporate into C-Dot Structures. The Journal of Physical Chemistry Letters 2020, 11 (19) , 8252-8258. https://doi.org/10.1021/acs.jpclett.0c01873
Kenneth R. Sims, Jr., Brian He, Hyun Koo, Danielle S.W. Benoit. Electrostatic Interactions Enable Nanoparticle Delivery of the Flavonoid Myricetin. ACS Omega 2020, 5 (22) , 12649-12659. https://doi.org/10.1021/acsomega.9b04101
Federica Moccia, Sarai Agustin-Salazar, Anna-Lisa Berg, Brunella Setaro, Raffaella Micillo, Elio Pizzo, Fabian Weber, Nohemi Gamez-Meza, Andreas Schieber, Pierfrancesco Cerruti, Lucia Panzella, Alessandra Napolitano. Pecan (Carya illinoinensis (Wagenh.) K. Koch) Nut Shell as an Accessible Polyphenol Source for Active Packaging and Food Colorant Stabilization. ACS Sustainable Chemistry & Engineering 2020, 8 (17) , 6700-6712. https://doi.org/10.1021/acssuschemeng.0c00356
Woojin Yang, Junhyuk Jo, Hyeongyeol Oh, Hohjai Lee, Won-jin Chung, Jiwon Seo. Peptoid Helix Displaying Flavone and Porphyrin: Synthesis and Intramolecular Energy Transfer. The Journal of Organic Chemistry 2020, 85 (3) , 1392-1400. https://doi.org/10.1021/acs.joc.9b02358
Tomomi Ujihara, Nobuyuki Hayashi. Mechanism of Copigmentation of Monoglucosylrutin with Caffeine. Journal of Agricultural and Food Chemistry 2020, 68 (1) , 323-331. https://doi.org/10.1021/acs.jafc.9b06235
Andrzej Sienkiewicz, Iwona Rusinek, Anna Siatecka, Sonia Losada-Barreiro. Flower Color Change Demonstration as a Visualization of Potential Harmful Effects Associated with Ammonia Gas on Living Organisms. Journal of Chemical Education 2019, 96 (9) , 1982-1987. https://doi.org/10.1021/acs.jchemed.9b00001
Chen Tan, Mohammad Arshadi, Michelle C. Lee, Mary Godec, Morteza Azizi, Bing Yan, Hamed Eskandarloo, Ted W. Deisenroth, Rupa Hiremath Darji, Toan Van Pho, Alireza Abbaspourrad. A Robust Aqueous Core–Shell–Shell Coconut-like Nanostructure for Stimuli-Responsive Delivery of Hydrophilic Cargo. ACS Nano 2019, 13 (8) , 9016-9027. https://doi.org/10.1021/acsnano.9b03049
Johan Mendoza, Nuno Basílio, Victor de Freitas, Fernando Pina. New Procedure To Calculate All Equilibrium Constants in Flavylium Compounds: Application to the Copigmentation of Anthocyanins. ACS Omega 2019, 4 (7) , 12058-12070. https://doi.org/10.1021/acsomega.9b01066
Cristina Alcalde-Eon, Claudia Pérez-Mestre, Rebeca Ferreras-Charro, Francisco J. Rivero, Francisco J. Heredia, María Teresa Escribano-Bailón. Addition of Mannoproteins and/or Seeds during Winemaking and Their Effects on Pigment Composition and Color Stability. Journal of Agricultural and Food Chemistry 2019, 67 (14) , 4031-4042. https://doi.org/10.1021/acs.jafc.8b06922
Vijayakumar R. Vishnu, Raveendran S. Renjith, Archana Mukherjee, Shirly Raichal Anil, Janardanan Sreekumar, Alummoottil N. Jyothi. Comparative Study on the Chemical Structure and In Vitro Antiproliferative Activity of Anthocyanins in Purple Root Tubers and Leaves of Sweet Potato (Ipomoea batatas). Journal of Agricultural and Food Chemistry 2019, 67 (9) , 2467-2475. https://doi.org/10.1021/acs.jafc.8b05473
Tomomi Ujihara, Nobuyuki Hayashi. Complex Structures of Monoglucosylrutin with ent-Gallocatechin-3-O-gallate and Epigallocatechin-3-O-gallate in Aqueous Solutions and the Mechanism of Color Change Induced by Complexation. Journal of Natural Products 2019, 82 (1) , 2-8. https://doi.org/10.1021/acs.jnatprod.7b00817
Imene Bayach, Anthony D’Aleó, Patrick Trouillas. Tuning Optical Properties of Chalcone Derivatives: A Computational Study. The Journal of Physical Chemistry A 2019, 123 (1) , 194-201. https://doi.org/10.1021/acs.jpca.8b08529
A. Alejo-Armijo, Livia Corici, Liliana Cseh, Diana Aparaschivei, Artur J. Moro, A. Jorge Parola, João C. Lima, Fernando Pina. Achieving Complexity at the Bottom. 2,6-Bis(arylidene)cyclohexanones and Anthocyanins: The Same General Multistate of Species. ACS Omega 2018, 3 (12) , 17853-17862. https://doi.org/10.1021/acsomega.8b02745
Laura A. Chatham, Leslie West, Mark A. Berhow, Karl E. Vermillion, John A. Juvik. Unique Flavanol-Anthocyanin Condensed Forms in Apache Red Purple Corn. Journal of Agricultural and Food Chemistry 2018, 66 (41) , 10844-10854. https://doi.org/10.1021/acs.jafc.8b04723
Paul M. Rose, Victoria Cantrill, Meryem Benohoud, Alenka Tidder, Christopher M. Rayner, Richard S. Blackburn. Application of Anthocyanins from Blackcurrant (Ribes nigrum L.) Fruit Waste as Renewable Hair Dyes. Journal of Agricultural and Food Chemistry 2018, 66 (26) , 6790-6798. https://doi.org/10.1021/acs.jafc.8b01044
Paula Araújo, Nuno Basílio, Ana Fernandes, Nuno Mateus, Victor de Freitas, Fernando Pina, Joana Oliveira. Impact of Lignosulfonates on the Thermodynamic and Kinetic Parameters of Malvidin-3-O-glucoside in Aqueous Solutions. Journal of Agricultural and Food Chemistry 2018, 66 (25) , 6382-6387. https://doi.org/10.1021/acs.jafc.8b02273
Johan Mendoza, Nuno Basílio, Fernando Pina, Tadao Kondo, Kumi Yoshida. Rationalizing the Color in Heavenly Blue Anthocyanin: A Complete Kinetic and Thermodynamic Study. The Journal of Physical Chemistry B 2018, 122 (19) , 4982-4992. https://doi.org/10.1021/acs.jpcb.8b01136
Chen Tan, Giovana B. Celli, Michelle Lee, Jonathan Licker, Alireza Abbaspourrad. Polyelectrolyte Complex Inclusive Biohybrid Microgels for Tailoring Delivery of Copigmented Anthocyanins. Biomacromolecules 2018, 19 (5) , 1517-1527. https://doi.org/10.1021/acs.biomac.8b00352
Alberto Fabrizio and Clémence Corminboeuf . How do London Dispersion Interactions Impact the Photochemical Processes of Molecular Switches?. The Journal of Physical Chemistry Letters 2018, 9 (3) , 464-470. https://doi.org/10.1021/acs.jpclett.7b03316
Cassio Pacheco da Silva, Renan Moraes Pioli, Liu Liu, Shasha Zheng, Mengjiao Zhang, Gustavo Thalmer de Medeiros Silva, Vânia Maria Teixeira Carneiro, and Frank H. Quina . Improved Synthesis of Analogues of Red Wine Pyranoanthocyanin Pigments. ACS Omega 2018, 3 (1) , 954-960. https://doi.org/10.1021/acsomega.7b01955
Kateřina Holá, Mária Sudolská, Sergii Kalytchuk, Dana Nachtigallová, Andrey L. Rogach, Michal Otyepka, and Radek Zbořil . Graphitic Nitrogen Triggers Red Fluorescence in Carbon Dots. ACS Nano 2017, 11 (12) , 12402-12410. https://doi.org/10.1021/acsnano.7b06399
Yebeen Kang, Eunmi Koh. Chlorogenic acid is more effective than aluminum ion for protecting anthocyanins in aqueous aronia solution against LED light. Journal of Food Composition and Analysis 2025, 143 , 107557. https://doi.org/10.1016/j.jfca.2025.107557
Sabrina Idir, Sabiha Achat, Luis Cruz, Olivier Dangles. Anthocyanin-rich extracts: Susceptibility to color loss by hydration and thermal degradation, influence of metal ions and endogenous copigments. Food Chemistry 2025, 481 , 144004. https://doi.org/10.1016/j.foodchem.2025.144004
Mariana C. Leal-Alcazar, Frida Bautista-Palestina, María del R. Rocha-Pizaña, Luis Mojica, Alan Javier Hernández-Álvarez, Diego A. Luna-Vital. Extraction, stabilization, and health application of betalains: An update. Food Chemistry 2025, 481 , 144011. https://doi.org/10.1016/j.foodchem.2025.144011
Giroon Ijod, Nur Izzati Mohamed Nawawi, Mohammed S. Qoms, Mohammad Rashedi Ismail Fitry, Muhamad Hafiz Abd Rahim, Dimitris Charalampopoulos, Rabiha Sulaiman, Noranizan Mohd Adzahan, Ezzat Mohamad Azman. Synergistic effects of intermolecular copigmentation and high-pressure processing on stabilizing mangosteen pericarp anthocyanins. Food Chemistry 2025, 480 , 143888. https://doi.org/10.1016/j.foodchem.2025.143888
Caiyun Liu, Lulu Wu, Zengshuai Zhang, Ziying Li, Mario Prejanò, Tiziana Marino, Yongsheng Tao, Yunkui Li. Copigmentation effect and mechanism of α-cyclodextrin on wine color quality and stability: Combining dynamics, thermodynamics, structural characterization and quantum mechanics. Food Hydrocolloids 2025, 163 , 111068. https://doi.org/10.1016/j.foodhyd.2025.111068
Oscar Zannou, Ilkay Koca, Reza Tahergorabi, Salam A. Ibrahim. Deep eutectic solvent as an alternative, green medium for enhancing the stability of blackberry (Rubus spp) pigments. Industrial Crops and Products 2025, 228 , 120866. https://doi.org/10.1016/j.indcrop.2025.120866
Zixuan Li, Zhipeng Gao, Donglin Su, Zhipeng Su, Yanjiao Fu, Wenbin Xiao, Fuhua Fu, Gaoyang Li, Lvhong Huang, Jiajing Guo, Yang Shan. Facile and green synthesis of nanocarriers from chondroitin sulfate-based and whey protein isolate with improved stability and biocompatibility for anthocyanins protection. Food Chemistry 2025, 476 , 143449. https://doi.org/10.1016/j.foodchem.2025.143449
Jiaheng Lyu, Jiming Li, Wenguang Jiang, Tingting Liu, Yan Xu, Ke Tang. Copigmentation effects of different phenolics on color stability of three basic anthocyanins in wines: Chromaticity, thermodynamics and molecular dynamics simulation. Food Chemistry 2025, 476 , 143499. https://doi.org/10.1016/j.foodchem.2025.143499
Gerui Ren, Xinpei Cai, Ying He, Lei Liu, Ruiqi Hu, Jiqi Wang, Qingbo Jiao, Yingjie Wu, Jiacheng Liu, Ying Huang, Min Huang, Hujun Xie, Kejun Cheng. Ferulic acid-regulated anthocyanin-based intelligent film: A promising strategy to improve stability, sensitivity, and biological activity. International Journal of Biological Macromolecules 2025, 305 , 141237. https://doi.org/10.1016/j.ijbiomac.2025.141237
Nadja Ulmann, Johnny Hioe, Didier Touraud, Eva Müller, Dominik Horinek, Werner Kunz. Sustainable polyphenolate assisted hydrotropic solubilization of riboflavin. Journal of Molecular Liquids 2025, 426 , 127465. https://doi.org/10.1016/j.molliq.2025.127465
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Fangfang Li, Quancai Sun, Long Chen, Ruojie Zhang, Zipei Zhang. Unlocking the health potential of anthocyanins: a structural insight into their varied biological effects. Critical Reviews in Food Science and Nutrition 2025, 65 (11) , 2134-2154. https://doi.org/10.1080/10408398.2024.2328176
Aleksandra Popowska, Joanna Oracz. Influence of Copigmentation and Encapsulation on Stability and Antioxidant Activity of Anthocyanins from Blue and Pink Cornflower (Centaurea cyanus L.) Flowers. Molecules 2025, 30 (7) , 1467. https://doi.org/10.3390/molecules30071467
Yuan Yuan, Caochuang Fang, Chaohan Li, Jiaqi You, Kun Ma. Identification and Evaluation of Colour Change in Rosemary and Biluochun Tea Infusions. Metabolites 2025, 15 (4) , 265. https://doi.org/10.3390/metabo15040265
Francisco Chamizo-González, Francisco J. Heredia, María Fernanda López-Molina, Francisco J. Rodríguez-Pulido, M. Lourdes González-Miret, Belén Gordillo. Theoretical Prediction of the Color Expression of Malvidin 3-Glucoside by in silico Tristimulus Colorimetry. Effects of Structure Conformational Changes and Molecular Interactions. Applied Sciences 2025, 15 (8) , 4238. https://doi.org/10.3390/app15084238
Xuechen Yao, Haoen Cai, Jiayi Kou, Yunxue Xie, Jin Li, Penghui Zhou, Fei He, Changqing Duan, Qiuhong Pan, Mengyao Qi, Yibin Lan. Dual-temperature dual-state fermentation: A novel approach to improve aroma and color characteristics of Marselan wines. Food Chemistry: X 2025, 27 , 102447. https://doi.org/10.1016/j.fochx.2025.102447
Damla Ezgi Uzun, Tugce Ceyhan, Merve Tomas, Esra Capanoglu. Recent advances in improving anthocyanin stability in black carrots. Critical Reviews in Food Science and Nutrition 2025, 3 , 1-23. https://doi.org/10.1080/10408398.2025.2469774
Shihan Bao, Jianing Li, Jiaqi Wang, Tian Lan, Mengyuan Wei, Xiangyu Sun, Yulin Fang, Tingting Ma. How Does Nature Create the Painting “Gradient Coloration of ‘Manicure Finger’ Grape”? Integrated Omics Unveil the Pigments Basis and Metabolism Networks of Its Formation. Food Frontiers 2025, 6 (2) , 921-939. https://doi.org/10.1002/fft2.513
Shaohua Zeng, Shuang Lin, Rong Jiang, Jinrong Wei, Ying Wang. Biotechnology Advances in Natural Food Colorant Acylated Anthocyanin Production. Food Frontiers 2025, 6 (2) , 698-715. https://doi.org/10.1002/fft2.527
Shiguang Chen, Zhiling Li, Dan Ren, Xiyu Wu, Dan Xu. Improved sensitivity of freshness indicator based on purple sweet potato anthocyanins through pH optimization and its application in flesh food monitoring during logistics. Innovative Food Science & Emerging Technologies 2025, 100 , 103929. https://doi.org/10.1016/j.ifset.2025.103929
Jingliang Zhu, Yaqian Geng, Yuan Huang, Chen Ma, Li Dong, Fang Chen, Xiaosong Hu, Lingjun Ma, Junfu Ji. Emerging Novel Processing Technologies Towards the Stabilization of Anthocyanins. Food Reviews International 2025, 41 (2) , 439-468. https://doi.org/10.1080/87559129.2024.2403525
Bojian Chen, Lirong Xiang, Danyue Zhao, Zunying Liu, Fei Jia. Unraveling Nature’s Color Palette: The Chemistry, Biosynthesis and Applications in Health Promotion of Anthocyanins—A Comprehensive Review. Food Reviews International 2025, 41 (2) , 491-520. https://doi.org/10.1080/87559129.2024.2404471
Xinjie Li, Fan Wang, Na Ta, Jinyong Huang. The compositions, characteristics, health benefits and applications of anthocyanins in Brassica crops. Frontiers in Plant Science 2025, 16 https://doi.org/10.3389/fpls.2025.1544099
María Fernanda López-Molina, Francisco J. Rodríguez-Pulido, Ana Belén Mora-Garrido, M. Lourdes González-Miret, Francisco J. Heredia. New approaches for screening grape seed peptides as colourimetric modulators by malvidin-3-O-glucoside stabilisation. Food Chemistry 2025, 464 , 141708. https://doi.org/10.1016/j.foodchem.2024.141708
Zhiying Li, Jinlong Tian, Qilin Tian, Zhihuan Zang, Yumeng Wang, Qiao Jiang, Yi Chen, Baoru Yang, Shufang Yang, Yiyun Yang, Bin Li. Improved uptake of anthocyanins-loaded nanoparticles based on phenolic acid-grafted zein and lecithin. Food Chemistry 2025, 466 , 142235. https://doi.org/10.1016/j.foodchem.2024.142235
Ruirui Li, Dongyue Yang, Zhiyu Li, Xiaohong Tang, Ke Zhong, Yan Ding, Xiaomei Han, Xueqiang Guan, Yuxia Sun. The effect of stem contact fermentation on the quality of Cabernet Sauvignon and Merlot wines from Yantai, China. Food Bioscience 2025, 64 , 105872. https://doi.org/10.1016/j.fbio.2025.105872
Katarina Delic, Claire Payan, Viktoriya Aleksovych, A. Jouin, A. Vignault, Kleopatra Chira, Michael Jourdes, Pierre-Louis Teissedre. Wine Phenolic Compounds: Chemistry and Biological Properties. 2025, 713-759. https://doi.org/10.1007/978-3-031-38663-3_218
Thomas Owen Hay, Melissa A. Fitzgerald, Joseph Robert Nastasi. Systematic application of UPLC-Q-ToF-MS/MS coupled with chemometrics for the identification of natural food pigments from Davidson plum and native currant. Food Chemistry: X 2025, 25 , 102072. https://doi.org/10.1016/j.fochx.2024.102072
Niloofar Moshfegh, Mehrdad Niakousary, Seyed Mohammad Hashem Hosseini, Seyed Mohammad Mazloomi, Azam Abbasi. Effect of maltodextrin and Persian gum as wall materials and tannic acid as copigment on some properties of encapsulated sour cherry anthocyanin microcapsules. Food Chemistry 2025, 463 , 141165. https://doi.org/10.1016/j.foodchem.2024.141165
Xiangxin Gu, Yaqiong Liu, Ran Suo, Qingquan Yu, Churan Xue, Jie Wang, Wenxiu Wang, Haiqi Wang, Yan Qiao. Effects of different low-temperature maceration times on the chemical and sensory characteristics of Syrah wine. Food Chemistry 2025, 463 , 141230. https://doi.org/10.1016/j.foodchem.2024.141230
Sarvpreet Singh, Nitisha Sendri, Bhanu Sharma, Pramod Kumar, Avisha Sharma, Narendra Vijay Tirpude, Rituraj Purohit, Pamita Bhandari. Copigmentation effect on red cabbage anthocyanins, investigation of their cellular viability and interaction mechanism. Food Research International 2025, 200 , 115427. https://doi.org/10.1016/j.foodres.2024.115427
Yuxi Liu, Rico F. Tabor, Piotr Pawliszak, David A. Beattie, Marta Krasowska, Benjamin W. Muir, San H. Thang, Chris Ritchie. Multi-stimuli-responsive polymers enabled by bio-inspired dynamic equilibria of flavylium chemistry. Chemical Science 2025, 122 https://doi.org/10.1039/D5SC00977D
Shaojun Zuo, Tongtong Li, Tong Chen, Jianing Li, Xinyou Liu. Degradation of Oil Paint Coating Based on Wood Under the Combined Effect of UV Light and Heat. Forests 2025, 16 (1) , 22. https://doi.org/10.3390/f16010022
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Abstract
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Scheme 1
Scheme 1. Prototypical Copigmentation Complexes^a
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Scheme a(A) Noncovalent association of a prototypical anthocyanin pigment and a prototypical flavonoid copigment (intermolecular copigmentation). (B) Prototypical acylated derivatives allowing copigmentation between the anthocyanin moiety and two phenolic acids covalently linked (intramolecular copigmentation).
Figure 1
Figure 1. Chemical structures of anthocyanidins (R₃ = OH) and anthocyanins (R₃ = glucose).
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Figure 2
Figure 2. Chemical structures of pyranoanthocyanins (flavylium cation form).
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Figure 3
Figure 3. Structural transformations of anthocyanins in acidic to neutral solution. Proton loss from C5-OH omitted for simplicity.
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Figure 4
Figure 4. Structural transformations of the 3′,4′-dihydroxy-7-O-β-d-glucopyranosyloxyflavylium ion. (A) Fast formation of the quinonoid base. Spectral measurements immediately after addition of pigment to buffer, pH = 2.0 → pH = 6.0. (B) Slow accumulation of trans-chalcone (C_trans). Spectral measurements on solutions equilibrated overnight, pH = 2.0 → pH = 4.0. Adapted with permission from ref 25. Copyright 2013 Elsevier Ltd.
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Figure 5
Figure 5. Chemical structures of series of copigments.
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Scheme 2
Scheme 2. π–π Stacking Interactions in Anthocyanins and Their Complexes^a
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Scheme a(A) Intermolecular copigmentation, (B) self-association, (C) intramolecular copigmentation in acylated anthocyanins, (D) self-association of acylated anthocyanins, (E) intercalation in intermolecular copigmentation, and (F) copigmentation in metal–anthocyanin complexes.
Figure 6
Figure 6. Chemical structures of three nonmetallic pigment···copigment assemblies.
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Figure 7
Figure 7. Chemical structures of two polyacylated anthocyanins.
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Figure 8
Figure 8. Chemical structures of polyacylated anthocyanins.
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Figure 9
Figure 9. Anthocyanin-flavone C- or O-glycoside pigments with a malonate bridge from leaves of (A) Oxalis triangularis and (B) Allium “Blue Perfume”.
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Figure 10
Figure 10. Structure of commelinin. Blue: malonylawobanin (MA), yellow and orange: flavocommelin (FC), red: Mg²⁺(A). A side view of a left-handed stacking of two MA units that coordinate to different Mg ions. (B) A side view of a copigmentation of MA and FC in a right-handed stacking arrangement. (C) A side view of a left-handed stacking of two FC units. (D) A side view of commelinin. (E) A skew view of a copigmentation between MA and FC. (F) A skew view of the self-association of two FC units. Adapted with permission from ref 1. Copyright 2009 The Royal Society of Chemistry.
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Figure 11
Figure 11. Chemical structure of the anthocyanin derived from Ceanothus papillosus petals.
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Figure 12
Figure 12. (A) Structure of protocyanins from Centaurea cyanus (cornflower). (B) X-ray diffraction crystal structure, showing the two metal ions Fe³⁺ and Mg²⁺ in the center of the supramolecular assembly. Adapted with permission from ref 1. Copyright 2009 The Royal Society of Chemistry.
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Figure 13
Figure 13. Copigmentation of malvin (malvidin 3,5-di-O-β-d-glucoside) by 7-O-sulfoquercetin. Reprinted with permission from ref 107. Copyright 2001 John Wiley & Sons.
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Figure 14
Figure 14. pH dependence of the copigmentation hyperchromic shift. Spectroscopic monitoring at λ_MAX of free flavylium. Simulations from eq 2 using the following parameters: CP concentration = 10 mM, pK′_h = 2.5, pK_a = 4.0, r_AHCP+ = 0.8, r_ACP = 0.9, r_A = 0.7. Hydroxycinnamic acids (red line): K_AHCP+ = 3 × 10² M^–1, K_ACP = 2 × 10² M^–1. Flavones and flavonols (green line): K_AHCP+ = 3 × 10³ M^–1, K_ACP = 10³ M^–1.
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Figure 15
Figure 15. Distribution diagram of anthocyanin forms in the presence of a copigment. Parameters: pK′_h = 2.5, pK_a = 4.0, pigment and copigment concentrations = 10 and 30 mM, respectively. (A) Hydroxycinnamic acid, K_AHCP = 3 × 10², K_ACP = 2 × 10² M^–1, pK′_h^CP (pH of a 1:1 mixture of colored and colorless forms) ≈ 3.5. (B) Flavone or flavonol, K_AHCP = 3 × 10² M⁻¹, K_AHCP = 3 × 10³ M^–1, pK′_h^CP ≈ 5.2.
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Figure 16
Figure 16. Morning glory (Pharbitis nil) anthocyanins (inspired from ref 135).
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Figure 17
Figure 17. Distribution diagram for a prototypical acylated anthocyanin forms showing the strong influence of noncovalent dimerization. Parameters: pK′_h = 3.0 (assuming partial protection against water addition owing to intramolecular copigmentation in monomer), pK_a = 4.0, pigment concentration = 10 mM. Tentative values for the dimerization constants: K_AH+/AH+ = 3 × 10⁴, K_AH+/A = 8 × 10⁴, K_A/A = 5 × 10⁴ M^–1.
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Figure 18
Figure 18. Schematic (1D) potential energy surface (PES) showing many local minima accessible by 1 ns-long MD simulation and the necessity to properly explore the entire PES to reach the real valley via long MD simulation or biased techniques to force random exploration. (The noncovalent complex represented here is just a pictorial representation.)
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Scheme 3
Scheme 3. Thermodynamics Cycle for the Formation of Copigmentation Complexes in Water (Comprising Complex Formation in the Gas Phase and the Transfer of the Process from the Gas Phase to Solvent)
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Figure 19
Figure 19. Molecular dynamics snapshot of the 3-OMe-cyanidin···quercetin noncovalent complex (the pigment 3-OMe-cyanidin in red; the copigment quercetin in yellow), showing the space between both partners depleted from water molecules.
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Figure 20
Figure 20. π–π Stacking complexes between quercetin (yellow) and vitamin E (green) in lipid bilayer membranes.
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Figure 21
Figure 21. Dispersion energy as a function of the interatomic distance for a set of selected atomic pairs.
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Figure 22
Figure 22. Sketch of the two main DFT-based corrections discussed: the statically averaged interaction (top) and the dynamically interacting densities (bottom).
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Figure 23
Figure 23. Five stable conformations of the 3-OMe-cyanidin··· quercetin noncovalent complex (A) side-view and top view showing the parallel-displaced arrangement; (B) side-view showing the intermolecular hydrogen bonding of conformers 2 and 5; (C) top view showing the supramolecular chirality in conformers 3 and 5; and (D) side-view showing the slight bending in conformers 1 and 5.
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Figure 24
Figure 24. Potential energy curve along the z-axis defined perpendicular to the planar π-conjugated system, as obtained by three methods of calculation.
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Scheme 4
Scheme 4. (A) Simplified MO diagram for CT and exciton formation of a DA and AA pair (H = HOMO, L = LUMO)^a
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Scheme aGrey arrows indicate lowest electronic transitions in a one-electron picture. (B) Resulting exciton states for rotated and laterally displaced AA pair (qualitative quantum-chemical corrected Kasha picture at π-stacking distance).
Figure 25
Figure 25. MO orbital diagram related to the maximum absorption wavelength HOMO and LUMO (left) and NTO analysis (right). Both schemes show the strong CT character of S₀ → S₁.
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References
This article references 362 other publications.
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  Spectral and kinetic studies were carried out on the transformations undergone in aq. soln. by flavylium ions and I (R = H, Me, MeO). Seven species were identified under various pH conditions, i.e., the flavylium ion, 2 pseudobases, 4-hydroxy adducts and the cis-2-hydroxychalcones and their ionized forms. Equil. between the various species are described and rate and equil. consts. were detd.
22. 22
  Pina, F.; Melo, M. J.; Laia, C. A. T.; Parola, A. J.; Lima, J. C. Chemistry and Applications of Flavylium Compounds: A Handful of Colours Chem. Soc. Rev. 2012, 41 (2) 869– 908 DOI: 10.1039/C1CS15126F
  22
  Chemistry and applications of flavylium compounds: a handful of colours
  Pina, Fernando; Melo, Maria J.; Laia, Cesar A. T.; Parola, A. Jorge; Lima, Joao C.
  Chemical Society Reviews (2012), 41 (2), 869-908CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
  A review. Flavylium compds. are versatile mols. that comprise anthocyanins, the ubiquitous colorants used by Nature to confer color to most flowers and fruits. They have found a wide range of applications in human technol., from the millenary color paints described by the Roman architect Vitruvius, to their use as food additives, combining color and antioxidant effects, and even as light absorbers in solar cells aiming at a greener solar energy conversion. Their rich complexity derives in part from their ability to switch between a variety of species (flavylium cations, neutral quinoidal bases, hemiketals and chalcones, and neg. charged phenolates) by means of external stimuli, such as pH, temp. and light. This crit. review describes (i) the historical advancements in the understanding of the equil. of their chem. reaction networks; (ii) their thermodn. and kinetics; (iii) the mechanisms underlying their color development, such as co-pigmentation and host-guest interactions; (iv) the photophysics and photochem. that lead to photochromism; and (v) applications in solar cells, models for optical memories, photochromic soft materials such as ionic liqs. and gels, and their properties in solid state materials (274 refs.).
23. 23
  Pina, F. Chemical Applications of Anthocyanins and Related Compounds. A Source of Bioinspiration J. Agric. Food Chem. 2014, 62 (29) 6885– 6897 DOI: 10.1021/jf404869m
  23
  Chemical Applications of Anthocyanins and Related Compounds. A Source of Bioinspiration
  Pina, Fernando
  Journal of Agricultural and Food Chemistry (2014), 62 (29), 6885-6897CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  A review. Independently of the natural or synthetic origin, flavylium derivs. follow the same network of chem. reactions. Actually, the flavylium cation is stable only at low pH values. Increasing the pH gives rise to the formation of several species: quinoidal bases, hemiketal, cis- and trans-chalcones, and their deprotonated forms. A deep knowledge of the thermodn. and kinetics of these species is an essential tool to practical applications of these compds., in particular, in the domain of food chem. In this work the network of chem. reactions involving flavylium derivs. is presented, and the resp. thermodn. and kinetics are discussed in detail, including the math. expressions and a step-by-step procedure to calc. all of the rate and equil. consts. of the system. Examples of systems possessing a high or low cis-trans isomerization barrier are shown. Recent practical applications of anthocyanins and related compds. illustrate the potential of the flavylium-based family of compds.
24. 24
  Nave, F.; Petrov, V.; Pina, F.; Teixeira, N.; Mateus, N.; de Freitas, V. Thermodynamic and Kinetic Properties of a Red Wine Pigment: Catechin-(4,8)-Malvidin-3- O -Glucoside J. Phys. Chem. B 2010, 114 (42) 13487– 13496 DOI: 10.1021/jp104749f
  There is no corresponding record for this reference.
25. 25
  Mora-Soumille, N.; Al Bittar, S.; Rosa, M.; Dangles, O. Analogs of Anthocyanins with a 3′,4′-Dihydroxy Substitution: Synthesis and Investigation of Their Acid–base, Hydration, Metal Binding and Hydrogen-Donating Properties in Aqueous Solution Dyes Pigm. 2013, 96 (1) 7– 15 DOI: 10.1016/j.dyepig.2012.07.006
  25
  Analogs of anthocyanins with a 3',4'-dihydroxy substitution: Synthesis and investigation of their acid-base, hydration, metal binding and hydrogen-donating properties in aqueous solution
  Mora-Soumille, Nathalie; Al Bittar, Sheiraz; Rosa, Maxence; Dangles, Olivier
  Dyes and Pigments (2013), 96 (1), 7-15CODEN: DYPIDX; ISSN:0143-7208. (Elsevier Ltd.)
  Glycosides of hydroxylated flavylium ions are proposed as pertinent analogs of anthocyanins, a major class of polyphenolic plant pigments. Anthocyanins with a 3',4'-dihydroxy substitution on the B-ring (catechol nucleus) are esp. important for their metal chelating and electron-donating (antioxidant) capacities. In this work, an efficient chem. synthesis of 3',4'-dihydroxy-7-O-β-D-glucopyranosyloxyflavylium chloride and its aglycon is reported. Then, the ability of the two pigments to undergo proton transfer (formation of colored quinonoid bases) and add water (formation of a colorless chalcone) is investigated: at equil. the colored quinonoid bases (kinetic products) are present in very minor concns. (<10% of the total pigment concn.) compared to the colorless chalcone (thermodn. product). The glucopyranosyloxyflavylium ion appears significantly less acidic than the aglycon. The thermodn. of the overall sequence of flavylium-chalcone conversion is not affected by the β-D-glucosyl moiety while the kinetics appears slower by a factor ca. 8. Although the glucopyranosyl-oxyflavylium ion and its aglycon display similar affinities for Al3+, the Al3+-glucoside complex is more stable than the Al3+-aglycon complex due to the higher sensitivity of the latter to water addn. and conversion into the corresponding chalcone. Finally, the glucopyranosyl-oxyflavylium ion and its aglycon are compared for their ability to reduce the 1,1-diphenyl-2-picrylhydrazyl radical in a mildly acidic water/MeOH (1:1) mixt. as a first evaluation of their antioxidant activity. Glycosidation at C7-OH results in a lower rate const. of first electron transfer to DPPH and a lower stoichiometry (total no. of 1,1-diphenyl-2-picrylhydrazyl radicals reduced per pigment mol.). Anthocyanins are difficult to ext. from plants in substantial amt. However, the analogs investigated in this work are of easy access by chem. synthesis and express the physico-chem. properties typical of anthocyanins. They can thus be regarded as valuable models for investigating the coloring, metal-binding and antioxidant properties of these important natural pigments.
26. 26
  Yan, Q.; Zhang, L.; Zhang, X.; Liu, X.; Yuan, F.; Hou, Z.; Gao, Y. Stabilization of Grape Skin Anthocyanins by Copigmentation with Enzymatically Modified Isoquercitrin (EMIQ) as a Copigment Food Res. Int. 2013, 50 (2) 603– 609 DOI: 10.1016/j.foodres.2011.04.007
  26
  Stabilization of grape skin anthocyanins by copigmentation with enzymatically modified isoquercitrin (EMIQ) as a copigment
  Yan, Qiuli; Zhang, Linhan; Zhang, Xiaofei; Liu, Xuan; Yuan, Fang; Hou, Zhanqun; Gao, Yanxiang
  Food Research International (2013), 50 (2), 603-609CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
  The thermal and light stability of grape skin anthocyanins with enzymically modified isoquercitrin (EMIQ) as a copigment was investigated at different pH levels of 3, 4 and 5. The ratios of anthocyanins to EMIQ were 2:1, 1:1, and 1:2 (wt./wt.), resp., in the thermal expts. at 90 °C, and EMIQ concns. (0.25, 0.5, and 1%, wt./wt.) were evaluated resp. in the light expts. Results revealed that the degrdn. of anthocyanins copigmented with EMIQ followed first-order reaction kinetics. The half life of anthocyanins extended significantly with the increase of EMIQ concn. (p < 0.05), moreover, the color stability increased due to the addn. of EMIQ as the total color difference values ΔE* were smaller for the copigmented anthocyanins. The magnitude of the bathochromic (λmax) shifted to the longest wavelength absorption band with the increasing copigment concn. for all pH levels. Results demonstrated that EMIQ was an effective copigment to stabilize grape skin anthocyanins.
27. 27
  Fanzone, M.; González-Manzano, S.; Pérez-Alonso, J.; Escribano-Bailón, M. T.; Jofré, V.; Assof, M.; Santos-Buelga, C. Evaluation of Dihydroquercetin-3-O-Glucoside from Malbec Grapes as Copigment of Malvidin-3-O-Glucoside Food Chem. 2015, 175, 166– 173 DOI: 10.1016/j.foodchem.2014.11.123
  27
  Evaluation of dihydroquercetin-3-O-glucoside from Malbec grapes as copigment of malvidin-3-O-glucoside
  Fanzone, Martin; Gonzalez-Manzano, Susana; Perez-Alonso, Joaquin; Escribano-Bailon, Maria Teresa; Jofre, Viviana; Assof, Mariela; Santos-Buelga, Celestino
  Food Chemistry (2015), 175 (), 166-173CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  Malbec is a wine grape variety of great phenolic potential characterized for its high levels of anthocyanins and dihydroflavonols. To evaluate the possible implication of dihydroflavonols in the expression of red wine color through reactions of copigmentation or condensation, assays were carried out in wine model systems with different malvidin-3-O-glucoside:dihydroquercetin-3-O-glucoside molar ratios. The addn. of increasing levels of dihydroquercetin-3-O-glucoside to a const. malvidin-3-O-glucoside concn. resulted in a hyperchromic effect assocd. with a darkening of the anthocyanin solns., greater quantity of color and visual satn., perceptible to the human eye. Copigmentation and thermodn. measurements showed that dihydroquercetin-3-O-glucoside can act as an anthocyanin copigment, similar to other usual wine components like flavanols or phenolic acids, although apparently less efficient than flavonols. The high levels of dihydroflavonols existing in Malbec wines in relation to other non-anthocyanin phenolics should make this family of compds. particularly important to explain the color expression in Malbec young red wines.
28. 28
  Baranac, J. M.; Petranovic, N. A.; Dimitric-Markovic, J. M. Spectrophotometric Study of Anthocyan Copigmentation Reactions. 2. Malvin and the Nonglycosidized Flavone Quercetin J. Agric. Food Chem. 1997, 45 (5) 1694– 1697 DOI: 10.1021/jf9606114
  28
  Spectrophotometric Study of Anthocyan Copigmentation Reactions. 2. Malvin and the Nonglycosidized Flavone Quercetin
  Baranac, Jelisaveta M.; Petranovic, Nadezda A.; Dimitric-Markovic, Jasmina M.
  Journal of Agricultural and Food Chemistry (1997), 45 (5), 1694-1697CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  Using UV-vis spectrophotometry we have established that a process of copigmentation takes place between an anthocyan mol., malvin chloride (malvidin 3,5-diglucoside), and a nonglycosidized pentahydroxyflavone, quercetin (3,5,7,3',4'-pentahydroxyflavone). The kinetic and thermodn. parameters, by which the process is characterized, were correlated to the structure, i.e., the nature and position of the substituents in the interacting mols.
29. 29
  Dimitrić-Marković, J. M.; Petranović, N. A.; Baranac, J. M. A Spectrophotometric Study of the Copigmentation of Malvin with Caffeic and Ferulic Acids J. Agric. Food Chem. 2000, 48 (11) 5530– 5536 DOI: 10.1021/jf000038v
  There is no corresponding record for this reference.
30. 30
  Dimitrić-Marković, J. M.; Baranac, J. M.; Brdaric, T. P. Electronic and Infrared Vibrational Analysis of Cyanidin-Quercetin Copigment Complex Spectrochim. Acta, Part A 2005, 62, 673– 680 DOI: 10.1016/j.saa.2005.02.036
  30
  Electronic and infrared vibrational analysis of cyanidin-quercetin copigment complex
  Dimitric Markovic, Jasmina M.; Baranac, Jelisaveta M.; Brdaric, Tanja P.
  Spectrochimica Acta, Part A: Molecular and Biomolecular Spectroscopy (2005), 62A (1-3), 673-680CODEN: SAMCAS; ISSN:1386-1425. (Elsevier B.V.)
  Copigment complex formation between cyanidin and quercetin, in aq. buffered solns., was studied by electronic absorption and IR vibrational spectroscopies. It was found that the assocn. of cyanidin with quercetin occurred at pH 3.0 and pH 5.0 including cyanidin flavylium ion and anhydrobase transformation forms, resp. The obtained copigmentation const. values of K = 2726.7 (pH 3.0) and K = 1093.1 (pH 5.0) indicated good assocn. ability of the investigated mols. IR spectra revealed the existence of hydrogen bonds in the copigment complexes structures. The anal. of the deconvoluted IR spectra indicated several types of hydrogen bonds, differently formed: the H-O ··· H bonds with the corresponding bands around 3500 cm-1 and bonds formed via H3O+, oxonium, ion of the mols. with the corresponding bands below 3000 cm-1.
31. 31
  Lambert, S. G.; Asenstorfer, R. E.; Williamson, N. M.; Iland, P. G.; Jones, G. P. Copigmentation between Malvidin-3-Glucoside and Some Wine Constituents and Its Importance to Colour Expression in Red Wine Food Chem. 2011, 125 (1) 106– 115 DOI: 10.1016/j.foodchem.2010.08.045
  31
  Copigmentation between malvidin-3-glucoside and some wine constituents and its importance to colour expression in red wine
  Lambert, Stephanie G.; Asenstorfer, Robert E.; Williamson, Natalie M.; Iland, Patrick G.; Jones, Graham P.
  Food Chemistry (2011), 125 (1), 106-115CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  Thermodn. parameters for intermol. copigmentation interactions involving malvidin-3-glucoside were detd. by UV/visible spectroscopy at wine pH (pH 3.6). These included assocn. consts., enthalpy and entropy changes, which were measured for chlorogenic acid, caffeic acid, quercetin, quercetin-3-glucoside, (-)-epicatechin, (+)-catechin, procyanidin dimer and seed tannin. Quercetin produced the strongest copigment (KCP = 2900 ± 1300), while the addn. of glucose at position 3 (quercetin-3-glucoside) reduced its effect by almost 10-fold. Malvidin-3-glucoside self-assocn. (KD = 3300 ± 300 mol-1 l) was thermodynamically favored over intermol. interaction with any of the copigments tested. No color enhancement due to self-assocn. was obsd. for malvidin-3-glucoside-derived pigments that cannot enter hydration reactions. In addn., malvidin-3-(6-O-p-coumaryl)glucoside did not show color enhancement suggesting that the p-coumaryl group prevents self-assocn. The malvidin-3-glucoside CD spectrum was not affected by indicated changes in malvidin-3-glucoside concn. These observations demonstrate that self-assocn. of malvidin-3-glucoside is more important than copigmentation in young red wine.
32. 32
  Malaj, N.; De Simone, B. C.; Quartarolo, A. D.; Russo, N. Spectrophotometric Study of the Copigmentation of Malvidin 3-O-Glucoside with P-Coumaric, Vanillic and Syringic Acids Food Chem. 2013, 141 (4) 3614– 3620 DOI: 10.1016/j.foodchem.2013.06.017
  There is no corresponding record for this reference.
33. 33
  Willstätter, R.; Zollinger, E. H. XVI. Über Die Farbstoffe Der Weintraube Und Der Heidelbeere, II Justus Liebigs Ann. Chem. 1917, 412 (2) 195– 216 DOI: 10.1002/jlac.19174120207
  There is no corresponding record for this reference.
34. 34
  Robinson, G. M.; Robinson, R. A Survey of Anthocyanins. I Biochem. J. 1931, 25 (5) 1687– 1705 DOI: 10.1042/bj0251687
  There is no corresponding record for this reference.
35. 35
  Asen, S.; Stewart, R. N.; Norris, K. H.; Massie, D. R. A Stable Blue Non-Metallic Co-Pigment Complex of Delphanin and C-Glycosylflavones in Prof. Blaauw Iris Phytochemistry 1970, 9 (3) 619– 627 DOI: 10.1016/S0031-9422(00)85702-7
  There is no corresponding record for this reference.
36. 36
  Asen, S.; Stewart, R. N.; Norris, K. H. Co-Pigmentation Effect of Quercetin Glycosides on Absorption Characteristics of Cyanidin Glycosides and Color of Red Wing Azalea Phytochemistry 1971, 10 (1) 171– 175 DOI: 10.1016/S0031-9422(00)90266-8
  36
  Copigmentation effect of quercetin glycosides on absorption characteristics of cyanidin glycosides and color of red wing azalea
  Asen, Sam; Stewart, Robert N.; Norris, Karl H.
  Phytochemistry (Elsevier) (1971), 10 (1), 171-5CODEN: PYTCAS; ISSN:0031-9422.
  A quercetin 5-methyl ether and 5 quercetin glycosides were isolated from flowers of Red Wing azalea but were found only in trace amts. in an orange sport of this cultivar. The anthocyanins (cyanidin glycosides) extd. from the orange and red flowers were identical, even though the absorbance spectra of the intact cells differed. The absorbance spectrum of the orange sport was simulated with a 10-3M aq. soln. of cyanidin 3,5-diglucoside at the pH of the tissue, 2.8. The absorbance spectrum of Red Wing was matched with cyanidin 3,5-diglucoside at the same concn. and pH, copigmented with the 3-rhamnoside or galactoside of quercetin.
37. 37
  Asen, S.; Stewart, R. N.; Norris, K. H. Co-Pigmentation of Anthocyanins in Plant Tissues and Its Effect on Color Phytochemistry 1972, 11 (3) 1139– 1144 DOI: 10.1016/S0031-9422(00)88467-8
  37
  Copigmentation of anthocyanins in plant tissues and its effect on color
  Asen, S.; Stewart, R. N.; Norris, K. H.
  Phytochemistry (Elsevier) (1972), 11 (3), 1139-44CODEN: PYTCAS; ISSN:0031-9422.
  Glycosides of the 6 common anthocyanidins all formed copigment complexes with flavonoids and other compds. at pH 2-5. The formation of copigment complexes resulted in a bathochromic shift in the visible λmax. of the anthocyanins and a large increase in extinction at pH 3 and higher. These complexes apparently formed with both the red flavylium salts and the purple anhydro bases. The increase in extinction at pH 3-5 was attributed to the stabilizing effect copigmentation had on the anhydro bases. The degree of copigmentation was a function of the concn. of the anthocyanins and the molar ratio of copigments to anthocyanins. Copigmentation offers an explanation for the infinite color variations that occur in flowers in a pH range where anthocyanins alone are virtually colorless.
38. 38
  Asen, S.; Norris, K. H.; Stewart, R. N. Copigmentation of Aurone and Flavone from Petals of Antirrhinum Majus Phytochemistry 1972, 11 (9) 2739– 2741 DOI: 10.1016/S0031-9422(00)86505-X
  There is no corresponding record for this reference.
39. 39
  Hoshino, T.; Matsumoto, U.; Goto, T. Self-Association of Some Anthocyanins in Neutral Aqueous Solution Phytochemistry 1981, 20 (8) 1971– 1976 DOI: 10.1016/0031-9422(81)84047-2
  There is no corresponding record for this reference.
40. 40
  Hoshino, T.; Matsumoto, U.; Harada, N.; Goto, T. Chiral Exciton Coupled Stacking of Anthocyanins: Interpretation of the Origin of Anomalous CD Induced by Anthocyanin Association Tetrahedron Lett. 1981, 22 (37) 3621– 3624 DOI: 10.1016/S0040-4039(01)81976-6
  There is no corresponding record for this reference.
41. 41
  Hoshino, T.; Matsumoto, U.; Goto, T. Evidences of the Self-Association of Anthocyanins I. Circular Dichroism of Cyanin Anhydrobase Tetrahedron Lett. 1980, 21 (18) 1751– 1754 DOI: 10.1016/S0040-4039(00)77827-0
  There is no corresponding record for this reference.
42. 42
  Hoshino, T.; Matsumoto, U.; Goto, T.; Harada, N. Evidence for the Self-Association of Anthocyanins IV. PMR Spectroscopic Evidence for the Vertical Stacking of Anthocyanin Molecules Tetrahedron Lett. 1982, 23 (4) 433– 436 DOI: 10.1016/S0040-4039(00)86852-5
  There is no corresponding record for this reference.
43. 43
  Hoshino, T.; Goto, T. Effects of pH and Concentration on the Self-Association of Malvin Quinonoidal Base: Electronic and Circular Dichroic Studies Tetrahedron Lett. 1990, 31 (11) 1593– 1596 DOI: 10.1016/0040-4039(90)80025-H
  There is no corresponding record for this reference.
44. 44
  Hoshino, T. Self-Association of Flavylium Cations of Anthocyanidin 3,5-Diglucosides Studied by Circular Dichroism and 1H NMR Phytochemistry 1992, 31 (2) 647– 653 DOI: 10.1016/0031-9422(92)90053-S
  44
  Anthocyanin self-aggregates. Part 7. Self-association of flavylium cations of anthocyanidin 3,5-diglucosides studied by circular dichroism and proton NMR
  Hoshino, Tsutomu
  Phytochemistry (1992), 31 (2), 647-53CODEN: PYTCAS; ISSN:0031-9422.
  Exciton coupling type CD was induced by increasing anthocyanin concn. in strongly acidic media. The higher the concn., the larger the CD magnitude. All anthocyanidin 3,5-diglucosides exhibited neg. signs in the first Cotton effect, which indicates that all the anthocyanins self-assoc. in a left-handed screw manner. Concn. dependence of proton chem. shifts were also obsd. with increase of anthocyanidin 3,5-diglucosides in a strongly acidic medium; upfield shifts of arom. rings by increasing pigment concns. demonstrated that anthocyanidin nuclei stack vertically. Analyses of proton chem. shifts based on the Dimicoli and Helene equation made possible the detn. of the self-assocn. of flavylium cations. The self-assocn. consts. for the most common natural anthocyanidin 3,5-diglucosides are given.
45. 45
  Hoshino, T. An Approximate Estimate of Self-Association Constants and the Self-Stacking Conformation of Malvin Quinonoidal Bases Studied by 1H NMR Phytochemistry 1991, 30 (6) 2049– 2055 DOI: 10.1016/0031-9422(91)85065-8
  There is no corresponding record for this reference.
46. 46
  Brouillard, R.; Mazza, G.; Saad, Z.; Albrecht-Gary, A. M.; Cheminat, A. The Co-Pigmentation Reaction of Anthocyanins: A Microprobe for the Structural Study of Aqueous Solutions J. Am. Chem. Soc. 1989, 111 (7) 2604– 2610 DOI: 10.1021/ja00189a039
  46
  The co-pigmentation reaction of anthocyanins: a microprobe for the structural study of aqueous solutions
  Brouillard, R.; Mazza, G.; Saad, Z.; Albrecht-Gary, A. M.; Cheminat, A.
  Journal of the American Chemical Society (1989), 111 (7), 2604-10CODEN: JACSAT; ISSN:0002-7863.
  Visible absorption spectrometry shows that, in acidic aq. solns., chlorogenic acid (I) forms a loose 1:1 complex with malvin chloride (II). The mol. interaction taking place between these two chem. species is characteristic of the copigmentation reaction of anthocyanins. For the first time the mechanism assocd. with this reaction is established. The equation describing the copigment effect is also given. The copigmentation reaction is a very fast process which is extremely influenced by temp. Increasing the temp. or adding MeOH, HCONH2, or NaCl always reduces the copigment effect. In fact, the extent of copigmentation is strictly under the control of the unique mol. structure of liq. water. Finally, the copigmentation phenomenon, which is widespread in higher plants, constitutes a simple, inexpensive, and very sensitive, microprobe for the structural studies of aq. solns.
47. 47
  Figueiredo, P.; Elhabiri, M.; Saito, N.; Brouillard, R. Anthocyanin Intramolecular Interactions. A New Mathematical Approach To Account for the Remarkable Colorant Properties of the Pigments Extracted from Matthiola Incana J. Am. Chem. Soc. 1996, 118 (20) 4788– 4793 DOI: 10.1021/ja9535064
  There is no corresponding record for this reference.
48. 48
  Figueiredo, P.; Elhabiri, M.; Toki, K.; Saito, N.; Dangles, O.; Brouillard, R. New Aspects of Anthocyanin Complexation. Intramolecular Copigmentation as a Means for Colour Loss? Phytochemistry 1996, 41 (1) 301– 308 DOI: 10.1016/0031-9422(95)00530-7
  There is no corresponding record for this reference.
49. 49
  Zhang, B.; Liu, R.; He, F.; Zhou, P.-P.; Duan, C.-Q. Copigmentation of Malvidin-3-O-Glucoside with Five Hydroxybenzoic Acids in Red Wine Model Solutions: Experimental and Theoretical Investigations Food Chem. 2015, 170, 226– 233 DOI: 10.1016/j.foodchem.2014.08.026
  49
  Copigmentation of malvidin-3-O-glucoside with five hydroxybenzoic acids in red wine model solutions: Experimental and theoretical investigations
  Zhang, Bo; Liu, Rui; He, Fei; Zhou, Pan-Pan; Duan, Chang-Qing
  Food Chemistry (2015), 170 (), 226-233CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  In the present research, the copigmentations of malvidin-3-O-glucoside with five hydroxybenzoic cofactors (p-hydroxybenzoic acid, protocatechuic acid, gallic acid, vanillic acid, and syringic acid) were investigated. The influence of the concn. of these cofactors and the reaction temp. was examd. The equil. const. (K), stoichiometric ratio (n) and the thermodn. parameters (ΔG°, ΔH°, ΔS°) related to the copigmentation were also reported here. Theor. calcns. were performed to identify the relative arrangement between the pigment and cofactors in the copigmentation complexes. Besides, the comparison of the relative binding free energies (ΔΔGbinding) derived from the theor. calcns. and exptl. data were made, and the binding strength of these copigmentation complexes was discussed with the interaction energies (ΔE). AIM anal. was also used to explore the main driving forces contributing to the copigmentation. In the comparison of the five studied cofactors, syringic acid had a stronger copigmentation effect than the other four phenolic acids investigated.
50. 50
  Teixeira, N.; Cruz, L.; Brás, N. F.; Mateus, N.; Ramos, M. J.; de Freitas, V. Structural Features of Copigmentation of Oenin with Different Polyphenol Copigments J. Agric. Food Chem. 2013, 61 (28) 6942– 6948 DOI: 10.1021/jf401174b
  50
  Structural Features of Copigmentation of Oenin with Different Polyphenol Copigments
  Teixeira, Natercia; Cruz, Luis; Bras, Natercia F.; Mateus, Nuno; Ramos, Maria Joao; de Freitas, Victor
  Journal of Agricultural and Food Chemistry (2013), 61 (28), 6942-6948CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  The copigmentation binding consts. (K) for the interaction of different copigments with oenin (major red wine anthocyanin) were detd. All tests were performed in a 12% ethanol citrate buffer soln. (0.2 M) at pH 3.5, with an ionic strength adjusted to 0.5 M by the addn. of sodium chloride. Over the past years, several copigmentation studies were made and many copigments were tested, but none of them included prodelphinidin B3 or a dimeric-type adduct like oenin-(O)-catechin, probably due to the difficulty in obtaining them. The data yielded from this study allowed concluding that (a) the presence of a pyrogallol group in the B ring of the flavan-3-ol structure slightly increases the copigmentation potential and (b) within all copigments tested oenin-(O)-catechin was revealed to be the best. According to computational studies performed on epicatechin/oenin, epigallocatechin/oenin, procyanidin B3/oenin, and oenin-(O)-catechin/oenin complexes, the ΔGbinding energy of the oenin-(O)-catechin/oenin complex is the most neg. compared to the other copigmentation complexes, hence being more stable and thermodynamically favored. All structural data show that oenin-(O)-catechin and epigallocatechin are closer to the pigment mol., which is in accordance with these two copigments having the highest exptl. copigmentation binding consts. for oenin.
51. 51
  Fossen, T.; Rayyan, S.; Holmberg, M. H.; Nimtz, M.; Andersen, Ø. M. Covalent Anthocyanin–flavone Dimer from Leaves of Oxalis Triangularis Phytochemistry 2007, 68 (5) 652– 662 DOI: 10.1016/j.phytochem.2006.10.030
  There is no corresponding record for this reference.
52. 52
  Saito, N.; Nakamura, M.; Shinoda, K.; Murata, N.; Kanazawa, T.; Kato, K.; Toki, K.; Kasai, H.; Honda, T.; Tatsuzawa, F. Covalent Anthocyanin–flavonol Complexes from the Violet-Blue Flowers of Allium “Blue Perfume. Phytochemistry 2012, 80, 99– 108 DOI: 10.1016/j.phytochem.2012.04.011
  There is no corresponding record for this reference.
53. 53
  Hayashi, K.; Abe, Y.; Mitsui, S. Blue Anthocyanin from the Flowers of Commelina, the Crystallisation and Some Properties Thereof Proc. Jpn. Acad. 1958, 34 (6) 373– 378
  53
  Anthocyanins. XXX. Blue anthocyanin from flowers of Commelina, the crystallization and some properties thereof
  Hayashi, Kozo; Abe, Yukihide; Mitsui, Seiji
  Proceedings of the Japan Academy (1958), 34 (), 373-8CODEN: PJACAW; ISSN:0021-4280.
  cf. C.A. 50, 16935g. Brilliant blue, prismatic crystals obtained after repeated fractionation and pptn. with water and EtOH were subjected to qual. chem. analysis and behavior. The substance contained an appreciable amt. of metallic elements of which Mg and K were inherent to the pigment mol. It is readily sol. in water but does not retain its color in org. solvents and is neither acid nor base. Paper electrophoresis indicated the existence of essential structural difference between the blue and red forms of anthocyanin. The org. components seemed to be delphinidin, glucose, and p-coumaric acid.
54. 54
  Shibata, K.; Shibata, Y.; Kasiwagi, I. Studies on Anthocyanins: Color Variationin Anthocyanins J. Am. Chem. Soc. 1919, 41 (2) 208– 220 DOI: 10.1021/ja01459a008
  There is no corresponding record for this reference.
55. 55
  Bloor, S. J. Blue Flower Colour Derived from Flavonol-Anthocyanin Co-Pigmentation in Ceanothus Papillosus Phytochemistry 1997, 45 (7) 1399– 1405 DOI: 10.1016/S0031-9422(97)00129-5
  There is no corresponding record for this reference.
56. 56
  Tamura, H.; Kondo, T.; Goto, T. The Composition of Commelinin, a Highly Associated Metalloanthocaynin Present in the Blue Flower Petals of Commelina Communis Tetrahedron Lett. 1986, 27 (16) 1801– 1804 DOI: 10.1016/S0040-4039(00)84379-8
  There is no corresponding record for this reference.
57. 57
  Kondo, T.; Ueda, M.; Isobe, M.; Goto, T. A New Molecular Mechanism of Blue Color Development with Protocyanin, a Supramolecular Pigment from Cornflower, Centaurea Cyanus Tetrahedron Lett. 1998, 39 (45) 8307– 8310 DOI: 10.1016/S0040-4039(98)01858-9
  There is no corresponding record for this reference.
58. 58
  Kondo, T.; Oyama, K.; Yoshida, K. Chiral Molecular Recognition on Formation of a Metalloanthocyanin: A Supramolecular Metal Complex Pigment from Blue Flowers of Salvia Patens Angew. Chem., Int. Ed. 2001, 40 (5) 894– 897 DOI: 10.1002/1521-3773(20010302)40:5<894::AID-ANIE894>3.3.CO;2-#
  There is no corresponding record for this reference.
59. 59
  Mori, M.; Kondo, T.; Yoshida, K. Cyanosalvianin, a Supramolecular Blue Metalloanthocyanin, from Petals of Salvia Uliginosa Phytochemistry 2008, 69 (18) 3151– 3158 DOI: 10.1016/j.phytochem.2008.03.015
  There is no corresponding record for this reference.
60. 60
  Yoshida, K.; Toyama-Kato, Y.; Kameda, K.; Kondo, T. Sepal Color Variation of Hydrangea Macrophylla and Vacuolar pH Measured with a Proton-Selective Microelectrode Plant Cell Physiol. 2003, 44 (3) 262– 268 DOI: 10.1093/pcp/pcg033
  There is no corresponding record for this reference.
61. 61
  Kondo, T.; Toyama-Kato, Y.; Yoshida, K. Essential Structure of Co-Pigment for Blue Sepal-Color Development of Hydrangea Tetrahedron Lett. 2005, 46 (39) 6645– 6649 DOI: 10.1016/j.tetlet.2005.07.146
  There is no corresponding record for this reference.
62. 62
  Tanaka, M.; Fujimori, T.; Uchida, I.; Yamaguchi, S.; Takeda, K. A Malonylated Anthocyanin and Flavonols in Blue Meconopsis Flowers Phytochemistry 2001, 56 (4) 373– 376 DOI: 10.1016/S0031-9422(00)00357-5
  There is no corresponding record for this reference.
63. 63
  Yoshida, K.; Kitahara, S.; Ito, D.; Kondo, T. Ferric Ions Involved in the Flower Color Development of the Himalayan Blue Poppy, Meconopsis Grandis Phytochemistry 2006, 67 (10) 992– 998 DOI: 10.1016/j.phytochem.2006.03.013
  There is no corresponding record for this reference.
64. 64
  Markham, K. R.; Mitchell, K. A.; Boase, M. R. Malvidin-3-O-Glucoside-5-O-(6-Acetylglucoside) and Its Colour Manifestation in “Johnson”s Blue’ and Other “Blue” Geraniums Phytochemistry 1997, 45 (2) 417– 423 DOI: 10.1016/S0031-9422(96)00831-X
  There is no corresponding record for this reference.
65. 65
  Yabuya, T.; Nakamura, M.; Iwashina, T.; Yamaguchi, M.; Takehara, T. Anthocyanin-Flavone Copigmentation in Bluish Purple Flowers of Japanese Garden Iris (Iris Ensata Thunb.) Euphytica 1997, 98 (3) 163– 167 DOI: 10.1023/A:1003152813333
  There is no corresponding record for this reference.
66. 66
  Bimpilas, A.; Tsimogiannis, D.; Balta-Brouma, K.; Lymperopoulou, T.; Oreopoulou, V. Evolution of Phenolic Compounds and Metal Content of Wine during Alcoholic Fermentation and Storage Food Chem. 2015, 178, 164– 171 DOI: 10.1016/j.foodchem.2015.01.090
  66
  Evolution of phenolic compounds and metal content of wine during alcoholic fermentation and storage
  Bimpilas, Andreas; Tsimogiannis, Dimitrios; Balta-Brouma, Kalliopi; Lymperopoulou, Theopisti; Oreopoulou, Vassiliki
  Food Chemistry (2015), 178 (), 164-171CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  Changes in the principal phenolic compds. and metal content during the vinification process and storage under modified atm. (50% N2, 50% CO2) of Merlot and Syrah wines, from grapes cultivated in Greece, have been investigated. Comparing the variation of metals at maceration process, with the variation of monomeric anthocyanins and flavonols, an inverse relationship was noticed, that can be attributed to complexing reactions of polyphenols with particular trace elements. Cu decreased rapidly, whereas a similar behavior that could be expected for Fe and Mn was not confirmed. Differences in the profile of anthocyanins and flavonols in the fresh Merlot and Syrah wines are reported. During 1 yr of storage monomeric anthocyanins declined almost tenfold, probably due to polymn. reactions and copigmentation. Also, a decrease in flavonol glycosides and increase in the resp. aglycons was obsd., attributed to enzymic hydrolysis. The concn. of total phenols and all metals remained practically const.
67. 67
  Hermosín Gutiérrez, I. Influence of Ethanol Content on the Extent of Copigmentation in a Cencibel Young Red Wine J. Agric. Food Chem. 2003, 51 (14) 4079– 4083 DOI: 10.1021/jf021029k
  There is no corresponding record for this reference.
68. 68
  Monagas, M.; Bartolomé, B. Anthocyanins and Anthocyanin-Derived Compounds. In Wine Chemistry and Biochemistry; Moreno-Arribas, M. V.; Polo, M. C., Eds.; Springer: New York, 2009; pp 439– 462.
  There is no corresponding record for this reference.
69. 69
  Rustioni, L.; Bedgood, D. R.; Failla, O.; Prenzler, P. D.; Robards, K. Copigmentation and Anti-Copigmentation in Grape Extracts Studied by Spectrophotometry and Post-Column-Reaction HPLC Food Chem. 2012, 132 (4) 2194– 2201 DOI: 10.1016/j.foodchem.2011.12.058
  There is no corresponding record for this reference.
70. 70
  De Rosso, M.; Tonidandel, L.; Larcher, R.; Nicolini, G.; Dalla Vedova, A.; De Marchi, F.; Gardiman, M.; Giust, M.; Flamini, R. Identification of New Flavonols in Hybrid Grapes by Combined Liquid Chromatography–mass Spectrometry Approaches Food Chem. 2014, 163, 244– 251 DOI: 10.1016/j.foodchem.2014.04.110
  There is no corresponding record for this reference.
71. 71
  Kelebek, H.; Canbas, A.; Selli, S. HPLC-DAD–MS Analysis of Anthocyanins in Rose Wine Made From Cv. Öküzgözü Grapes, and Effect of Maceration Time on Anthocyanin Content Chromatographia 2007, 66 (3–4) 207– 212 DOI: 10.1365/s10337-007-0277-8
  There is no corresponding record for this reference.
72. 72
  Gordillo, B.; Rodríguez-Pulido, F. J.; González-Miret, M. L.; Quijada-Morín, N.; Rivas-Gonzalo, J. C.; García-Estévez, I.; Heredia, F. J.; Escribano-Bailón, M. T. Application of Differential Colorimetry To Evaluate Anthocyanin–Flavonol–Flavanol Ternary Copigmentation Interactions in Model Solutions J. Agric. Food Chem. 2015, 63 (35) 7645– 7653 DOI: 10.1021/acs.jafc.5b00181
  There is no corresponding record for this reference.
73. 73
  Somers, T. C.; Vérette, E. Phenolic Composition of Natural Wine Types. In Wine Analysis; Linskens, P. D. H.-F.; Jackson, P. D. J. F., Eds.; Modern Methods of Plant Analysis; Springer: Berlin, 1988; pp 219– 257.
  There is no corresponding record for this reference.
74. 74
  González-Manzano, S.; Dueñas, M.; Rivas-Gonzalo, J. C.; Escribano-Bailón, M. T.; Santos-Buelga, C. Studies on the Copigmentation between Anthocyanins and Flavan-3-Ols and Their Influence in the Colour Expression of Red Wine Food Chem. 2009, 114 (2) 649– 656 DOI: 10.1016/j.foodchem.2008.10.002
  74
  Studies on the copigmentation between anthocyanins and flavan-3-ols and their influence in the colour expression of red wine
  Gonzalez-Manzano, Susana; Duenas, Montserrat; Rivas-Gonzalo, Julian C.; Escribano-Bailon, M. Teresa; Santos-Buelga, Celestino
  Food Chemistry (2009), 114 (2), 649-656CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier B.V.)
  With the aim of evaluating the importance of the copigmentation process between anthocyanins and flavanols on the color expression of red wine, assays were carried out in wine model systems with mixts. of compds. obtained from two Vitis vinifera grape varieties (Graciano and Tempranillo). Spectrophotometric and chromatic analyses were performed to evaluate the magnitude of the copigmentation and the modifications induced in the color of the solns. Measurement of the changes in the anthocyanin hydration const. (Kh) was also used to det. the strength of the copigmentation process. All the flavanols assayed induced significant changes in the color, perceptible to the human eye, of the wine-like anthocyanin solns. at concns. similar to those that can exist in red wines. The percentage contribution of the copigmentation with flavanols to the color of the anthocyanin solns. was found to range from 2% to 20%. The extent of this effect was related not only to the concn. of flavanols but also to the qual. compn. of the flavanol prepns., as influenced by the part of the grape (either skin or seed) and the variety considered. Divergences were found between the evaluation of the copigmentation based on chromatic parameters in the CIELAB color space and that based on the measurement at visible λ max, as the latter does not consider the integral color changes produced in the visible spectrum. The results obtained confirmed the importance of the qual. phenolic compn., detd. in the wine by the type of grape and winemaking practices, to the prodn. of an effective copigmentation process.
75. 75
  Fernandes, A.; Brás, N. F.; Mateus, N.; Freitas, V. de. A Study of Anthocyanin Self-Association by NMR Spectroscopy New J. Chem. 2015, 39 (4) 2602– 2611 DOI: 10.1039/C4NJ02339K
  There is no corresponding record for this reference.
76. 76
  Heras-Roger, J.; Pomposo-Medina, M.; Díaz-Romero, C.; Darias-Martín, J. Copigmentation, Colour and Antioxidant Activity of Single-Cultivar Red Wines Eur. Food Res. Technol. 2014, 239 (1) 13– 19 DOI: 10.1007/s00217-014-2185-0
  76
  Copigmentation, colour and antioxidant activity of single-cultivar red wines
  Heras-Roger, J.; Pomposo-Medina, M.; Diaz-Romero, C.; Darias-Martin, J.
  European Food Research and Technology (2014), 239 (1), 13-19CODEN: EFRTFO; ISSN:1438-2377. (Springer)
  A hundred and thirty-six single-cultivar red wines of different vintages were collected from several wineries in the Canary Islands in order to study the magnitude of the copigmentation phenomenon and the antioxidant activity. The contribution of free anthocyanins, copigmented anthocyanins and polymeric pigments to the color of wine, as well as the total phenols, the antioxidant activity (2,2-diphenyl-1-picrylhydrazyl, DPPH method) and the chromatic characteristics of the wines were detd. The influence of ageing time and the climatic conditions on these parameters was also studied. The wines made with Merlot, Ruby Cabernet and Syrah cultivars showed the highest parameters of color, and the largest contribution to the copigmented anthocyanins was from the Ruby Cabernet, Listan negro and Syrah cultivars. The copigmented anthocyanins and the free anthocyanins decrease with the age of the wine, and the antioxidant activity of the samples appears to be related to the total phenol content. An influence of the climatic conditions on color parameters has been found. The correlation study between parameters suggests that the parameters b* and L* could be used as suitable indicators of evolution or oxidn. stage of red wines.
77. 77
  García-Marino, M.; Escudero-Gilete, M. L.; Heredia, F. J.; Escribano-Bailón, M. T.; Rivas-Gonzalo, J. C. Color-Copigmentation Study by Tristimulus Colorimetry (CIELAB) in Red Wines Obtained from Tempranillo and Graciano Varieties Food Res. Int. 2013, 51 (1) 123– 131 DOI: 10.1016/j.foodres.2012.11.035
  77
  Color-copigmentation study by tristimulus colorimetry (CIELAB) in red wines obtained from Tempranillo and Graciano varieties
  Garcia-Marino, Matilde; Escudero-Gilete, Maria Luisa; Heredia, Francisco Jose; Escribano-Bailon, Maria Teresa; Rivas-Gonzalo, Julian Carlos
  Food Research International (2013), 51 (1), 123-131CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
  A study of the changes of copigmentation phenomenon in wines elaborated from different varieties has been undertaken. Colorimetric measurement of Tempranillo (T) and Graciano (G) monovarietal wines, and two 80:20 blend wines: M, (grape blending T and G, co-maceration) and W (wine blending T and G, co-vinification) was performed by spectrophotometry. Significant differences (p < 0.05) were found among the color of the wines. The Graciano cv. afforded somewhat darker and more colorful wines than the other wines. The color difference values, ΔE*ab suggested that co-vinification (W) led to wines being more similar to T than the co-maceration (M). The ΔE*ab[w-c] between untreated wines - whole wines, w - and the wines dild. to eliminate copigmentation - cor. wines, c - was 14.2 CIELAB units in the initial stages of winemaking and 6.7 in the final stages. M had a greater proportion of color due to copigmentation than the monovarietal wines. Evaluation of this parameter confirms the importance of copigmentation process into wine color during the early stages of the vinification. Also, through the full spectrum, quant. data obtained allow a visual interpretation of the changes involved. In addn., with the aging in bottle, M wines had more stable color and more different color than W wines.
78. 78
  Schwarz, M.; Picazo-Bacete, J. J.; Winterhalter, P.; Hermosín-Gutiérrez, I. Effect of Copigments and Grape Cultivar on the Color of Red Wines Fermented after the Addition of Copigments J. Agric. Food Chem. 2005, 53 (21) 8372– 8381 DOI: 10.1021/jf051005o
  There is no corresponding record for this reference.
79. 79
  Aleixandre-Tudó, J. L.; Álvarez, I.; Lizama, V.; García, M. J.; Aleixandre, J. L.; Du Toit, W. J. Impact of Caffeic Acid Addition on Phenolic Composition of Tempranillo Wines from Different Winemaking Techniques J. Agric. Food Chem. 2013, 61 (49) 11900– 11912 DOI: 10.1021/jf402713d
  There is no corresponding record for this reference.
80. 80
  Gris, E. F.; Ferreira, E. A.; Falcão, L. D.; Bordignon-Luiz, M. T. Influence of Ferulic Acid on Stability of Anthocyanins from Cabernet Sauvignon Grapes in a Model System and a Yogurt System Int. J. Food Sci. Technol. 2007, 42 (8) 992– 998 DOI: 10.1111/j.1365-2621.2006.01335.x
  80
  Influence of ferulic acid on stability of anthocyanins from Cabernet Sauvignon grapes in a model system and a yogurt system
  Gris, Eliana Fortes; Ferreira, Eduardo Antonio; Falcao, Leila Denise; Bordignon-Luiz, Marilde Terezinha
  International Journal of Food Science and Technology (2007), 42 (8), 992-998CODEN: IJFTEZ; ISSN:0950-5423. (Blackwell Publishing Ltd.)
  The influence of different factors on the stability of the anthocyanin crude ext. from Cabernet Sauvignon grape skins was investigated. In a model system, the factors evaluated were as follows: temp. 4 ± 1 °C and 29 ± 3 °C, presence and absence of light, pH 3.0 and 4.0 and presence of ferulic acid. The influence of the addn. of ferulic acid to anthocyanins was investigated in a yogurt system stored at 4 ± 1 °C. The results obtained for anthocyanin degrdn. velocity const. and for the half-life time of anthocyanins in a model system and in a yogurt system showed that ferulic acid significantly increased the stability of the anthocyanins crude ext.
81. 81
  Talcott, S. T.; Peele, J. E.; Brenes, C. H. Red Clover Isoflavonoids as Anthocyanin Color Enhancing Agents in Muscadine Wine and Juice Food Res. Int. 2005, 38 (10) 1205– 1212 DOI: 10.1016/j.foodres.2005.05.004
  81
  Red clover isoflavonoids as anthocyanin color enhancing agents in muscadine wine and juice
  Talcott, Stephen T.; Peele, Janelle E.; Brenes, Carmen H.
  Food Research International (2005), 38 (10), 1205-1212CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
  Isoflavonoid exts. from red clover (Trifolium pratense) leaves were found to enhance overall color and stability of anthocyanin 3,5-diglucosides present in muscadine grape (Vitis rotundifolia) juice and wine through intermol. copigmentation reactions. Predominant isoflavonoids present in red clover included formononetin, biochanin A, and prunetin and were the major polyphenolics identified to influence anthocyanin color and stability. Since red clover isoflavonoids have poor water soly. characteristics, this allowed for removal of extraneous non-isoflavonoid compds. using hot water and subsequent extn. with ethanol. Isoflavonoid soly. was evaluated as a function of ethanol concn. with recoveries up to 57% found in 20% solns. Changes in max. absorbance, total sol. phenolics, isoflavonoids, and anthocyanins were evaluated in muscadine juice and wine following the addn. of isoflavonoid exts. with max. color enhancement found at an anthocyanin to cofactor ratio of 1:8, after which their soly. was prohibitive. Addnl., dried leaves and ethanolic exts. of red clover were added prior to and following fermn. of muscadine wine (11% ethanol) stimulating the natural copigmentation that takes place during red wine fermn. and aging processes. Once fermn. was complete, finished wines were evaluated over a 9-wk storage period at 20 and 37°. Despite low levels of isoflavonoids present, color improvement and anthocyanin stability was obsd. in the wines during storage. Little information is available on copigmentation reactions occurring in actual food systems, yet red clover isoflavonoids proved to be novel and effective color enhancing compds. when used in low concns. in young muscadine wines.
82. 82
  Liu, S.; Fu, Y.; Nian, S. Buffering Colour Fluctuation of Purple Sweet Potato Anthocyanins to Acidity Variation by Surfactants Food Chem. 2014, 162, 16– 21 DOI: 10.1016/j.foodchem.2014.04.029
  82
  Buffering color fluctuation of purple sweet potato anthocyanins to acidity variation by surfactants
  Liu, Songbai; Fu, Yuanqing; Nian, Si
  Food Chemistry (2014), 162 (), 16-21CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  Anthocyanins are intriguing natural pigments with beneficial bioactivities and their color is extremely susceptible to acidity variation. Minimization of color fluctuation is essential to maintain quality consistency in food industry. A new strategy employing surfactants to mimic encapsulation was attempted with typical anionic, cationic and nonionic surfactants and proved effective although the traditional copigmentation method was inactive. The exceptional color fluctuation buffering effect of anionic surfactants esp. SDS was revealed and then carefully analyzed by colorimetric and spectroscopic methods. The outstanding activity of SDS presumably resulted from effective shielding of anthocyanins from external acidity through strong interaction with the pos. charged flavylium cations owing to its anionic nature. These results suggest SDS is a valuable additive for buffering color fluctuation of anthocyanins. The strategy of surfactant will be useful for buffering color fluctuation of natural colorants.
83. 83
  Kovac, V.; Alonso, E.; Bourzeix, M.; Revilla, E. Effect of Several Enological Practices on the Content of Catechins and Proanthocyanidins of Red Wines J. Agric. Food Chem. 1992, 40 (10) 1953– 1957 DOI: 10.1021/jf00022a045
  There is no corresponding record for this reference.
84. 84
  Canals, R.; del Carmen Llaudy, M.; Canals, J. M.; Zamora, F. Influence of the Elimination and Addition of Seeds on the Colour, Phenolic Composition and Astringency of Red Wine Eur. Food Res. Technol. 2008, 226 (5) 1183– 1190 DOI: 10.1007/s00217-007-0650-8
  84
  Influence of the elimination and addition of seeds on the colour, phenolic composition and astringency of red wine
  Canals, Roser; del Carmen Llaudy, Maria; Canals, Joan Miquel; Zamora, Fernando
  European Food Research and Technology (2008), 226 (5), 1183-1190CODEN: EFRTFO; ISSN:1438-2377. (Springer GmbH)
  Several winemaking techniques were developed to eliminate seeds to prevent the release of high amts. of very astringent proanthocyanidins, esp. when the grapes are unripe. However, there is no scientific information on the effects of this practice. The aim of this paper is to study how the elimination and addn. of seeds influence the color, phenolic compn. and astringency of red wine. The elimination of around 80% of the seeds led to a significant decrease of color intensity and anthocyanin concn. The addn. of seeds originated wines with a greater concn. of total anthocyanin, but did not significantly affect the wine color. These wines also presented significantly higher levels of proanthocyanidins, a greater proportion of epicatechin-3-gallate, a lower mean d.p., and, in particular, a drastic increase in astringency. Wines obtained with the elimination of seeds, on the other hand, had exactly the opposite characteristics.
85. 85
  Escribano-Bailon, M. T.; Santos-Buelga, C. Anthocyanin Copigmentation - Evaluation, Mechanisms and Implications for the Colour of Red Wines Curr. Org. Chem. 2012, 16 (6) 715– 723 DOI: 10.2174/138527212799957977
  85
  Anthocyanin copigmentation - evaluation, mechanisms and implications for the colour of red wines
  Escribano-Bailon, Maite T.; Santos-Buelga, Celestino
  Current Organic Chemistry (2012), 16 (6), 715-723CODEN: CORCFE; ISSN:1385-2728. (Bentham Science Publishers Ltd.)
  A review. Copigmentation is the main color-stabilizing mechanism in plants and in food products of vegetable origin. It is a spontaneous and exothermic process that consists of the stacking of an org. mol., called copigment, on the planar polarizable moieties of the anthocyanin colored forms. Although this phenomenon has long been described, there are some aspects that are still not well understood or controversial like the nature of the interaction pigment to copigment, the way to quantify the extent of the process, its effect on other anthocyanin properties like astringency or reactivity. In this article a review of the most significant advances achieved in the last years in the field of intramol. and intermol. copigmentation is presented. Also, the most recent findings regarding wine copigments and their effects on the color of red wines are revised.
86. 86
  Quijada-Morín, N.; Dangles, O.; Rivas-Gonzalo, J. C.; Escribano-Bailón, M. T. Physico-Chemical and Chromatic Characterization of Malvidin 3-Glucoside-Vinylcatechol and Malvidin 3-Glucoside-Vinylguaiacol Wine Pigments J. Agric. Food Chem. 2010, 58 (17) 9744– 9752 DOI: 10.1021/jf102238v
  There is no corresponding record for this reference.
87. 87
  Oliveira, J.; Mateus, N.; Silva, A. M. S.; de Freitas, V. Equilibrium Forms of Vitisin B Pigments in an Aqueous System Studied by NMR and Visible Spectroscopy J. Phys. Chem. B 2009, 113 (32) 11352– 11358 DOI: 10.1021/jp904776k
  There is no corresponding record for this reference.
88. 88
  Brouillard, R.; Dangles, O. Anthocyanin Molecular Interactions: The First Step in the Formation of New Pigments during Wine Aging? Food Chem. 1994, 51 (4) 365– 371 DOI: 10.1016/0308-8146(94)90187-2
  There is no corresponding record for this reference.
89. 89
  Wrolstad, R. E.; Erlandson, J. A. Effect of Metal Ions on the Color of Strawberry Puree J. Food Sci. 1973, 38 (3) 460– 463 DOI: 10.1111/j.1365-2621.1973.tb01454.x
  There is no corresponding record for this reference.
90. 90
  Starr, M. S.; Francis, F. J. Effect of Metallic Ions on Color and Pigment Content of Cranberry Juice Cocktail J. Food Sci. 1973, 38 (6) 1043– 1046 DOI: 10.1111/j.1365-2621.1973.tb02144.x
  There is no corresponding record for this reference.
91. 91
  Kallio, H.; Pallasaho, S.; Kärppä, J.; Linko, R. R. Comparison of the Half-Lives of the Anthocyanins in the Juice of Crowberry, Empetrum Nigrum J. Food Sci. 1986, 51 (2) 408– 410 DOI: 10.1111/j.1365-2621.1986.tb11142.x
  There is no corresponding record for this reference.
92. 92
  Osawa, Y. Chapter 2 - Copigmentation of Anthocyanins. In Anthocyanins As Food Colors; Markakis, P., Ed.; Academic Press, 1982; pp 41– 68.
  There is no corresponding record for this reference.
93. 93
  Rein, M. J.; Heinonen, M. Stability and Enhancement of Berry Juice Color J. Agric. Food Chem. 2004, 52 (10) 3106– 3114 DOI: 10.1021/jf035507i
  There is no corresponding record for this reference.
94. 94
  Maccarone, E.; Maccarrone, A.; Rapisarda, P. Stabilization of Anthocyanins of Blood Orange Fruit Juice J. Food Sci. 1985, 50 (4) 901– 904 DOI: 10.1111/j.1365-2621.1985.tb12976.x
  There is no corresponding record for this reference.
95. 95
  Wilska-Jeszka, J.; Korzuchowska, A. Anthocyanins and Chlorogenic Acid Copigmentation - Influence on the Colour of Strawberry and Chokeberry Juices Z. Lebensm.-Unters. Forsch. 1996, 203 (1) 38– 42 DOI: 10.1007/BF01267767
  95
  Anthocyanins and chlorogenic acid copigmentation. Influence on the color of strawberry and chokeberry juices
  Wilska-Jeszka, Jadwiga; Korzuchowska, Anna
  Zeitschrift fuer Lebensmittel-Untersuchung und -Forschung (1996), 203 (1), 38-42CODEN: ZLUFAR; ISSN:0044-3026. (Springer)
  The effect of copigmentation on chlorogenic acid with anthocyanins in strawberry and chokeberry juices was investigated. Chlorogenic acid, at concns. greater than that of anthocyanins, enhanced the color intensity of these juices. The max. copigmentation effect in both juices was obsd. at pH 3.4. In the investigated range of the copigment/pigment ratio, i.e. 1:1 to 50:1, absorbance increased (ΔA) linearly with copigment content, ΔA/g chlorogenic acid was greater in chokeberry than in strawberry juices. In solns. of purified pigments of these fruits, smaller copigmentation effects were obsd. than in juices under the same conditions, which indicated the participation of natural copigments present in fruits in the copigmentation process.
96. 96
  Hernández-Herrero, J. A.; Frutos, M. J. Influence of Rutin and Ascorbic Acid in Colour, Plum Anthocyanins and Antioxidant Capacity Stability in Model Juices Food Chem. 2015, 173, 495– 500 DOI: 10.1016/j.foodchem.2014.10.059
  There is no corresponding record for this reference.
97. 97
  Sari, P.; Wijaya, C. H.; Sajuthi, D.; Supratman, U. Colour Properties, Stability, and Free Radical Scavenging Activity of Jambolan (Syzygium Cumini) Fruit Anthocyanins in a Beverage Model System: Natural and Copigmented Anthocyanins Food Chem. 2012, 132 (4) 1908– 1914 DOI: 10.1016/j.foodchem.2011.12.025
  There is no corresponding record for this reference.
98. 98
  Fischer, U. A.; Carle, R.; Kammerer, D. R. Thermal Stability of Anthocyanins and Colourless Phenolics in Pomegranate (Punica Granatum L.) Juices and Model Solutions Food Chem. 2013, 138 (2–3) 1800– 1809 DOI: 10.1016/j.foodchem.2012.10.072
  There is no corresponding record for this reference.
99. 99
  Pan, Y.-Z.; Guan, Y.; Wei, Z.-F.; Peng, X.; Li, T.-T.; Qi, X.-L.; Zu, Y.-G.; Fu, Y.-J. Flavonoid C-Glycosides from Pigeon Pea Leaves as Color and Anthocyanin Stabilizing Agent in Blueberry Juice Ind. Crops Prod. 2014, 58, 142– 147 DOI: 10.1016/j.indcrop.2014.04.029
  99
  Flavonoid C-glycosides from pigeon pea leaves as color and anthocyanin stabilizing agent in blueberry juice
  Pan, You-Zhi; Guan, Yue; Wei, Zuo-Fu; Peng, Xiao; Li, Ting-Ting; Qi, Xiao-Lin; Zu, Yuan-Gang; Fu, Yu-Jie
  Industrial Crops and Products (2014), 58 (), 142-147CODEN: ICRDEW; ISSN:0926-6690. (Elsevier B.V.)
  The influences of flavonoid C-glycoside exts. from pigeon pea leaves (FCGE) and its main components vitexin and orientin on the color and anthocyanins stability of blueberry juice were investigated in the thermal expts. The color of juice was enhanced by FCGE and its main components in a molar ratio of 1:1 (anthocyanins/copigment). The satd. color of juice with FCGE and its main components could hold for a significantly longer time. Addnl., copigment FCGE, vitexin and orientin significantly enhanced the stability of anthocyanins. Half-life of anthocyanins in juice samples with FCGE (1:1), orientin and vitexin increased 87%, 79%, and 62%, resp. These results indicated FCGE showed dramatic effect on the color and anthocyanins stability of juice. Furthermore, juice samples with copigments possessed higher total phenolics content and higher DPPH radical-scavenging activity. Therefore, natural, easily available, inexpensive FCGE has potential as color enhancer and anthocyanins stabilizer in food industry.
100. 100
  Goto, T.; Kondo, T. Struktur Und Molekulare Stapelung von Anthocyanen—Variation Der Blütenfarben Angew. Chem. 1991, 103 (1) 17– 33 DOI: 10.1002/ange.19911030105
  There is no corresponding record for this reference.
101. 101
  Liao, H.; Cai, Y.; Haslam, E. Polyphenol Interactions. Anthocyanins: Co-Pigmentation and Colour Changes in Red Wines J. Sci. Food Agric. 1992, 59 (3) 299– 305 DOI: 10.1002/jsfa.2740590305
  101
  Polyphenol interactions. Part 6. Anthocyanins: co-pigmentation and color changes in red wines
  Liao, Hua; Cai, Ya; Haslam, Edwin
  Journal of the Science of Food and Agriculture (1992), 59 (3), 299-305CODEN: JSFAAE; ISSN:0022-5142.
  Anthocyanin co-pigmentation is reviewed and its relevance to the color and appearance of young red wines is outlined. Reactions between flavan-3-ols, such as are present in red wines, and the anthocyanin malvin to give yellow-orange pigments (absorbance max. ∼440 nm) are reported. Possible structures for these new pigments are discussed as is their probable contribution to the changing hues of red wines as they age.
102. 102
  Brouillard, R.; Wigand, M.-C.; Dangles, O.; Cheminat, A. pH and Solvent Effects on the Copigmentation Reaction of Malvin with Polyphenols, Purine and Pyrimidine Derivatives J. Chem. Soc., Perkin Trans. 2 1991, 8) 1235– 1241 DOI: 10.1039/p29910001235
  102
  The pH and solvent effects on the copigmentation reaction of malvin with polyphenols, purine and pyrimidine derivatives
  Brouillard, Raymond; Wigand, Marie Claude; Dangles, Olivier; Cheminat, Annie
  Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1972-1999) (1991), (8), 1235-41CODEN: JCPKBH; ISSN:0300-9580.
  The influence of pH on the copigmentation reaction of malvin has been investigated from an exptl. and theor. viewpoint. The general equation for the copigment effect, when monitored by visible absorption spectrometry, is derived and is in good agreement with results obtained in the case of three different copigments, namely chlorogenic acid, caffeine and adenosine. In particular, it is demonstrated that assocn. of malvin with the copigment occurs for all colored malvin species and the corresponding stability consts. are given. Some tannins and purine or pyrimidine derivs. have also been tested for their ability to act as copigments; some assoc. quite strongly with malvin. Water exerted the greatest effect on the extent of the copigmentation phenomenon. Such a result seems to indicate that the strength of the copigment effect parallels the cohesion of the H-bonded tetrahedral network of water mols.
103. 103
  Baranac, J. M.; Petranovic, N. A.; Dimitric-Markovic, J. M. Spectrophotometric Study of Anthocyan Copigmentation Reactions J. Agric. Food Chem. 1996, 44 (5) 1333– 1336 DOI: 10.1021/jf950420l
  There is no corresponding record for this reference.
104. 104
  Oszmiański, J.; Bakowska, A.; Piacente, S. Thermodynamic Characteristics of Copigmentation Reaction of Acylated Anthocyanin Isolated from Blue Flowers ofScutellaria Baicalensis Georgi with Copigments J. Sci. Food Agric. 2004, 84 (12) 1500– 1506 DOI: 10.1002/jsfa.1815
  104
  Thermodynamic characteristics of copigmentation reaction of acylated anthocyanin isolated from blue flowers of Scutellaria baicalensis Georgi with copigments
  Oszmianski, Jan; Bakowska, Anna; Piacente, Sonia
  Journal of the Science of Food and Agriculture (2004), 84 (12), 1500-1506CODEN: JSFAAE; ISSN:0022-5142. (John Wiley & Sons Ltd.)
  Anthocyanin exts. are increasingly used as food colorants. So far, anthocyanins have not been broadly used in foods and beverages, since they are not as stable as synthetic dyes. Copigmentation between anthocyanins and copigments is the main color-stabilizing mechanism. The process of copigmentation between isolated acylated anthocyanin and rutin, QSA or baicalin has been obsd. using UV-vis spectrophotometry. The thermodn. parameters were correlated to the structure and position of the substituents in the interacting mols. The acylated anthocyanin was isolated from cultivars of Scutellaria baicalensis Georgi flowers and purified by column chromatog. by our own method and has been identified by 1H-/13C-NMR spectroscopy and electrospray mass spectrometry as delphinidin-3-O-(6-O-malonyl)-β-D-glucopyranosyl-5-O-β-D-glucopyranoside.
105. 105
  Ferreira da Silva, P.; Lima, J. C.; Freitas, A. A.; Shimizu, K.; Maçanita, A. L.; Quina, F. H. Charge-Transfer Complexation as a General Phenomenon in the Copigmentation of Anthocyanins J. Phys. Chem. A 2005, 109 (32) 7329– 7338 DOI: 10.1021/jp052106s
  105
  Charge-Transfer Complexation as a General Phenomenon in the Copigmentation of Anthocyanins
  Ferreira da Silva, Palmira; Lima, Joao C.; Freitas, Adilson A.; Shimizu, Karina; Macanita, Antonio L.; Quina, Frank H.
  Journal of Physical Chemistry A (2005), 109 (32), 7329-7338CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Color intensification of anthocyanin solns. in the presence of natural polyphenols (copigmentation) is re-interpreted in terms of charge transfer from the copigment to the anthocyanin. Flavylium cations are shown to be excellent electron acceptors (Ered ≈ -0.3 V vs SCE). It is also demonstrated, for a large series of anthocyanin-copigment pairs, that the std. Gibbs free energy of complex formation decreases linearly with EAAnthoc-IPCop, the difference between the electron affinity of the anthocyanin, EAAnthoc, and the ionization potential of the copigment, IPCop. Based on this correlation, copigmentation strengths of potential candidates for copigments can be predicted.
106. 106
  Galland, S.; Mora, N.; Abert-Vian, M.; Rakotomanomana, N.; Dangles, O. Chemical Synthesis of Hydroxycinnamic Acid Glucosides and Evaluation of Their Ability To Stabilize Natural Colors via Anthocyanin Copigmentation J. Agric. Food Chem. 2007, 55 (18) 7573– 7579 DOI: 10.1021/jf071205v
  106
  Chemical synthesis of hydroxycinnamic acid glucosides and evaluation of their ability to stabilize natural colors via anthocyanin copigmentation
  Galland, Stephanie; Mora, Nathalie; Abert-Vian, Maryline; Rakotomanomana, Njara; Dangles, Olivier
  Journal of Agricultural and Food Chemistry (2007), 55 (18), 7573-7579CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  This work describes the chem. synthesis of O-aryl-β-D-glucosides and 1-O-β-D-glucosyl esters of hydroxycinnamic acids. In particular, O-aryl-β-D-glucosides were efficiently prepd. via a simple diastereoselective glycosylation procedure using phase transfer conditions. Despite the lability of its ester linkage, 1-O-β-D-caffeoylglucose could also be obtained using a Lewis acid catalyzed glycosylation step and a set of protective groups that can be removed under neutral conditions. Hydroxycinnamic acid O-aryl-β-D-glucosides were then quant. investigated for their affinity for the naturally occurring anthocyanin malvin (pigment). Formation of the π-stacking mol. complexes (copigmentation) was characterized in terms of binding consts. and enthalpy and entropy changes. The glucosyl moiety did not significantly alter these thermodn. parameters, in line with a binding process solely involving the polyphenolic nuclei.
107. 107
  Alluis, B.; Dangles, O. Quercetin (=2-(3,4-Dihydroxyphenyl)-3,5,7-Trihydroxy-4H-1-Benzopyran-4-One) Glycosides and Sulfates: Chemical Synthesis, Complexation, and Antioxidant Properties Helv. Chim. Acta 2001, 84 (5) 1133– 1156 DOI: 10.1002/1522-2675(20010516)84:5<1133::AID-HLCA1133>3.3.CO;2-Q
  There is no corresponding record for this reference.
108. 108
  Nave, F.; Brás, N. F.; Cruz, L.; Teixeira, N.; Mateus, N.; Ramos, M. J.; Di Meo, F.; Trouillas, P.; Dangles, O.; De Freitas, V. Influence of a Flavan-3-Ol Substituent on the Affinity of Anthocyanins (Pigments) toward Vinylcatechin Dimers and Proanthocyanidins (Copigments) J. Phys. Chem. B 2012, 116 (48) 14089– 14099 DOI: 10.1021/jp307782y
  108
  Influence of a Flavan-3-ol Substituent on the Affinity of Anthocyanins (Pigments) toward Vinylcatechin Dimers and Proanthocyanidins (Copigments)
  Nave, Frederico; Bras, Natercia F.; Cruz, Luis; Teixeira, Natercia; Mateus, Nuno; Ramos, Maria J.; Di Meo, Florent; Trouillas, Patrick; Dangles, Olivier; De Freitas, Victor
  Journal of Physical Chemistry B (2012), 116 (48), 14089-14099CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  The aim of this study is to investigate interactions possibly taking place in red wine between three flavanols (copigments, CP), i.e., two epimeric vinylcatechin dimers (CP1 and CP2) and catechin dimer B3 (CP3), and a specific pigment resulting from the condensation between the main grape anthocyanin malvidin 3-O-glucoside (oenin) and catechin, catechin-(4→8)-oenin. By comparison with our previous work on oenin itself, the influence of the catechin moiety of the anthocyanin in the binding is established. The thermodn. parameters show that both vinylcatechin dimers exhibit a higher affinity for catechin-(4→8)-oenin, in comparison with proanthocyanidin B3, as previously obsd. with oenin. However, the corresponding binding consts. are weaker, probably due to steric hindrance in the anthocyanin brought by the flavanol nucleus. Consequently, catechin-(4→8)-oenin should be much less stabilized by copigmentation in hydroalcoholic soln. than oenin. Quantum mechanics and mol. dynamics simulations are also performed to interpret the binding data, to specify the relative arrangement of the pigment and copigment mols. within the complexes, and to interpret their absorption properties in the visible range.
109. 109
  Dangles, O.; Elhajji, H. Synthesis of 3-Methoxy-and 3-B-D-Glucopyranosy1oxy) Flavylium Ions. Influence of the Flavylium Substitution Pattern on the Reactivity of Anthocyanins in Aqueous Solution Helv. Chim. Acta 1994, 77 (6) 1595– 1610 DOI: 10.1002/hlca.19940770616
  There is no corresponding record for this reference.
110. 110
  Cruz, L.; Brás, N. F.; Teixeira, N.; Mateus, N.; Ramos, M. J.; Dangles, O.; De Freitas, V. Vinylcatechin Dimers Are Much Better Copigments for Anthocyanins than Catechin Dimer Procyanidin B3 J. Agric. Food Chem. 2010, 58 (5) 3159– 3166 DOI: 10.1021/jf9037419
  110
  Vinylcatechin Dimers Are Much Better Copigments for Anthocyanins than Catechin Dimer Procyanidin B3
  Cruz, Luis; Bras, Natercia F.; Teixeira, Natercia; Mateus, Nuno; Joao Ramos, Maria; Dangles, Olivier; De Freitas, Victor
  Journal of Agricultural and Food Chemistry (2010), 58 (5), 3159-3166CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  The binding consts. (K) for the interaction of three copigments (CP), two epimeric vinylcatechin dimers (CP1 and CP2), and catechin dimer B3 (CP3) with two pigments, malvidin-3-glucoside (oenin) and malvidin-3,5-diglucoside (malvin), were detd. The K values clearly show that both vinylcatechin dimers have much higher affinity for oenin and malvin than dimer B3: KCP2 > KCP1 » KCP3. Quantum mechanics and mol. dynamics calcns. were also performed to interpret the binding data and specify the relative arrangement of the pigment and copigment mols. within the complexes.
111. 111
  Malien-Aubert, C.; Dangles, O.; Amiot, M. J. Influence of Procyanidins on the Color Stability of Oenin Solutions J. Agric. Food Chem. 2002, 50 (11) 3299– 3305 DOI: 10.1021/jf011392b
  111
  Influence of Procyanidins on the Color Stability of Oenin Solutions
  Malien-Aubert, Celine; Dangles, Olivier; Amiot, Marie Josephe
  Journal of Agricultural and Food Chemistry (2002), 50 (11), 3299-3305CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  The aim of the present work was to specify the influence of the polymn. degree on the color stability of anthocyanins using model solns. under higher thermal conditions simulating rapid food aging. Results showed that an increase in polymeric degree improves the color stability of oenin. Solns. contg. a catechin tetramer, purified from brown rice, displayed a remarkable stability. Flavanols as monomers, (+)-catechin and (-)-epicatechin, appeared to decrease stability with the formation of a xanthylium salt leading to yellowish solns. For the dimers, procyanidin B2 and B3, different behaviors on red color stability have been obsd. corresponding to their different susceptibility to cleavage upon heating. In the presence of the trimeric procyanidin C2, the red color appeared more stable. However, the HPLC chromatograms showed a decrease in the amplitude of the peaks of oenin and procyanidin C2. Concomitantly, a new peak appeared with a maximal absorption in the red region. This newly formed pigment probably came from the condensation of oenin and procyanidin C2.
112. 112
  Benesi, H. A.; Hildebrand, J. H. A Spectrophotometric Investigation of the Interaction of Iodine with Aromatic Hydrocarbons J. Am. Chem. Soc. 1949, 71 (8) 2703– 2707 DOI: 10.1021/ja01176a030
  112
  A spectrophotometric investigation of the interaction of iodine with aromatic hydrocarbons
  Benesi, H. A.; Hildebrand, J. H.
  Journal of the American Chemical Society (1949), 71 (), 2703-7CODEN: JACSAT; ISSN:0002-7863.
  cf. C.A. 42, 8172g. The absorption spectra of I2 in C6H5CF3, benzene, toluene, o- and p-xylene, and mesitylene were measured in the region 270-700 mμ. In the visible region, the absorption peaks of these solns. showed moderate shifts toward shorter wave lengths in the order listed above. With the exception of I2 in C6H5CF3, each of the aromatic hydrocarbon solns. had an intense absorption band in the ultraviolet region which was shown to be characteristic of a complex contg. one I2 and one aromatic hydrocarbon mol. The equil. between I2 and the aromatic hydrocarbons was investigated in the neutral solvents CCl4 and C7H14, and the results show that the iodine-mesitylene complex is more stable than the iodine-benzene complex. These findings are strong evidence for an acid-base interaction between I2 and aromatic hydrocarbons. Absorption measurements also were made of I2 in CCl4, CS2, C7H14, Et2O, Me2CO, and 1,1-dichloroethane. No absorption bands analogous to those of the aromatic hydrocarbon solns. were found in the region 270-400 mμ.
113. 113
  Dangles, O.; Brouillard, R. Polyphenol Interactions. The Copigmentation Case: Thermodynamic Data from Temperature Variation and Relaxation Kinetics. Medium Effect Can. J. Chem. 1992, 70 (8) 2174– 2189 DOI: 10.1139/v92-273
  There is no corresponding record for this reference.
114. 114
  Di Meo, F.; Sancho Garcia, J. C.; Dangles, O.; Trouillas, P. Highlights on Anthocyanin Pigmentation and Copigmentation: A Matter of Flavonoid Π-Stacking Complexation To Be Described by DFT-D J. Chem. Theory Comput. 2012, 8 (6) 2034– 2043 DOI: 10.1021/ct300276p
  114
  Highlights on Anthocyanin Pigmentation and Copigmentation: A Matter of Flavonoid π-Stacking Complexation To Be Described by DFT-D
  Di Meo, Florent; Sancho Garcia, Juan Carlos; Dangles, Olivier; Trouillas, Patrick
  Journal of Chemical Theory and Computation (2012), 8 (6), 2034-2043CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Anthocyanidins are a class of π-conjugated systems responsible for red, blue, and purple colors of plants. They exhibit the capacity of aggregation in the presence of other natural compds. including flavonols. Such complexations induce color modulation in plants, which is known as copigmentation. It is largely driven by π-interactions existing between pigments and copigments. In this work, the energies of copigmentation-complexation and self-assocn. are systematically evaluated for an anthocyanidin/flavonol couple prototype (3-O-methylcyanidin/quercetin). To describe noncovalent interactions, DFT-D appears mandatory to reach a large accuracy. Due to the chem. complexity of this phenomenon, we also aim at assessing the relevance of both B3P86-D2 and ωB97X-D functionals. The benchmarking has shown that B3P86-D2 possesses enough accuracy when dealing with π-π interactions with respect to both spin component scaled Moller-Plesset second-order perturbation theory post Hartree-Fock method and exptl. data. UV-vis absorption properties are then evaluated with time-dependent DFT for the different complexes. The use of range-sepd. hybrid functionals, such as ωB97X-D, helped to correctly disentangle and interpret the origin of the UV-vis exptl. shifts attributed to the subtle copigmentation phenomenon.
115. 115
  Awika, J. M. Behavior of 3-Deoxyanthocyanidins in the Presence of Phenolic Copigments Food Res. Int. 2008, 41 (5) 532– 538 DOI: 10.1016/j.foodres.2008.03.002
  115
  Behavior of 3-deoxyanthocyanidins in the presence of phenolic copigments
  Awika, Joseph M.
  Food Research International (2008), 41 (5), 532-538CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
  Anthocyanin stability and color intensity are generally improved in the presence of copigments in moderately acidic environments. The 3-deoxyanthocyanins on the other hand are fairly stable to color loss due to change in pH. It is unknown, therefore, how they behave in the presence of copigments. We studied the effects of common phenolic copigments, tannic, ferulic, and O-coumaric acids, and rutin on behavior and stability of six 3-deoxyanthocyandins over 4.5 mo. Tannic and ferulic acid produced the most significant bathochromic shift, whereas rutin had no bathochromic effect. None of the copigments produced a significant hyperchromic shift with the pigments, implying colored species of the pigments were predominant under conditions used. Ferulic and tannic acids were the most effective at improving color stability of 5-hydroxylated pigments, whereas tannic acid and rutin improved the stability of 5-methoxylated pigments the most. Substitution at C-5 was key to overall behavior of the 3-deoxyanthocyanidins.
116. 116
  El Hajji, H.; Dangles, O.; Figueiredo, P.; Brouillard, R. 3′-(β-D-Glycopyranosyloxy) Flavylium Ions: Synthesis and Investigation of Their Properties in Aqueous Solution. Hydrogen Bonding as a Mean of Colour Variation Helv. Chim. Acta 1997, 80 (2) 398– 413 DOI: 10.1002/hlca.19970800206
  There is no corresponding record for this reference.
117. 117
  Limón, P. M.; Gavara, R.; Pina, F. Thermodynamics and Kinetics of Cyanidin 3-Glucoside and Caffeine Copigments J. Agric. Food Chem. 2013, 61 (22) 5245– 5251 DOI: 10.1021/jf4006643
  There is no corresponding record for this reference.
118. 118
  Melo, M. J.; Moncada, M. C.; Pina, F. On the Red Colour of Raspberry (Rubus Idaeus) Tetrahedron Lett. 2000, 41 (12) 1987– 1991 DOI: 10.1016/S0040-4039(00)00080-0
  There is no corresponding record for this reference.
119. 119
  Gierschner, J.; Lüer, L.; Milián-Medina, B.; Oelkrug, D.; Egelhaaf, H.-J. Highly Emissive H-Aggregates or Aggregation-Induced Emission Quenching? The Photophysics of All-Trans Para-Distyrylbenzene J. Phys. Chem. Lett. 2013, 4 (16) 2686– 2697 DOI: 10.1021/jz400985t
  119
  Highly Emissive H-Aggregates or Aggregation-Induced Emission Quenching? The Photophysics of All-Trans para-Distyrylbenzene
  Gierschner, Johannes; Luer, Larry; Milian-Medina, Begona; Oelkrug, Dieter; Egelhaaf, Hans-Joachim
  Journal of Physical Chemistry Letters (2013), 4 (16), 2686-2697CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The present Perspective critically reexamines the photophysics of para-distyrylbenzene (DSB) as a prototype of herringbone-arranged H-aggregates to resolve the apparent contradiction of the frequently reported aggregation-induced emission quenching in H-aggregates on one side and highly emissive DSB crystals on the other and discusses the signatures and fate of excitons in single- and polycryst. samples, including size and polarization effects.
120. 120
  Gierschner, J.; Park, S. Y. Luminescent Distyrylbenzenes: Tailoring Molecular Structure and Crystalline Morphology J. Mater. Chem. C 2013, 1 (37) 5818– 5832 DOI: 10.1039/c3tc31062k
  120
  Luminescent distyrylbenzenes: tailoring molecular structure and crystalline morphology
  Gierschner, Johannes; Park, Soo Young
  Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2013), 1 (37), 5818-5832CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
  A review. The last few years have seen a steady increase in small mol. based conjugated materials, which promise innovative (opto)electronic applications. This requires however a systematic understanding of structure-property relationships, which can only be achieved via libraries of structurally well-defined single cryst. materials based on systematically designed mol. structures. In this feature article, we are presenting structure-property relationships of functionalized distyrylbenzene (DSB), which is one of the most extensively investigated π-conjugated mol. materials. This will provide a general insight into the specific implications of intermol. arrangements on their solid state optoelectronic properties, discussing H- vs. J-aggregation, herringbone vs. π-stacks, the occurrence of excimers, size effects, and polycrystallinity. The systematic insight into DSB functionalization will then suggest pathways towards targeted mol. design strategies, with special focus on the cyano-vinylene motif (DCS materials) which allows for highly fluorescence solid state samples due to synergetic packing effects promoted by its twist elasticity and secondary bonding interaction. Finally, recent advances in the application of DSB-/DCS-based materials are shortly reviewed.
121. 121
  Gonnet, J.-F. Colour Effects of Co-Pigmentation of Anthocyanins revisited—1. A Colorimetric Definition Using the CIELAB Scale Food Chem. 1998, 63 (3) 409– 415 DOI: 10.1016/S0308-8146(98)00053-3
  There is no corresponding record for this reference.
122. 122
  Gordillo, B.; Rodríguez-Pulido, F. J.; Escudero-Gilete, M. L.; González-Miret, M. L.; Heredia, F. J. Comprehensive Colorimetric Study of Anthocyanic Copigmentation in Model Solutions. Effects of pH and Molar Ratio J. Agric. Food Chem. 2012, 60 (11) 2896– 2905 DOI: 10.1021/jf2046202
  122
  Comprehensive Colorimetric Study of Anthocyanic Copigmentation in Model Solutions. Effects of pH and Molar Ratio
  Gordillo, Belen; Rodriguez-Pulido, Francisco J.; Escudero-Gilete, M. Luisa; Gonzalez-Miret, M. Lourdes; Heredia, Francisco J.
  Journal of Agricultural and Food Chemistry (2012), 60 (11), 2896-2905CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  New colorimetric variables were defined in the uniform CIELAB color space to assess the quant. and qual. color changes induced by copigmentation and their incidence on visual perception. The copigmentation process was assayed in model solns. between malvidin 3-glucoside and 3 phenolic compds. (catechin, epicatechin, and caffeic acid) as a function of the pH and the pigment/copigment molar ratio. Along the pH variation, the greatest magnitude of copigmentation was obtained at pH 3.0, being significantly higher with epicatechin and caffeic acid. At high acidic pH, the main contribution of copigmentation to the total color was qual., whereas between pH 2.0 and 4.0, the main colorimetric contribution was quant. The contribution of epicatechin and caffeic acid to the color changes was more marked for the quant. characteristics. On contrast, particularly at higher pH values, the qual. contribution was more important in catechin copigmented solns. Increasing copigment concn. induced perceptible color changes at molar ratios higher than 1:2, consisting in a bluish and darkening effect of the anthocyanin solns. Among the different CIELAB attributes, hue difference was the best correlated parameter with the increase of copigment concn., proving the relevance of this physicochem. phenomenon on the qual. changes of anthocyanin color.
123. 123
  Gonnet, J.-F. Colour Effects of Co-Pigmentation of Anthocyanins revisited—2.A Colorimetric Look at the Solutions of Cyanin Co-Pigmented Byrutin Using the CIELAB Scale Food Chem. 1999, 66 (3) 387– 394 DOI: 10.1016/S0308-8146(99)00088-6
  There is no corresponding record for this reference.
124. 124
  Xu, H.; Liu, X.; Yan, Q.; Yuan, F.; Gao, Y. A Novel Copigment of Quercetagetin for Stabilization of Grape Skin Anthocyanins Food Chem. 2015, 166, 50– 55 DOI: 10.1016/j.foodchem.2014.05.125
  124
  A novel copigment of quercetagetin for stabilization of grape skin anthocyanins
  Xu, Honggao; Liu, Xuan; Yan, Qiuli; Yuan, Fang; Gao, Yanxiang
  Food Chemistry (2015), 166 (), 50-55CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  The thermal and light stability of grape skin anthocyanins combined with quercetagetin was investigated at designed pH values of 3, 4 and 5. The molar ratios of anthocyanins to quercetagetin were 1:10, 1:20 and 1:40 for thermally treatment at 70 °C, 80 °C and 90 °C, resp., and the ratios were tested at 5:1, 1:1, 1:5 and 1:10 in the light exposure expts. The degrdn. reaction of anthocyanins in the presence of quercetagetin followed the first-order kinetic model. The half-life (t1/2) of anthocyanins was extended significantly with the increase of quercetagetin concn. (p < 0.05). The total color difference values (ΔE*) for the anthocyanin solns. with quercetagetin were smaller than those without copigment under the same exptl. conditions (pH and light exposure time). Compared with epigallocatechin gallate (EGCG), tea polyphenols (TP), myricitrin and rutin, quercetagetin was the most effective copigment to stabilize grape skin anthocyanins.
125. 125
  Shao, P.; Zhang, J.; Fang, Z.; Sun, P. Complexing of Chlorogenic Acid with B-Cyclodextrins: Inclusion Effects, Antioxidative Properties and Potential Application in Grape Juice Food Hydrocolloids 2014, 41, 132– 139 DOI: 10.1016/j.foodhyd.2014.04.003
  There is no corresponding record for this reference.
126. 126
  Mistry, T. V.; Cai, Y.; Lilley, T. H.; Haslam, E. Polyphenol Interactions. Part 5. Anthocyanin Co-Pigmentation J. Chem. Soc., Perkin Trans. 2 1991, 8) 1287– 1296 DOI: 10.1039/p29910001287
  126
  Polyphenol interactions. Part 5. Anthocyanin copigmentation
  Mistry, Tarankumar V.; Cai, Ya; Lilley, Terence H.; Haslam, Edwin
  Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1972-1999) (1991), (8), 1287-96CODEN: JCPKBH; ISSN:0300-9580.
  In aq. media, anthocyanins undergo several structural transformations and exist in a series of equil. between carbinol-base, flavylium cation, quinonoidal anhydro-base and chalcone forms. A detailed interpretation of the 1H-NMR (400 MHz) spectra of malvin in D2O is given for the first time in the context of these equil. The phenomenon of copigmentation is reviewed and the efficacy of various phenolic flavonoids, galloyl and hexahydroxycinnamyl esters as natural copigments is detd. quant. DNA, RNA and ATP also act as effective copigments for malvin in the form the flavylium ion but both caffeine and theophylline preferentially stabilize the quinonoidal-base forms of the anthocyanin. At pH 3.5 to 7.0, they give rise to stable violet through to blue and finally green colors. 1H-NMR studies of all these intermol. copigmentation reactions are reported and the phenomenon is provisionally interpreted in terms of hydrophobically reinforced π-π stacking of anthocyanin and copigment mols. in the aq. environment.
127. 127
  Son, T.-D.; Chachaty, C. Nucleoside Conformations: XIV. Conformation of Adenosine Monophosphates in Aqueous Solution by Proton Magnetic Resonance Spectroscopy Biochim. Biophys. Acta, Nucleic Acids Protein Synth. 1974, 335 (1) 1– 13 DOI: 10.1016/0005-2787(74)90234-2
  There is no corresponding record for this reference.
128. 128
  Leydet, Y.; Gavara, R.; Petrov, V.; Diniz, A. M.; Jorge Parola, A.; Lima, J. C.; Pina, F. The Effect of Self-Aggregation on the Determination of the Kinetic and Thermodynamic Constants of the Network of Chemical Reactions in 3-Glucoside Anthocyanins Phytochemistry 2012, 83, 125– 135 DOI: 10.1016/j.phytochem.2012.06.022
  128
  The effect of self-aggregation on the determination of the kinetic and thermodynamic constants of the network of chemical reactions in 3-glucoside anthocyanins
  Leydet, Yoann; Gavara, Raquel; Petrov, Vesselin; Diniz, Ana M.; Parola, A. Jorge; Lima, Joao C.; Pina, Fernando
  Phytochemistry (Elsevier) (2012), 83 (), 125-135CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Ltd.)
  The six most common 3-glucoside anthocyanins, pelargonidin-3-glucoside, peonidin-3-glucoside, delphinidin-3-glucoside, malvidin-3-glucoside, cyanidin-3-glucoside and petunidin-3-glucoside were studied in great detail by NMR, UV-vis absorption and stopped flow. For each anthocyanin, the thermodn. and kinetic consts. of the network of chem. reactions were calcd. at different anthocyanin concn., from 6 × 10-6 M up to 8 × 10-4 M; an increasing of the flavylium cation acidity const. to give quinoidal base and a decreasing of the flavylium cation hydration const. to give hemiketal were obsd. by increasing the anthocyanin concn. These effects are attributed to the self-aggregation of the flavylium cation and quinoidal base, which is stronger in the last case. The UV-vis and 1H NMR spectral variations resulting from the increasing of the anthocyanin concn. were discussed in terms of two aggregation models; monomer-dimer and isodesmic, the last one considering the formation of higher order aggregates possessing the same aggregation const. of the dimer. The self-aggregation const. of flavylium cation at pH = 1.0, calcd. by both models increases by increasing the no. of methoxy (-OCH3) or hydroxy (-OH) substituents following the order: myrtillin (2 -OH), oenin (2 -OCH3), 3-OGl-petunidin (1 -OH, 1 -OCH3), kuromanin (1 -OH), 3-OGl-peonidin (1 -OCH3) and callistephin (none). Evidence for flavylium aggregates possessing a shape between J and H was achieved, as well as for the formation of higher order aggregates.
129. 129
  Dimicoli, J. L.; Hélène, C. Complex Formation between Purine and Indole Derivatives in Aqueous Solutions. Proton Magnetic Resonance Studies J. Am. Chem. Soc. 1973, 95 (4) 1036– 1044 DOI: 10.1021/ja00785a008
  There is no corresponding record for this reference.
130. 130
  Alluis, B.; Pérol, N.; El Hajji, H.; Dangles, O. Water-Soluble Flavonol (=3Hydroxy2-Phenyl-4H-1-Benzopyran-4-One) Derivatives: Chemical Synthesis, Colouring, and Antioxidant Properties Helv. Chim. Acta 2000, 83 (2) 428– 443 DOI: 10.1002/(SICI)1522-2675(20000216)83:2<428::AID-HLCA428>3.3.CO;2-A
  There is no corresponding record for this reference.
131. 131
  Hondo, T.; Yoshida, K.; Nakagawa, A.; Kawai, T.; Tamura, H.; Goto, T. Structural Basis of Blue-Colour Development in Flower Petals from Commelina Communis Nature 1992, 358 (6386) 515– 518 DOI: 10.1038/358515a0
  There is no corresponding record for this reference.
132. 132
  Shiono, M.; Matsugaki, N.; Takeda, K. Phytochemistry: Structure of the Blue Cornflower Pigment Nature 2005, 436 (7052) 791– 791 DOI: 10.1038/436791a
  There is no corresponding record for this reference.
133. 133
  Dufour, C.; Sauvaitre, I. Interactions between Anthocyanins and Aroma Substances in a Model System. Effect on the Flavor of Grape-Derived Beverages J. Agric. Food Chem. 2000, 48 (5) 1784– 1788 DOI: 10.1021/jf990877l
  133
  Interactions between anthocyanins and aroma substances in a model system. Effect on the flavor of grape-derived beverages
  Dufour, Claire; Sauvaitre, Isabelle
  Journal of Agricultural and Food Chemistry (2000), 48 (5), 1784-1788CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  Evaluation of the sensory quality of wine or grape-derived beverages led the authors to study the interactions between flavors and anthocyanins, the colored family of polyphenols. The flavylium cation-ligand complexation, resulting in copigmentation (rise in pigment visible absorption with a concomitant bathochromic shift), was investigated using visible absorption spectroscopy. Sole volatile phenols were found to markedly interact with malvidin-3,5-O-diglucoside. With series of guaiacyl-derived aroma substances, acyl-substituted ligands proved to be better copigments than alkyl-substituted ones. Assocn. consts. and 1:1 complex stoichiometry were further detd. for several substrates. Decreasing binding to malvin was obsd. for acetosyringone, syringaldehyde, acetovanillone, vanillin, 3,5-dimethoxyphenol, and 4-ethylguaiacol. Addn. of 10% ethanol lowered by one-third the assocn. consts. for malvin-ligand couples and for malvidin-3-O-glucoside with acetosyringone and syringaldehyde. The main driving force was ascribed to hydrophobicity, although this study evidenced an influence of the ligand substitution pattern on copigmentation.
134. 134
  Tuominen, A.; Sinkkonen, J.; Karonen, M.; Salminen, J.-P. Sylvatiins, Acetylglucosylated Hydrolysable Tannins from the Petals of Geranium Sylvaticum Show Co-Pigment Effect Phytochemistry 2015, 115, 239– 251 DOI: 10.1016/j.phytochem.2015.01.005
  134
  Sylvatiins, acetylglucosylated hydrolysable tannins from the petals of Geranium sylvaticum show co-pigment effect
  Tuominen, Anu; Sinkkonen, Jari; Karonen, Maarit; Salminen, Juha-Pekka
  Phytochemistry (Elsevier) (2015), 115 (), 239-251CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Ltd.)
  Four hydrolysable tannins, named as sylvatiins A (1), B (2), C (3) and D (4), were isolated from the petals of Geranium sylvaticum. On the basis of spectrometric evidence of NMR anal. (1H NMR, 13C NMR, DQF-COSY, TOCSY, NOESY, HSQC and HMBC), CD and ESI-MS/MS, sylvatiins A, B and C were characterized as galloyl glucoses contg. one or two acetylglucoses attached to the 3-OH of the galloyl group, whereas sylvatiin D was found to have a chebulinic acid core contg. acetylglucose attached in a similar way. The potential of these compds. to act as defensive compds. against herbivores was evaluated using the radial diffusion assay that measures the protein pptn. capacity. In addn., the capacity of sylvatiins to act as co-pigments with anthocyanins of G. sylvaticum petals was measured in vitro at different pH values. Sylvatiins A and D maintained efficiently the purple flower color near the natural pH of petal cells. The amt. of sylvatiins was changed according to the flower color; deep purple petals with higher amt. of anthocyanin contained more sylvatiins A and C than whiter petals. It was concluded that G. sylvaticum petal cells may accumulate sylvatiins for intermol. co-pigmentation purposes.
135. 135
  Dangles, O.; Saito, N.; Brouillard, R. Kinetic and Thermodynamic Control of Flavylium Hydration in the Pelargonidin-Cinnamic Acid Complexation. Origin of the Extraordinary Flower Color Diversity of Pharbitis Nil J. Am. Chem. Soc. 1993, 115 (8) 3125– 3132 DOI: 10.1021/ja00061a011
  There is no corresponding record for this reference.
136. 136
  Eiro, M. J.; Heinonen, M. Anthocyanin Color Behavior and Stability during Storage: Effect of Intermolecular Copigmentation J. Agric. Food Chem. 2002, 50 (25) 7461– 7466 DOI: 10.1021/jf0258306
  136
  Anthocyanin Color Behavior and Stability during Storage: Effect of Intermolecular Copigmentation
  Eiro, Maarit J.; Heinonen, Marina
  Journal of Agricultural and Food Chemistry (2002), 50 (25), 7461-7466CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  Intermol. copigmentation reactions are significantly responsible for the manifold color expression of fruits, berries, and their products. These reactions were investigated with 5 anthocyanins and 5 phenolic acids acting as copigments. The stability of the pigment-copigment complexes formed was studied during a storage period of 6 mo. The study was conducted using a UV-visible spectrophotometer to monitor the hyperchromic effect and the bathochromic shift of the complexes. The greatest copigmentation reactions took place in malvidin 3-glucoside solns. The strongest copigments for all anthocyanins were ferulic and rosmarinic acids. The immediate reaction of rosmarinic acid with malvidin 3-glucoside resulted in the biggest bathochromic shift (19 nm) and the strongest hyperchromic effect, increasing the color intensity by 260%. The color induced by rosmarinic acid was not very stable. The color intensity of pelargonidin 3-glucoside increased greatly throughout the storage period with the addn. of ferulic and caffeic acids.
137. 137
  Houbiers, C.; Lima, J. C.; Maçanita, A. L.; Santos, H. Color Stabilization of Malvidin 3-Glucoside: Self-Aggregation of the Flavylium Cation and Copigmentation with the Z-Chalcone Form J. Phys. Chem. B 1998, 102 (18) 3578– 3585 DOI: 10.1021/jp972320j
  There is no corresponding record for this reference.
138. 138
  Elhabiri, M.; Figueiredo, P.; Toki, K.; Figueiredo, P.; Toki, K.; Saito, N.; Brouillard, R.; Figueiredo, P.; Toki, K. Anthocyanin–aluminium and – gallium Complexes in Aqueoussolution J. Chem. Soc., Perkin Trans. 2 1997, 2) 355– 362 DOI: 10.1039/a603851d
  138
  Anthocyanin-aluminum and -gallium complexes in aqueous solution
  Elhabiri, M.; Figueiredo, P.; Toki, K.; Saito, N.; Brouillard, R.
  Journal of the Chemical Society, Perkin Transactions 2: Physical Organic Chemistry (1997), (2), 355-362CODEN: JCPKBH; ISSN:0300-9580. (Royal Society of Chemistry)
  Complexation of aluminum and gallium ions with synthetic anthocyanin models and natural anthocyanins extd. from the blue flowers of Evolvulus pilosus cv 'Blue Daze' and the violet flowers of Matthiola incana has been thoroughly investigated in aq. soln. From UV-VIS spectroscopic data collected at pH 2-5, the presence of complexes, involving not only the colored forms but also the colorless forms of the pigments is demonstrated. A theor. treatment is developed for the calcn. of the corresponding stability consts. The pigments studied throughout this work can be divided into two series, one sharing a cyanidin chromophore and the other a delphinidin one. Within both series, individual pigments are distinguished according to the degree and type of glycosidation and/or acylation. Intramol. effects such as copigmentation of anthocyanin-aluminum complexes and the effect of the presence of a malonyl group on the formation of those complexes are discussed. These results are important to plant pigmentation and, for instance, a narrow pH domain in which color amplification due to complexation is at a max. has been found.
139. 139
  Al Bittar, S.; Mora, N.; Loonis, M.; Dangles, O. Chemically Synthesized Glycosides of Hydroxylated Flavylium Ions as Suitable Models of Anthocyanins: Binding to Iron Ions and Human Serum Albumin, Antioxidant Activity in Model Gastric Conditions Molecules 2014, 19 (12) 20709– 20730 DOI: 10.3390/molecules191220709
  There is no corresponding record for this reference.
140. 140
  Kasha, M.; Rawls, H. R.; Ashraf El-Bayoumi, M. The Exciton Model in Molecular Spectroscopy Pure Appl. Chem. 1965, 11 (3–4) 371– 392 DOI: 10.1351/pac196511030371
  140
  Exciton model in molecular spectroscopy
  Kasha, Michael; Rawls, Henry R.; El-Bayoumi, M. Ashraf
  Pure and Applied Chemistry (1965), 11 (3-4), 371-92CODEN: PACHAS; ISSN:0033-4545.
  A summary is presented of the application of the mol. exciton model to dimers, trimers, and double and triple mols. In those cases where no significant exciton effect is observable in the singlet-singlet absorption spectrum for the composite mol., the enhancement of lowest triplet state excitation may still be conspicuous and significant.
141. 141
  Yoshida, K.; Toyama, Y.; Kameda, K.; Kondo, T. Contribution of Each Caffeoyl Residue of the Pigment Molecule of Gentiodelphin to Blue Color Development Phytochemistry 2000, 54 (1) 85– 92 DOI: 10.1016/S0031-9422(00)00049-2
  There is no corresponding record for this reference.
142. 142
  Yoshida, K.; Kondo, T.; Goto, T. Intramolecular Stacking Conformation of Gentiodelphin, a Diacylated Anthocyanin from Gentiana Makinoi Tetrahedron 1992, 48 (21) 4313– 4326 DOI: 10.1016/S0040-4020(01)80442-7
  There is no corresponding record for this reference.
143. 143
  Nerdal, W.; Andersen, Ø. M. Evidence for Self-Association of the Anthocyanin Petanin in Acidified, Methanolic Solution Using Two-Dimensional Nuclear Overhauser Enhancement NMR Experiments and Distance Geometry Calculations Phytochem. Anal. 1991, 2 (6) 263– 270 DOI: 10.1002/pca.2800020606
  143
  Evidence for self-association of the anthocyanin petanin in acidified, methanolic solution using two-dimensional nuclear Overhauser enhancement NMR experiments and distance geometry calculations
  Nerdal, Willy; Andersen, Oeyvind M.
  Phytochemical Analysis (1991), 2 (6), 263-70CODEN: PHANEL; ISSN:0958-0344.
  A new mechanism is described for self-assocn. of anthocyanins in soln. Petanin [petunidin 3-O-[6-O-(4-O-E-p-coumaroyl-α-L-rhamnopyranosyl)-β-D-glucopyranoside]-5-O-β-D-glucopuranoside] was studied in acidified methanolic soln. using the nuclear Overhauser enhancement (NOESY) NMR technique. Intra- and inter-mol. NOESY cross-peaks were obsd., and the corresponding proton-proton distance bounds were used in distance geometry calcns. to det. the stacking of the petanin aglycons. The orientation of two self-assocd. petanin aglycons was found to be head-to-tail along both the long and the short aglycon axis. Lack of obsd. NOESY cross-peaks between protons of the coumaroyl group and the aglycon indicated absence of intramol. stacking of the stable petanin mols. Non-coplanarity between the planes of the benzopyrylium and the Ph rings was also indicated.
144. 144
  Nerdal, W.; Andersen, Ø. M. Intermolecular Aromatic Acid Association of an Anthocyanin (petanin) Evidenced by Two-Dimensional Nuclear Overhauser Enhancement Nuclear Magnetic Resonance Experiments and Distance Geometry Calculations Phytochem. Anal. 1992, 3 (4) 182– 189 DOI: 10.1002/pca.2800030408
  144
  Intermolecular aromatic acid association of an anthocyanin (petanin) evidence by two-dimensional nuclear Overhauser enhancement nuclear magnetic resonance experiments and distance geometry calculations
  Nerdal, Willy; Andersen, Oeyvind M.
  Phytochemical Analysis (1992), 3 (4), 182-9CODEN: PHANEL; ISSN:0958-0344.
  A new mechanism for the mol. assocn. of the arom acid of an anthocyanin using two-dimensional 1H NOESY expts., is described.
145. 145
  Yoshida, K.; Kondo, T.; Goto, T. Unusually Stable Monoacylated Anthocyanin from Purple Yam Dioscorea Alata Tetrahedron Lett. 1991, 32 (40) 5579– 5580 DOI: 10.1016/0040-4039(91)80088-N
  There is no corresponding record for this reference.
146. 146
  Mori, M.; Miki, N.; Ito, D.; Kondo, T.; Yoshida, K. Structure of Tecophilin, a Tri-Caffeoylanthocyanin from the Blue Petals of Tecophilaea Cyanocrocus, and the Mechanism of Blue Color Development Tetrahedron 2014, 70 (45) 8657– 8664 DOI: 10.1016/j.tet.2014.09.046
  146
  Structure of tecophilin, a tri-caffeoylanthocyanin from the blue petals of Tecophilaea cyanocrocus, and the mechanism of blue color development
  Mori, Mihoko; Miki, Naoko; Ito, Daisuke; Kondo, Tadao; Yoshida, Kumi
  Tetrahedron (2014), 70 (45), 8657-8664CODEN: TETRAB; ISSN:0040-4020. (Elsevier Ltd.)
  The pigment, tecophilin, in blue flowers of Tecophilaea cyanocrocus was isolated and the structure was detd. to be 3-O-(6-O-α-L-rhamnopyranosyl-β-D-glucopyranosyl)-7-O-(6-O-(4-O-(2-O-(4-O-β-D-glucopyranosyl-(E)-caffeoyl)-6-O-(4-O-β-D-glucopyranosyl-(E)-caffeoyl)-β-D-glucopyranosyl)-(E)-caffeoyl)-β-D-glucopyranosyl)delphinidin. The reprodn. expt. of the same color as petals according to the results of chem. anal. and measurement of vacuolar pH of blue cells clarified that the blue color solely develops by tecophilin without interaction of metal ions nor co-pigments. 1H NMR anal. and CD spectrum indicate the co-existence of clockwise intermol. self-assocn. of the delphinidin nuclei and intramol. π-π stacking between the chromophore and caffeoyl residues to derive bathochromic shift of the absorption spectrum and stabilize the color by preventing hydration reaction.
147. 147
  Terahara, N.; Callebaut, A.; Ohba, R.; Nagata, T.; Ohnishi-Kameyama, M.; Suzuki, M. Triacylated Anthocyanins from Ajuga Reptans Flowers and Cell Cultures Phytochemistry 1996, 42 (1) 199– 203 DOI: 10.1016/0031-9422(95)00838-1
  There is no corresponding record for this reference.
148. 148
  Terahara, N.; Toki, K.; Saito, N.; Honda, T.; Matsui, T.; Osajima, Y. Eight New Anthocyanins, Ternatins C1-C5 and D3 and Preternatins A3 and C4 from Young Clitoria Ternatea Flowers J. Nat. Prod. 1998, 61 (11) 1361– 1367 DOI: 10.1021/np980160c
  There is no corresponding record for this reference.
149. 149
  Escribano-Bailón, T.; Dangles, O.; Brouillard, R. Coupling Reactions between Flavylium Ions and Catechin Phytochemistry 1996, 41 (6) 1583– 1592 DOI: 10.1016/0031-9422(95)00811-X
  149
  Coupling reactions between flavylium ions and catechin
  Escribano-Bailon, Teresa; Dangles, Olivier; Brouillard, Raymond
  Phytochemistry (1996), 41 (6), 1583-92CODEN: PYTCAS; ISSN:0031-9422. (Elsevier)
  In order to model natural polymeric pigments present in old red wines, new covalent adducts have been synthesized upon condensation of synthetic flavylium ions (models of anthocyanins) with catechin (model of tannins) in the presence and in the absence of acetaldehyde. These new pigments have been investigated by 1D and 2D NMR, HPLC, FAB-mass and UV-visible spectroscopies and mol. modeling. The two flavylium salts used in this work (3,4'-dimethoxy-7-hydroxyflavylium chloride and 5,7-dihydroxy-3,4'-dimethoxyflavylium chloride) display quite different reactivities toward catechin. The electronic donating effect of the catechin moiety and the formation of noncovalent dimers in acidic aq. or methanolic soln. should be mainly responsible for the improved stability of the flavylium chromophore in the new pigments.
150. 150
  Dueñas, M.; Fulcrand, H.; Cheynier, V. Formation of Anthocyanin–flavanol Adducts in Model Solutions Anal. Chim. Acta 2006, 563 (1–2) 15– 25 DOI: 10.1016/j.aca.2005.10.062
  There is no corresponding record for this reference.
151. 151
  Dueñas, M.; Salas, E.; Cheynier, V.; Dangles, O.; Fulcrand, H. UV–Visible Spectroscopic Investigation of the 8,8-Methylmethine Catechin-Malvidin 3-Glucoside Pigments in Aqueous Solution: Structural Transformations and Molecular Complexation with Chlorogenic Acid J. Agric. Food Chem. 2006, 54 (1) 189– 196 DOI: 10.1021/jf0516989
  There is no corresponding record for this reference.
152. 152
  Chassaing, S.; Lefeuvre, D.; Jacquet, R.; Jourdes, M.; Ducasse, L.; Galland, S.; Grelard, A.; Saucier, C.; Teissedre, P.-L.; Dangles, O. Physicochemical Studies of New Anthocyano-Ellagitannin Hybrid Pigments: About the Origin of the Influence of Oak C-Glycosidic Ellagitannins on Wine Color Eur. J. Org. Chem. 2010, 2010 (1) 55– 63 DOI: 10.1002/ejoc.200901133
  There is no corresponding record for this reference.
153. 153
  Bloor, S. J. Overview of Methods for Analysis and Identification of Flavonoids Methods Enzymol. 2001, 335, 3– 14 DOI: 10.1016/S0076-6879(01)35227-8
  There is no corresponding record for this reference.
154. 154
  Dangles, O.; Saito, N.; Brouillard, R. Anthocyanin Intramolecular Copigment Effect Phytochemistry 1993, 34 (1) 119– 124 DOI: 10.1016/S0031-9422(00)90792-1
  There is no corresponding record for this reference.
155. 155
  Figueiredo, P.; George, F.; Tatsuzawa, F.; Toki, K.; Saito, N.; Brouillard, R. New Features of Intramolecular Copigmentation by Acylated Anthocyanins Phytochemistry 1999, 51, 125– 132 DOI: 10.1016/S0031-9422(98)00685-2
  155
  New features of intramolecular copigmentation by acylated anthocyanins
  Figueiredo, Paulo; George, Florian; Tatsuzawa, Fumi; Toki, Kenjiro; Saito, Norio; Brouillard, Raymond
  Phytochemistry (1999), 51 (1), 125-132CODEN: PYTCAS; ISSN:0031-9422. (Elsevier Science Ltd.)
  Three series of structurally related anthocyanins, extd. from the red-purple flowers of Dendrobium "Pramot", xLaeliocattleya cv. Mini Purple, Bletilla striata and Phalaenopsis all belonging to the Orchidaceae family and another series extd. from the pink flowers of Senecio cruentus (Compositae) allowed the confirmation of the existence of strong intramol. copigmentation effects. These interactions confer stability to the colored forms of the mols., in a wide range of slightly acidic to neutral aq. media. Moreover, the existence of structural relationships among the four series stressed the different influences exerted by the diverse substituent groups. The existence of a malonylglucoside attached to position 3 of all but three of the mols. put forward a new role for the malonyl residue, in this particular position.
156. 156
  Fleschhut, J.; Kratzer, F.; Rechkemmer, G.; Kulling, S. E. Stability and Biotransformation of Various Dietary Anthocyanins in Vitro Eur. J. Nutr. 2006, 45 (1) 7– 18 DOI: 10.1007/s00394-005-0557-8
  156
  Stability and biotransformation of various dietary anthocyanins in vitro
  Fleschhut, Jens; Kratzer, Frank; Rechkemmer, Gerhard; Kulling, Sabine E.
  European Journal of Nutrition (2006), 45 (1), 7-18CODEN: EJNUFZ; ISSN:1436-6207. (Steinkopff Verlag)
  Background Anthocyanins, which are found in high concns. in fruit and vegetable, may play a beneficial role in retarding or reversing the course of chronic degenerative diseases. However, little is known about the biotransformation and the metab. of anthocyanins so far. Aim of the study The aim of the study was to investigate possible transformation pathways of anthocyanins by human fecal microflora and by rat liver microsomes as a source of cytochrome P 450 enzymes as well as of glucuronyltransferases. Methods Pure anthocyanins, an aq. ext. of red radish as well as the assumed degrdn. products were incubated with human fecal suspension. The incubation mixts. were purified by solid-phase extn. and analyzed by HPLC/DAD/MS and GC/MS. Quantification was done by the external std. method. Furthermore the biotransformation of anthocyanins by incubation with rat liver microsomes in the presence of the cofactor NADPH (as a model for the phase I oxidn.) and in the presence of activated glucuronic acid (as a model for the phase II glucuronidation) was investigated. Results Glycosylated and acylated anthocyanins were rapidly degraded by the intestinal microflora after anaerobic incubation with a human fecal suspension. The major stable products of anthocyanin degrdn. are the corresponding phenolic acids derived from the B-ring of the anthocyanin skeleton. Anthocyanins were not metabolized by cytochrome P 450 enzymes, neither hydroxylated nor demethylated. However they were glucuronidated by rat liver microsomes to several products. Conclusions The gut microflora seem to play an important role in the biotransformation of anthocyanins. A rapid degrdn. could be one major reason for the poor bioavailability of anthocyanins in pharmacokinetic studies described so far in the literature. The formation of phenolic acids as the major stable degrdn. products gives an important hint to the fate of anthocyanins in vivo.
157. 157
  Lopes, P.; Richard, T.; Saucier, C.; Teissedre, P.-L.; Monti, J.-P.; Glories, Y. Anthocyanone A: A Quinone Methide Derivative Resulting from Malvidin 3- O -Glucoside Degradation J. Agric. Food Chem. 2007, 55 (7) 2698– 2704 DOI: 10.1021/jf062875o
  There is no corresponding record for this reference.
158. 158
  Sadilova, E.; Carle, R.; Stintzing, F. C. Thermal Degradation of Anthocyanins and Its Impact on Color Andin Vitro Antioxidant Capacity Mol. Nutr. Food Res. 2007, 51 (12) 1461– 1471 DOI: 10.1002/mnfr.200700179
  158
  Thermal degradation of anthocyanins and its impact on color and in vitro antioxidant capacity
  Sadilova, Eva; Carle, Reinhold; Stintzing, Florian C.
  Molecular Nutrition & Food Research (2007), 51 (12), 1461-1471CODEN: MNFRCV; ISSN:1613-4125. (Wiley-VCH Verlag GmbH & Co. KGaA)
  The aim of the current study was to thoroughly investigate the structural changes of anthocyanins at pH 3.5 in purified fractions from black carrot, elderberry and strawberry heated over 6 h at 95°C. Degrdn. products were monitored by HPLC-DAD-MS3 to elucidate the prevailing degrdn. pathways. In addn., alterations of color and antioxidant properties obsd. upon heating were scrutinized. Most interestingly, the degrdn. pathways at pH 3.5 were found to differ from those at pH 1. Among others, chalcone glycosides were detected at 320 nm in heat-treated elderberry and strawberry pigment isolates, and opening of the pyrylium ring initiated anthocyanin degrdn. In the case of acylated anthocyanins, acyl-glycoside moieties were split off from the flavylium backbone, first. Finally, for all pigment isolates, phenolic acids and phloroglucinaldehyde were the terminal degrdn. products as remainders of the B- and A-ring, resp. Maximum and min. antioxidant stabilizing capacities were found in black carrot and strawberry, resp., which was explained by the high degree of acylation in the former. After heating, decline of trolox equiv. antioxidant capacity (TEAC) was obsd. in all samples, which was attributed to both anthocyanins and their colorless degrdn. products following thermal exposure. As deduced from the ratio of TEAC value and anthocyanin content, the loss of anthocyanin bioactivity could not be compensated by the antioxidant capacity of newly formed colorless phenolics upon heating.
159. 159
  Yang, J.; Hu, W.; Usvyat, D.; Matthews, D.; Schütz, M.; Chan, G. K.-L. Ab Initio Determination of the Crystalline Benzene Lattice Energy to Sub-Kilojoule/mol Accuracy Science 2014, 345 (6197) 640– 643 DOI: 10.1126/science.1254419
  159
  Ab initio determination of the crystalline benzene lattice energy to sub-kilojoule/mole accuracy
  Yang, Jun; Hu, Weifeng; Usvyat, Denis; Matthews, Devin; Schuetz, Martin; Chan, Garnet Kin-Lic
  Science (Washington, DC, United States) (2014), 345 (6197), 640-643CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  Computation of lattice energies to an accuracy sufficient to distinguish polymorphs is a fundamental bottleneck in crystal structure prediction. For the lattice energy of the prototypical benzene crystal, we combined the quantum chem. advances of the last decade to attain sub-kilojoule per mol accuracy, an order-of-magnitude improvement in certainty over prior calcns. that necessitates revision of the exptl. extrapolation to 0 K. Our computations reveal the nature of binding by improving on previously inaccessible or inaccurate multibody and many-electron contributions and provide revised ests. of the effects of temp., vibrations, and relaxation. Our demonstration raises prospects for definitive first-principles resoln. of competing polymorphs in mol. crystal structure prediction.
160. 160
  Cavalcanti, R. N.; Santos, D. T.; Meireles, M. A. A. Non-Thermal Stabilization Mechanisms of Anthocyanins in Model and Food systems—An Overview Food Res. Int. 2011, 44 (2) 499– 509 DOI: 10.1016/j.foodres.2010.12.007
  160
  Non-thermal stabilization mechanisms of anthocyanins in model and food systems-An overview
  Cavalcanti, Rodrigo N.; Santos, Diego T.; Meireles, Maria Angela A.
  Food Research International (2011), 44 (2), 499-509CODEN: FORIEU; ISSN:0963-9969. (Elsevier B.V.)
  A review. Phenolic compds. are part of the secondary metab. of plants and are of great importance for their survival in unfavorable environment. A class of phenolic compds. easily found in the Plant Kingdom, is anthocyanins, a flavonoid category. They are water-sol. pigments that confer the bright red, blue, and purple colors of fruits and vegetables and promote several health benefits due to their diverse biol. activities. Different factors affect the color and stability of these compds. including pH, temp., light, presence of copigments, self-assocn., metallic ions, enzymes, oxygen, ascorbic acid, sugar, among others. For this reason many studies have been conducted with the aim to increase the stability of these substances. Therefore, the present review highlights studies on the stabilization of anthocyanins and presents latent anthocyanin stabilization mechanisms and demonstrates the potentiality of the main techniques used: assocn. and encapsulation.
161. 161
  Rodrigues, R. F.; Ferreira da Silva, P.; Shimizu, K.; Freitas, A. A.; Kovalenko, S. A.; Ernsting, N. P.; Quina, F. H.; Maçanita, A. Ultrafast Internal Conversion in a Model Anthocyanin-Polyphenol Complex: Implications for the Biological Role of Anthocyanins in Vegetative Tissues of Plants Chem. - Eur. J. 2009, 15 (6) 1397– 1402 DOI: 10.1002/chem.200801207
  161
  Ultrafast internal conversion in a model anthocyanin-polyphenol complex: implications for the biological role of anthocyanins in vegetative tissues of plants
  Rodrigues, Rita Franca; Ferreira da Silva, Palmira; Shimizu, Karina; Freitas, Adilson A.; Kovalenko, Sergey A.; Ernsting, Nikolaus P.; Quina, Frank H.; Macanita, Antonio
  Chemistry - A European Journal (2009), 15 (6), 1397-1402CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  The red flavylium cations of anthocyanins form ground-state charge-transfer complexes with several naturally occurring electron-donor copigments, such as hydroxylated flavones and hydroxycinnamic or benzoic acids. Excitation of the 7-methoxy-4-methyl-flavylium-protocatechuic acid complex results in ultrafast (240 fs) internal conversion to the ground state of the complex by way of a low-lying charge-transfer state. Thus, both uncomplexed anthocyanins, whose excited state decays by fast (5-20 ps) excited-state proton transfer, and anthocyanin-copigment complexes have highly efficient mechanisms of deactivation that are consistent with the proposed protective role of anthocyanins against excess solar radiation in the vegetative tissues of plants.
162. 162
  Ferreira da Silva, P.; Paulo, L.; Barbafina, A.; Elisei, F.; Quina, F. H.; Maçanita, A. L. Photoprotection and the Photophysics of Acylated Anthocyanins Chem. - Eur. J. 2012, 18 (12) 3736– 3744 DOI: 10.1002/chem.201102247
  162
  Photoprotection and the Photophysics of Acylated Anthocyanins
  Ferreira da Silva, Palmira; Paulo, Luisa; Barbafina, Adrianna; Eisei, Fausto; Quina, Frank H.; Macanita, Antonio L.
  Chemistry - A European Journal (2012), 18 (12), 3736-3744CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  The proposed role of anthocyanins in protecting plants against excess solar radiation is consistent with the occurrence of ultrafast (5-25 ps) excited-state proton transfer as the major deexcitation pathway of these mols. However, because natural anthocyanins absorb mainly in the visible region of the spectra, with only a narrow absorption band in the UV-B region, this highly efficient deactivation mechanism would essentially only protect the plant from visible light. On the other hand, ground-state charge-transfer complexes of anthocyanins with naturally occurring electron-donor copigments, such as hydroxylated flavones, flavonoids, and hydroxycinnamic or benzoic acids, do exhibit high UV-B absorptivities that complement that of the anthocyanins. In this work, we report a comparative study of the photophysics of the naturally occurring anthocyanin cyanin, intermol. cyanin-coumaric acid complexes, and an acylated anthocyanin, i.e., cyanin with a pendant coumaric ester copigment. Both inter- and intramol. anthocyanin-copigment complexes are shown to have ultrafast energy dissipation pathways comparable to those of model flavylium cation-copigment complexes. However, from the standpoint of photoprotection, the results indicate that the covalent attachment of copigment mols. to the anthocyanin represents a much more efficient strategy by providing the plant with significant UV-B absorption capacity and at the same time coupling this absorption to efficient energy dissipation pathways (ultrafast internal conversion of the complexed form and fast energy transfer from the excited copigment to the anthocyanin followed by adiabatic proton transfer) that avoid net photochem. damage.
163. 163
  Song, B. J.; Sapper, T. N.; Burtch, C. E.; Brimmer, K.; Goldschmidt, M.; Ferruzzi, M. G. Photo- and Thermodegradation of Anthocyanins from Grape and Purple Sweet Potato in Model Beverage Systems J. Agric. Food Chem. 2013, 61 (6) 1364– 1372 DOI: 10.1021/jf3044007
  There is no corresponding record for this reference.
164. 164
  Malien-Aubert, C.; Dangles, O.; Amiot, M. J. Color Stability of Commercial Anthocyanin-Based Extracts in Relation to the Phenolic Composition. Protective Effects by Intra- and Intermolecular Copigmentation J. Agric. Food Chem. 2001, 49 (1) 170– 176 DOI: 10.1021/jf000791o
  There is no corresponding record for this reference.
165. 165
  Cabrita, L.; Petrov, V.; Pina, F. On the Thermal Degradation of Anthocyanidins: Cyanidin RSC Adv. 2014, 4 (36) 18939 DOI: 10.1039/c3ra47809b
  165
  On the thermal degradation of anthocyanidins: cyanidin
  Cabrita, Luis; Petrov, Vesselin; Pina, Fernando
  RSC Advances (2014), 4 (36), 18939-18944CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)
  Cyanidin was studied by direct pH jumps (from equilibrated solns. at very low pH values to higher pH values) and reverse pH jumps (from equilibrated or not equilibrated solns. at higher pH values to very low ones). The kinetic steps of the direct and reverse pH jumps were followed by stopped flow, absorption spectroscopy and HPLC, at different timescales. The pH dependent rate const. of the slower kinetic process to reach the equil. follows a bell shaped curve as described for many synthetic flavylium compds. Unlike anthocyanins, it was proved that there is no pH dependent reversibility in the system, since the chalcone suffers an irreversible degrdn. process. The math. expression to describe the bell shaped behavior was deduced. These results contribute to explain why in plants glycosylation is crucial for the stabilization of the anthocyanins.
166. 166
  Schneider, H.-J. Dispersive Interactions in Solution Complexes Acc. Chem. Res. 2015, 48 (7) 1815– 1822 DOI: 10.1021/acs.accounts.5b00111
  166
  Dispersive Interactions in Solution Complexes
  Schneider, Hans-Joerg
  Accounts of Chemical Research (2015), 48 (7), 1815-1822CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  Dispersive interactions are known to play a major role in mol. assocns. in the gas phase and in the solid state. In soln., however, their significance has been disputed in recent years on the basis of several arguments. A major problem until now has been the sepn. of dispersive and hydrophobic effects, which are both maximized in water due the low polarizability of this most important medium. Analyses of complexes between porphyrins and systematically varied substrates in water have allowed us to discriminate dispersive from hydrophobic effects, as the latter turned out to be negligible for complexations with flat surfaces such as porphyrins. Also, for the first time, it has become possible to obtain binding free energy increments ΔΔG for a multitude of org. residues including halogen, amide, amino, ether, carbonyl, ester, nitro, sulfur, unsatured, and cyclopropane groups, which turned out to be additive. Binding contributions for satd. residues are unmeasurably small, with ΔΔG > 1 kJ/mol, but they increase to, e.g., ΔΔG = 5 kJ/mol for a nitro group, a value not far from, e.g., that of a stacking pyridine ring. Stacking interactions of heteroarenes with porphyrins depend essentially on the size of the arenes, in line with polarizabilities, and seem to be rather independent of the position of nitrogen within the rings. Measurements of halogen derivs. indicate that complexes with porphyrins, cyclodextrins, and pillarenes as hosts in different media consistently show increasing stability from fluorine to iodine as the substituent. This, and the obsd. sequence with other substrates, is in line with the expected increase in dispersive forces with increasing polarizability. Induced dipoles, which also would increase with polarizability, can be ruled out as providing the driving source in view of the data with halides: the obsd. stability sequence is opposite the change of electronegativity from fluorine to iodine. The same holds for the solvent effect obsd. in ethanol-water mixts. Dispersive contributions vary not only with the polarizability of the used media but also with the interacting receptor sites; it has been shown that for cucurbiturils the polarizability inside the cavity is extremely low, which also explains why hydrophobic effects are maximized with these hosts. Complexations with other known host compds., however, such as those between cryptands or cavitands with, e.g., noble gases, bear the signature of dominating dispersive forces. Some recent examples illustrate that such van der Waals forces can also play an important role in complexations with proteins. Again, a clue for this is the increase in ΔG for inhibitor binding by 7 kJ/mol for, e.g., a bromine in comparison to a fluorine deriv.
167. 167
  Hunter, C. A.; Sanders, J. K. M. The Nature of.pi.-.pi. Interactions J. Am. Chem. Soc. 1990, 112 (14) 5525– 5534 DOI: 10.1021/ja00170a016
  167
  The nature of π-π interactions
  Hunter, Christopher A.; Sanders, Jeremy K. M.
  Journal of the American Chemical Society (1990), 112 (14), 5525-34CODEN: JACSAT; ISSN:0002-7863.
  A simple model of the charge distribution in a π-system is used to explain the strong geometrical requirements for interactions between arom. mols. The key feature of the model is that it considers the σ-framework and the π-electrons sep. and demonstrates that net favorable π-π interactions are actually the result of π-σ attractions that overcome π-π repulsions. The calcns. correlate with observations made on porphyrin π-π interactions both in soln. and in the cryst. state. By using an idealized π-atom, some general rules for predicting the geometry of favorable π-π interactions are derived. In particular a favorable offset or slipped geometry is predicted. These rules successfully predict the geometry of intermol. interactions in the crystal structures of arom. mols. and rationalize a range of host-guest phenomena. The theory demonstrates that the electron donor-acceptor concept can be misleading: it is the properties of the atoms at the points of intermol. contact rather than the overall mol. properties which are important.
168. 168
  Hwang, J.; Li, P.; Carroll, W. R.; Smith, M. D.; Pellechia, P. J.; Shimizu, K. D. Additivity of Substituent Effects in Aromatic Stacking Interactions J. Am. Chem. Soc. 2014, 136 (40) 14060– 14067 DOI: 10.1021/ja504378p
  168
  Additivity of Substituent Effects in Aromatic Stacking Interactions
  Hwang, Jungwun; Li, Ping; Carroll, William R.; Smith, Mark D.; Pellechia, Perry J.; Shimizu, Ken D.
  Journal of the American Chemical Society (2014), 136 (40), 14060-14067CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The goal of this study was to exptl. test the additivity of the electrostatic substituent effects (SEs) for the arom. stacking interaction. The additivity of the SEs was assessed using a small mol. model system that could adopt an offset face-to-face arom. stacking geometry. The intramol. interactions of these mol. torsional balances were quant. measured via the changes in a folded/unfolded conformational equil. Five different types of substituents were examd. (CH3, OCH3, Cl, CN, and NO2) that ranged from electron-donating to electron-withdrawing. The strength of the intramol. stacking interactions was measured for 21 substituted arom. stacking balances and 21 control balances in chloroform soln. The obsd. stability trends were consistent with additive SEs. Specifically, additive SE models could predict SEs with an accuracy from ±0.01 to ±0.02 kcal/mol. The additive SEs were consistent with Wheeler and Houk's direct SE model. However, the indirect or polarization SE model cannot be ruled out as it shows similar levels of additivity for two to three substituent systems, which were the no. of substituents in our model system. SE additivity also has practical utility as the SEs can be accurately predicted. This should aid in the rational design and optimization of systems that utilize arom. stacking interactions.
169. 169
  Cockroft, S. L.; Hunter, C. A.; Lawson, K. R.; Perkins, J.; Urch, C. J. Electrostatic Control of Aromatic Stacking Interactions J. Am. Chem. Soc. 2005, 127 (24) 8594– 8595 DOI: 10.1021/ja050880n
  169
  Electrostatic Control of Aromatic Stacking Interactions
  Cockroft, Scott L.; Hunter, Christopher A.; Lawson, Kevin R.; Perkins, Julie; Urch, Christopher J.
  Journal of the American Chemical Society (2005), 127 (24), 8594-8595CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  A supramol. approach has been used to investigate the free energies of intermol. arom. stacking interactions. Chem. double mutant cycles have been used to measure the effect of a range of substituents on face-to-face stacking interactions with Ph and pentafluorophenyl rings. Electrostatic effects dominate the trends in interaction energy.
170. 170
  Meyer, E. A.; Castellano, R. K.; Diederich, F. Interactions with Aromatic Rings in Chemical and Biological Recognition Angew. Chem., Int. Ed. 2003, 42 (11) 1210– 1250 DOI: 10.1002/anie.200390319
  170
  Interactions with aromatic rings in chemical and biological recognition
  Meyer, Emmanuel A.; Castellano, Ronald K.; Diederich, Francois
  Angewandte Chemie, International Edition (2003), 42 (11), 1210-1250CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Intermol. interactions involving arom. rings are key processes in both chem. and biol. recognition. Their understanding is essential for rational drug design and lead optimization in medicinal chem. Different approaches-biol. studies, mol. recognition studies with artificial receptors, crystallog. database mining, gas-phase studies, and theor. calcns. - are pursued to generate a profound understanding of the structural and energetic parameters of individual recognition modes involving arom. rings. This review attempts to combine and summarize the knowledge gained from these investigations. The review focuses mainly on examples with biol. relevance since one of its aims it to enhance the knowledge of mol. recognition forces that is essential for drug development.
171. 171
  Salonen, L. M.; Ellermann, M.; Diederich, F. Aromatic Rings in Chemical and Biological Recognition: Energetics and Structures Angew. Chem., Int. Ed. 2011, 50 (21) 4808– 4842 DOI: 10.1002/anie.201007560
  171
  Aromatic rings in chemical and biological recognition: energetics and structures
  Salonen, Laura M.; Ellermann, Manuel; Diederich, Francois
  Angewandte Chemie, International Edition (2011), 50 (21), 4808-4842CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. This review describes a multidimensional treatment of mol. recognition phenomena involving arom. rings in chem. and biol. systems. It summarizes new results reported since the appearance of an earlier review in 2003 in host-guest chem., biol. affinity assays and biostructural anal., data base mining in the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB), and advanced computational studies. Topics addressed are arene-arene, perfluoroarene-arene, S···arom., cation-π, and anion-π interactions, as well as hydrogen bonding to π systems. The generated knowledge benefits, in particular, structure-based hit-to-lead development and lead optimization both in the pharmaceutical and in the crop protection industry. It equally facilitates the development of new advanced materials and supramol. systems, and should inspire further utilization of interactions with arom. rings to control the stereochem. outcome of synthetic transformations.
172. 172
  Hunter, C. A. Quantifying Intermolecular Interactions: Guidelines for the Molecular Recognition Toolbox Angew. Chem., Int. Ed. 2004, 43 (40) 5310– 5324 DOI: 10.1002/anie.200301739
  172
  Quantifying intermolecular interactions: Guidelines for the molecular recognition toolbox
  Hunter, Christopher A.
  Angewandte Chemie, International Edition (2004), 43 (40), 5310-5324CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Mol. recognition events in soln. are affected by many different factors that have hampered the development of an understanding of intermol. interactions at a quant. level. Tendency is to partition these effects into discrete phenomenol. fields that are classified, named, and divorced: arom. interactions, cation-T interactions, CH-O hydrogen bonds, short strong hydrogen bonds, and hydrophobic interactions to name a few. To progress in the field, the authors need to develop an integrated quant. appreciation of the relative magnitudes of all of the different effects that might influence the mol. recognition behavior of a given system. In an effort to navigate undergraduates through the vast and sometimes contradictory literature on the subject, I have developed an approach that treats theor. ideas and exptl. observations about intermol. interactions in the gas phase, the solid state, and soln. from a single simplistic viewpoint. The key features are outlined here, and although many of the ideas will be familiar, the aim is to provide a semiquant. thermodn. ranking of these effects in soln. at room temp.
173. 173
  Trouillas, P.; Di Meo, F.; Gierschner, J.; Linares, M.; Sancho-García, J. C.; Otyepka, M. Optical Properties of Wine Pigments: Theoretical Guidelines with New Methodological Perspectives Tetrahedron 2015, 71 (20) 3079– 3088 DOI: 10.1016/j.tet.2014.10.046
  There is no corresponding record for this reference.
174. 174
  London, F. The General Theory of Molecular Forces Trans. Faraday Soc. 1937, 33 (0) 8b– 26 DOI: 10.1039/tf937330008b
  There is no corresponding record for this reference.
175. 175
  Chandler, D. Interfaces and the Driving Force of Hydrophobic Assembly Nature 2005, 437 (7059) 640– 647 DOI: 10.1038/nature04162
  175
  Interfaces and the driving force of hydrophobic assembly
  Chandler, David
  Nature (London, United Kingdom) (2005), 437 (7059), 640-647CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  A review. The hydrophobic effect - the tendency for oil and water to segregate - is important in diverse phenomena, from the cleaning of laundry, to the creation of micro-emulsions to make new materials, to the assembly of proteins into functional complexes. This effect is multifaceted depending on whether hydrophobic mols. are individually hydrated or driven to assemble into larger structures. Despite the basic principles underlying the hydrophobic effect being qual. well understood, only recently have theor. developments begun to explain and quantify many features of this ubiquitous phenomenon.
176. 176
  Biedermann, F.; Nau, W. M.; Schneider, H.-J. The Hydrophobic Effect Revisited—Studies with Supramolecular Complexes Imply High-Energy Water as a Noncovalent Driving Force Angew. Chem., Int. Ed. 2014, 53 (42) 11158– 11171 DOI: 10.1002/anie.201310958
  176
  The Hydrophobic Effect Revisited-Studies with Supramolecular Complexes Imply High-Energy Water as a Noncovalent Driving Force
  Biedermann, Frank; Nau, Werner M.; Schneider, Hans-Joerg
  Angewandte Chemie, International Edition (2014), 53 (42), 11158-11171CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Traditional descriptions of the hydrophobic effect from entropic arguments or the calcn. of solvent-occupied surfaces must be questioned in view of new results obtained with supramol. complexes. In these studies, it was possible to sep. hydrophobic from dispersive interactions, which are strongest in aq. systems. Even very hydrophobic alkanes assoc. significantly only in cavities contg. water mols. with an insufficient no. of possible hydrogen bonds. The replacement of high-energy water in cavities by guest mols. is the essential enthalpic driving force for complexation, as borne out by data for complexes of cyclodextrins, cyclophanes, and cucurbiturils, for which complexation enthalpies of up to -100 kJ mol-1 were reached for encapsulated alkyl residues. Water-box simulations were used to characterize the different contributions from high-energy water and enabled the calcn. of the assocn. free enthalpies for selected cucurbituril complexes to within a 10% deviation from exptl. values. Cavities in artificial receptors are more apt to show the enthalpic effect of high-energy water than those in proteins or nucleic acids, because they bear fewer or no functional groups in the inner cavity to stabilize interior water mols.
177. 177
  Waters, M. L. Aromatic Interactions Acc. Chem. Res. 2013, 46 (4) 873– 873 DOI: 10.1021/ar4000828
  177
  Aromatic Interactions
  Waters, Marcey L.
  Accounts of Chemical Research (2013), 46 (4), 873CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  There is no expanded citation for this reference.
178. 178
  Yang, L.; Adam, C.; Nichol, G. S.; Cockroft, S. L. How Much Do van Der Waals Dispersion Forces Contribute to Molecular Recognition in Solution? Nat. Chem. 2013, 5 (12) 1006– 1010 DOI: 10.1038/nchem.1779
  178
  How much do van der Waals dispersion forces contribute to molecular recognition in solution?
  Yang, Lixu; Adam, Catherine; Nichol, Gary S.; Cockroft, Scott L.
  Nature Chemistry (2013), 5 (12), 1006-1010CODEN: NCAHBB; ISSN:1755-4330. (Nature Publishing Group)
  The emergent properties that arise from self-assembly and mol. recognition phenomena are a direct consequence of noncovalent interactions. Gas-phase measurements and computational methods point to the dominance of dispersion forces in mol. assocn., but solvent effects complicate the unambiguous quantification of these forces in soln. Here, the authors used synthetic mol. balances to measure interactions between apolar alkyl chains in 31 org., fluorous and aq. solvent environments. The exptl. interaction energies are an order of magnitude smaller than ests. of dispersion forces between alkyl chains that were derived from vaporization enthalpies and dispersion-cor. calcns. Instead, cohesive solvent-solvent interactions are the major driving force behind apolar assocn. in soln. Probably theor. models that implicate important roles for dispersion forces in mol. recognition events should be interpreted with caution in solvent-accessible systems.
179. 179
  Mackerell, A. D. Empirical Force Fields for Biological Macromolecules: Overview and Issues J. Comput. Chem. 2004, 25 (13) 1584– 1604 DOI: 10.1002/jcc.20082
  179
  Empirical force fields for biological macromolecules: Overview and issues
  MacKerell, Alexander D., Jr.
  Journal of Computational Chemistry (2004), 25 (13), 1584-1604CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A review. Empirical force field-based studies of biol. macromols. are becoming a common tool for investigating their structure-activity relationships at an at. level of detail. Such studies facilitate interpretation of exptl. data and allow for information not readily accessible to exptl. methods to be obtained. A large part of the success of empirical force field-based methods is the quality of the force fields combined with the algorithmic advances that allow for more accurate reprodn. of exptl. observables. Presented is an overview of the issues assocd. with the development and application of empirical force fields to biomol. systems. This is followed by a summary of the force fields commonly applied to the different classes of biomols.; proteins, nucleic acids, lipids, and carbohydrates. In addn., issues assocd. with computational studies on "heterogeneous" biomol. systems and the transferability of force fields to a wide range of org. mols. of pharmacol. interest are discussed.
180. 180
  Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. Development and Testing of a General Amber Force Field J. Comput. Chem. 2004, 25 (9) 1157– 1174 DOI: 10.1002/jcc.20035
  180
  Development and testing of a general Amber force field
  Wang, Junmei; Wolf, Romain M.; Caldwell, James W.; Kollman, Peter A.; Case, David A.
  Journal of Computational Chemistry (2004), 25 (9), 1157-1174CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  We describe here a general Amber force field (GAFF) for org. mols. GAFF is designed to be compatible with existing Amber force fields for proteins and nucleic acids, and has parameters for most org. and pharmaceutical mols. that are composed of H, C, N, O, S, P, and halogens. It uses a simple functional form and a limited no. of atom types, but incorporates both empirical and heuristic models to est. force consts. and partial at. charges. The performance of GAFF in test cases is encouraging. In test I, 74 crystallog. structures were compared to GAFF minimized structures, with a root-mean-square displacement of 0.26 Å, which is comparable to that of the Tripos 5.2 force field (0.25 Å) and better than those of MMFF 94 and CHARMm (0.47 and 0.44 Å, resp.). In test II, gas phase minimizations were performed on 22 nucleic acid base pairs, and the minimized structures and intermol. energies were compared to MP2/6-31G* results. The RMS of displacements and relative energies were 0.25 Å and 1.2 kcal/mol, resp. These data are comparable to results from Parm99/RESP (0.16 Å and 1.18 kcal/mol, resp.), which were parameterized to these base pairs. Test III looked at the relative energies of 71 conformational pairs that were used in development of the Parm99 force field. The RMS error in relative energies (compared to expt.) is about 0.5 kcal/mol. GAFF can be applied to wide range of mols. in an automatic fashion, making it suitable for rational drug design and database searching.
181. 181
  Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules J. Am. Chem. Soc. 1996, 118 (9) 2309– 2309 DOI: 10.1021/ja955032e
  181
  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules [ Erratum for J. Am. Chem. Soc. 1995, 117, 5179-5197 ]
  Cornell, Wendy D.; Cieplak, Piotr; Bayly, Christopher I.; Gould, Ian R.; Merz, Kenneth M. Jr.; Ferguson, David M.; Spellmeyer, David C.; Fox, Thomas; Caldwell, James W.; Kollman, Peter A.
  Journal of the American Chemical Society (1996), 118 (9), 2309CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  There is no expanded citation for this reference.
182. 182
  Zgarbová, M.; Otyepka, M.; Sponer, J.; Hobza, P.; Jurecka, P. Large-Scale Compensation of Errors in Pairwise-Additive Empirical Force Fields: Comparison of AMBER Intermolecular Terms with Rigorous DFT-SAPT Calculations Phys. Chem. Chem. Phys. 2010, 12 (35) 10476– 10493 DOI: 10.1039/c002656e
  There is no corresponding record for this reference.
183. 183
  Šponer, J.; Banáš, P.; Jurečka, P.; Zgarbová, M.; Kührová, P.; Havrila, M.; Krepl, M.; Stadlbauer, P.; Otyepka, M. Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome J. Phys. Chem. Lett. 2014, 5 (10) 1771– 1782 DOI: 10.1021/jz500557y
  183
  Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome
  Sponer, Jiri; Banas, Pavel; Jurecka, Petr; Zgarbova, Marie; Kuhrova, Petra; Havrila, Marek; Krepl, Miroslav; Stadlbauer, Petr; Otyepka, Michal
  Journal of Physical Chemistry Letters (2014), 5 (10), 1771-1782CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  A review. We present a brief overview of explicit solvent mol. dynamics (MD) simulations of nucleic acids. We explain phys. chem. limitations of the simulations, namely, the mol. mechanics (MM) force field (FF) approxn. and limited time scale. Further, we discuss relations and differences between simulations and expts., compare std. and enhanced sampling simulations, discuss the role of starting structures, comment on different versions of nucleic acid FFs, and relate MM computations with contemporary quantum chem. Despite its limitations, we show that MD is a powerful technique for studying the structural dynamics of nucleic acids with a fast growing potential that substantially complements exptl. results and aids their interpretation.
184. 184
  Adcock, S. A.; McCammon, J. A. Molecular Dynamics: Survey of Methods for Simulating the Activity of Proteins Chem. Rev. 2006, 106 (5) 1589– 1615 DOI: 10.1021/cr040426m
  184
  Molecular dynamics: Survey of methods for simulating the activity of proteins
  Adcock, Stewart A.; McCammon, J. Andrew
  Chemical Reviews (Washington, DC, United States) (2006), 106 (5), 1589-1615CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Mol. dynamics simulations (MDS) of proteins have provided many insights into the internal motions of these biomols. Simulation of in silico models aids in the interpretation and reconciliation of exptl. data. With ongoing advances in both methodol. and computational resources, MDS are being extended to larger systems and longer time scales. This enables the investigation of motions and conformational changes that have functional implications and yields information that is not available though any other means. Today's results suggest that (subject to the continuing utilization of synergies between expt. and simulation) the applications of MDS will command an increasingly crit. role in the understanding of biol. systems.
185. 185
  Case, D. A.; Cheatham, T. E.; Darden, T.; Gohlke, H.; Luo, R.; Merz, K. M.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. The Amber Biomolecular Simulation Programs J. Comput. Chem. 2005, 26 (16) 1668– 1688 DOI: 10.1002/jcc.20290
  185
  The amber biomolecular simulation programs
  Case, David A.; Cheatham, Thomas E., III; Darden, Tom; Gohlke, Holger; Luo, Ray; Merz, Kenneth M., Jr.; Onufriev, Alexey; Simmerling, Carlos; Wang, Bing; Woods, Robert J.
  Journal of Computational Chemistry (2005), 26 (16), 1668-1688CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  The authors describe the development, current features, and some directions for future development of the Amber package of computer programs. This package evolved from a program that was constructed in the late 1970s to do Assisted Model Building with Energy Refinement, and now contains a group of programs embodying a no. of powerful tools of modern computational chem., focused on mol. dynamics and free energy calcns. of proteins, nucleic acids, and carbohydrates.
186. 186
  Brooks, B. R.; Brooks, C. L.; MacKerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S. CHARMM: The Biomolecular Simulation Program J. Comput. Chem. 2009, 30 (10) 1545– 1614 DOI: 10.1002/jcc.21287
  186
  CHARMM: The biomolecular simulation program
  Brooks, B. R.; Brooks, C. L., III; Mackerell, A. D., Jr.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; Caflisch, A.; Caves, L.; Cui, Q.; Dinner, A. R.; Feig, M.; Fischer, S.; Gao, J.; Hodoscek, M.; Im, W.; Kuczera, K.; Lazaridis, T.; Ma, J.; Ovchinnikov, V.; Paci, E.; Pastor, R. W.; Post, C. B.; Pu, J. Z.; Schaefer, M.; Tidor, B.; Venable, R. M.; Woodcock, H. L.; Wu, X.; Yang, W.; York, D. M.; Karplus, M.
  Journal of Computational Chemistry (2009), 30 (10), 1545-1614CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A review. CHARMM (Chem. at HARvard Mol. Mechanics) is a highly versatile and widely used mol. simulation program. It has been developed over the last three decades with a primary focus on mols. of biol. interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small mol. ligands, as they occur in soln., crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, mol. minimization, dynamics, and anal. techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calcns. with CHARMM can be performed using a no. of different energy functions and models, from mixed quantum mech.-mol. mech. force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009.
187. 187
  Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable Molecular Dynamics with NAMD J. Comput. Chem. 2005, 26 (16) 1781– 1802 DOI: 10.1002/jcc.20289
  187
  Scalable molecular dynamics with NAMD
  Phillips, James C.; Braun, Rosemary; Wang, Wei; Gumbart, James; Tajkhorshid, Emad; Villa, Elizabeth; Chipot, Christophe; Skeel, Robert D.; Kale, Laxmikant; Schulten, Klaus
  Journal of Computational Chemistry (2005), 26 (16), 1781-1802CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  NAMD is a parallel mol. dynamics code designed for high-performance simulation of large biomol. systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical mol. dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temp. and pressure controls used. Features for steering the simulation across barriers and for calcg. both alchem. and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomol. system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the mol. graphics/sequence anal. software VMD and the grid computing/collab. software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.
188. 188
  Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, Flexible, and Free J. Comput. Chem. 2005, 26 (16) 1701– 1718 DOI: 10.1002/jcc.20291
  188
  GROMACS: Fast, flexible, and free
  Van Der Spoel, David; Lindahl, Erik; Hess, Berk; Groenhof, Gerrit; Mark, Alan E.; Berendsen, Herman J. C.
  Journal of Computational Chemistry (2005), 26 (16), 1701-1718CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  This article describes the software suite GROMACS (Groningen MAchine for Chem. Simulation) that was developed at the University of Groningen, The Netherlands, in the early 1990s. The software, written in ANSI C, originates from a parallel hardware project, and is well suited for parallelization on processor clusters. By careful optimization of neighbor searching and of inner loop performance, GROMACS is a very fast program for mol. dynamics simulation. It does not have a force field of its own, but is compatible with GROMOS, OPLS, AMBER, and ENCAD force fields. In addn., it can handle polarizable shell models and flexible constraints. The program is versatile, as force routines can be added by the user, tabulated functions can be specified, and analyses can be easily customized. Nonequil. dynamics and free energy detns. are incorporated. Interfaces with popular quantum-chem. packages (MOPAC, GAMES-UK, GAUSSIAN) are provided to perform mixed MM/QM simulations. The package includes about 100 utility and anal. programs. GROMACS is in the public domain and distributed (with source code and documentation) under the GNU General Public License. It is maintained by a group of developers from the Universities of Groningen, Uppsala, and Stockholm, and the Max Planck Institute for Polymer Research in Mainz. Its Web site is http://www.gromacs.org.
189. 189
  Leach, A. R. Molecular Modelling: Principles and Applications; Pearson, 2001.
  There is no corresponding record for this reference.
190. 190
  Vashisth, H.; Skiniotis, G.; Brooks, C. L. Collective Variable Approaches for Single Molecule Flexible Fitting and Enhanced Sampling Chem. Rev. 2014, 114 (6) 3353– 3365 DOI: 10.1021/cr4005988
  There is no corresponding record for this reference.
191. 191
  Bruccoleri, R. E.; Karplus, M. Conformational Sampling Using High-Temperature Molecular Dynamics Biopolymers 1990, 29 (14) 1847– 1862 DOI: 10.1002/bip.360291415
  There is no corresponding record for this reference.
192. 192
  Chocholoušová, J.; Vacek, J.; Hobza, P. Acetic Acid Dimer in the Gas Phase, Nonpolar Solvent, Microhydrated Environment, and Dilute and Concentrated Acetic Acid: Ab Initio Quantum Chemical and Molecular Dynamics Simulations J. Phys. Chem. A 2003, 107 (17) 3086– 3092 DOI: 10.1021/jp027637k
  192
  Acetic Acid Dimer in the Gas Phase, Nonpolar Solvent, Microhydrated Environment, and Dilute and Concentrated Acetic Acid: Ab Initio Quantum Chemical and Molecular Dynamics Simulations
  Chocholousova, Jana; Vacek, Jaroslav; Hobza, Pavel
  Journal of Physical Chemistry A (2003), 107 (17), 3086-3092CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Theor. study of the acetic acid dimer, its microhydration and its behavior in water and chloroform soln. was performed. To characterize the system, the authors adopted ab initio methods at the DFT and RI MP2 (the resoln. of the identity approxn. MP2) levels for the gas-phase calcns., PCM (polarizable continuum model) approxn. using the polarizable conductor calcn. model (COSMO) for description of solvent, and const. energy (NVE) and const. temp. (NVT) mol. dynamics simulations for gas phase and explicit solvent calcns., resp. The cyclic structure of the acetic acid dimer is the most stable in the gas phase only. During microhydration, the water mols. are incorporated in the dimer leading to water-sepd. structures. This conclusion is based on ab initio quantum chem. calcns., as well as on mol. dynamics simulations. The fact that the cyclic structure does not appear in water soln. is in agreement with previous theor. and exptl. results. Extending the search also on other acetic acid dimer structures, acetic acid does not form any dimer structure in water soln. The cyclic structure also probably is stable in chloroform soln.
193. 193
  Zelený, T.; Hobza, P.; Kabelác, M. Microhydration of Guanine···cytosine Base Pairs, a Theoretical Study on the Role of Water in Stability, Structure and Tautomeric Equilibrium Phys. Chem. Chem. Phys. 2009, 11 (18) 3430– 3435 DOI: 10.1039/b819350a
  There is no corresponding record for this reference.
194. 194
  Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding Chem. Phys. Lett. 1999, 314 (1–2) 141– 151 DOI: 10.1016/S0009-2614(99)01123-9
  194
  Replica-exchange molecular dynamics method for protein folding
  Sugita, Y.; Okamoto, Y.
  Chemical Physics Letters (1999), 314 (1,2), 141-151CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
  We have developed a formulation for mol. dynamics algorithm for the replica-exchange method. The effectiveness of the method for the protein-folding problem is tested with the penta-peptide Met-enkephalin. The method can overcome the multiple-min. problem by exchanging non-interacting replicas of the system at several temps. From only one simulation run, one can obtain probability distributions in canonical ensemble for a wide temp. range using multiple-histogram re-weighting techniques, which allows the calcn. of any thermodn. quantity as a function of temp. in that range.
195. 195
  Beck, D. A. C.; White, G. W. N.; Daggett, V. Exploring the Energy Landscape of Protein Folding Using Replica-Exchange and Conventional Molecular Dynamics Simulations J. Struct. Biol. 2007, 157 (3) 514– 523 DOI: 10.1016/j.jsb.2006.10.002
  There is no corresponding record for this reference.
196. 196
  Laio, A.; Parrinello, M. Escaping Free-Energy Minima Proc. Natl. Acad. Sci. U. S. A. 2002, 99 (20) 12562– 12566 DOI: 10.1073/pnas.202427399
  196
  Escaping free-energy minima
  Laio, Alessandro; Parrinello, Michele
  Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
197. 197
  Barducci, A.; Bonomi, M.; Parrinello, M. Metadynamics Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1 (5) 826– 843 DOI: 10.1002/wcms.31
  197
  Metadynamics
  Barducci, Alessandro; Bonomi, Massimiliano; Parrinello, Michele
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2011), 1 (5), 826-843CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. Metadynamics is a powerful technique for enhancing sampling in mol. dynamics simulations and reconstructing the free-energy surface as a function of few selected degrees of freedom, often referred to as collective variables (CVs). In metadynamics, sampling is accelerated by a history-dependent bias potential, which is adaptively constructed in the space of the CVs. Since its first appearance, significant improvements have been made to the original algorithm, leading to an efficient, flexible, and accurate method that has found many successful applications in several domains of science. Here, we discuss first the theory underlying metadynamics and its recent developments. In particular, we focus on the crucial issue of choosing an appropriate set of CVs and on the possible strategies to alleviate this difficulty. Later in the second part, we present a few recent representative applications, which we have classified into three main classes: solid-state physics, chem. reactions, and biomols.
198. 198
  Brás, N. F.; Cruz, L.; Fernandes, P. A.; De Freitas, V.; Ramos, M. J. Conformational Study of Two Diasteroisomers of Vinylcatechin Dimers in a Methanol Solution Int. J. Quantum Chem. 2011, 111 (7–8) 1498– 1510 DOI: 10.1002/qua.22631
  There is no corresponding record for this reference.
199. 199
  Kollman, P. A.; Massova, I.; Reyes, C.; Kuhn, B.; Huo, S.; Chong, L.; Lee, M.; Lee, T.; Duan, Y.; Wang, W. Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models Acc. Chem. Res. 2000, 33 (12) 889– 897 DOI: 10.1021/ar000033j
  199
  Calculating Structures and Free Energies of Complex Molecules: Combining Molecular Mechanics and Continuum Models
  Kollman, Peter A.; Massova, Irina; Reyes, Carolina; Kuhn, Bernd; Huo, Shuanghong; Chong, Lillian; Lee, Matthew; Lee, Taisung; Duan, Yong; Wang, Wei; Donini, Oreola; Cieplak, Piotr; Srinivasan, Jaysharee; Case, David A.; Cheatham, Thomas E., III
  Accounts of Chemical Research (2000), 33 (12), 889-897CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  A review, with 63 refs. A historical perspective on the application of mol. dynamics (MD) to biol. macromols. is presented. Recent developments combining state-of-the-art force fields with continuum solvation calcns. have allowed us to reach the fourth era of MD applications in which one can often derive both accurate structure and accurate relative free energies from mol. dynamics trajectories. We illustrate such applications on nucleic acid duplexes, RNA hairpins, protein folding trajectories, and protein-ligand, protein-protein, and protein-nucleic acid interactions.
200. 200
  Bahar, I.; Lezon, T. R.; Bakan, A.; Shrivastava, I. H. Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins Chem. Rev. 2010, 110 (3) 1463– 1497 DOI: 10.1021/cr900095e
  200
  Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins
  Bahar, Ivet; Lezon, Timothy R.; Bakan, Ahmet; Shrivastava, Indira H.
  Chemical Reviews (Washington, DC, United States) (2010), 110 (3), 1463-1497CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Structural dynamics and function of membrane proteins are discussed in relation to principal component anal. of exptl. resolved conformations, normal mode anal. and elastic network models.
201. 201
  Andricioaei, I.; Karplus, M. On the Calculation of Entropy from Covariance Matrices of the Atomic Fluctuations J. Chem. Phys. 2001, 115 (14) 6289– 6292 DOI: 10.1063/1.1401821
  201
  On the calculation of entropy from covariance matrices of the atomic fluctuations
  Andricioaei, Ioan; Karplus, Martin
  Journal of Chemical Physics (2001), 115 (14), 6289-6292CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  An ad hoc method for calcg. the entropy of a biomol. system from the covariance matrix of the at. fluctuations is analyzed. It is shown that its essential assumption can be eliminated by a quasiharmonic anal. The computer time required for use of the latter is of the same order as that of the former.
202. 202
  Tsui, V.; Case, D. A. Theory and Applications of the Generalized Born Solvation Model in Macromolecular Simulations Biopolymers 2000, 56 (4) 275– 291 DOI: 10.1002/1097-0282(2000)56:4<275::AID-BIP10024>3.0.CO;2-E
  202
  Theory and applications of the generalized Born solvation model in macromolecular simulations
  Tsui V; Case D A
  Biopolymers (2000-2001), 56 (4), 275-91 ISSN:0006-3525.
  Generalized Born (GB) models provide an attractive way to include some thermodynamic aspects of aqueous solvation into simulations that do not explicitly model the solvent molecules. Here we discuss our recent experience with this model, presenting in detail the way it is implemented and parallelized in the AMBER molecular modeling code. We compare results using the GB model (or GB plus a surface-area based "hydrophobic" term) to explicit solvent simulations for a 10 base-pair DNA oligomer, and for the 108-residue protein thioredoxin. A slight modification of our earlier suggested parameters makes the GB results more like those found in explicit solvent, primarily by slightly increasing the strength of NH [bond] O and NH [bond] N internal hydrogen bonds. Timing and energy stability results are reported, with an eye toward using these model for simulations of larger macromolecular systems and longer time scales.
203. 203
  Rocchia, W.; Alexov, E.; Honig, B. Extending the Applicability of the Nonlinear Poisson–Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions J. Phys. Chem. B 2001, 105 (28) 6507– 6514 DOI: 10.1021/jp010454y
  203
  Extending the applicability of the nonlinear Poisson-Boltzmann equation: multiple dielectric constants and multivalent ions
  Rocchia, W.; Alexov, E.; Honig, B.
  Journal of Physical Chemistry B (2001), 105 (28), 6507-6514CODEN: JPCBFK; ISSN:1089-5647. (American Chemical Society)
  A new version of the DelPhi program, which provides numerical solns. to the nonlinear Poisson-Boltzmann (PB) equation, is reported. The program can divide space into multiple regions contg. different dielec. consts. and can treat systems contg. mixed salt solns. where the valence and concn. of each ion is different. The electrostatic free energy is calcd. by decompg. the various energy terms into Coulombic interactions so that that the calcd. free energies are independent of the lattice used to solve the PB equation. This, together with algorithms that optimally position polarization charges on the mol. surface, leads to a significant decrease in the dependence of the electrostatic free energy on the resoln. of the lattice used to solve the PB equation and, hence, to a remarkable improvement in the precision of the calcd. values. The Gauss-Seidel algorithm used in the current version of DelPhi is retained so that the new program retains many of the optimization features of the old one. The program uses dynamic memory allocation and can easily handle systems requiring large grid dimensions - for example, a 3003 system can be conveniently treated on a single SGI R12000 processor. An algorithm that ests. the best relaxation parameter to solve the nonlinear equation for a given system is described, and is implemented in the program at run time. A no. of applications of the program are presented.
204. 204
  Baker, C. M.; Lopes, P. E. M.; Zhu, X.; Roux, B.; MacKerell, A. D. Accurate Calculation of Hydration Free Energies Using Pair-Specific Lennard-Jones Parameters in the CHARMM Drude Polarizable Force Field J. Chem. Theory Comput. 2010, 6 (4) 1181– 1198 DOI: 10.1021/ct9005773
  204
  Accurate Calculation of Hydration Free Energies using Pair-Specific Lennard-Jones Parameters in the CHARMM Drude Polarizable Force Field
  Baker, Christopher M.; Lopes, Pedro E. M.; Zhu, Xiao; Roux, Benoit; MacKerell, Alexander D.
  Journal of Chemical Theory and Computation (2010), 6 (4), 1181-1198CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Lennard-Jones (LJ) parameters for a variety of model compds. have previously been optimized within the CHARMM Drude polarizable force field to reproduce accurately pure liq. phase thermodn. properties as well as addnl. target data. While the polarizable force field resulting from this optimization procedure has been shown to satisfactorily reproduce a wide range of exptl. ref. data across numerous series of small mols., a slight but systematic overestimate of the hydration free energies has also been noted. Here, the reprodn. of exptl. hydration free energies is greatly improved by the introduction of pair-specific LJ parameters between solute heavy atoms and water oxygen atoms that override the std. LJ parameters obtained from combining rules. The changes are small and a systematic protocol is developed for the optimization of pair-specific LJ parameters and applied to the development of pair-specific LJ parameters for alkanes, alcs., and ethers. The resulting parameters not only yield hydration free energies in good agreement with exptl. values, but also provide a framework upon which other pair-specific LJ parameters can be added as new compds. are parametrized within the CHARMM Drude polarizable force field. Detailed anal. of the contributions to the hydration free energies reveals that the dispersion interaction is the main source of the systematic errors in the hydration free energies. This information suggests that the systematic error may result from problems with the LJ combining rules and is combined with anal. of the pair-specific LJ parameters obtained in this work to identify a preliminary improved combining rule.
205. 205
  Allinger, N. L. Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms J. Am. Chem. Soc. 1977, 99 (25) 8127– 8134 DOI: 10.1021/ja00467a001
  205
  Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms
  Allinger, Norman L.
  Journal of the American Chemical Society (1977), 99 (25), 8127-34CODEN: JACSAT; ISSN:0002-7863.
  An improved force field for mol.-mechanics calcns. of the structures and energies of hydrocarbons is presented. The problem of simultaneously obtaining a sufficiently large gauche butane interaction energy while keeping the H atoms small enough for good structural predictions was solved with 1- and 2-fold rotational barriers. For 42 selected diverse types of hydrocarbons, the std. deviation between the calcd. and exptl. heats of formation is 0.42 kcal/mol, compared with an av. reported exptl. error for the same group of compds. of 0.40 kcal/mol.
206. 206
  Charlton, A. J.; Davis, A. L.; Jones, D. P.; Lewis, J. R.; Davies, A. P.; Haslam, E.; Williamson, M. P. The Self-Association of the Black Tea Polyphenol Theaflavin and Its Complexation with Caffeine J. Chem. Soc. Perkin Trans. 2 2000, 2) 317– 322 DOI: 10.1039/a906380c
  There is no corresponding record for this reference.
207. 207
  Kunsági-Máté, S.; Szabó, K.; Nikfardjam, M. P.; Kollár, L. Determination of the Thermodynamic Parameters of the Complex Formation between Malvidin-3-O-Glucoside and Polyphenols. Copigmentation Effect in Red Wines J. Biochem. Biophys. Methods 2006, 69 (1–2) 113– 119 DOI: 10.1016/j.jbbm.2006.03.014
  207
  Determination of the thermodynamic parameters of the complex formation between malvidin-3-O-glucoside and polyphenols. Copigmentation effect in red wines
  Kunsagi-Mate, Sandor; Szabo, Kornelia; Nikfardjam, Martin P.; Kollar, Laszlo
  Journal of Biochemical and Biophysical Methods (2006), 69 (1-2), 113-119CODEN: JBBMDG; ISSN:0165-022X. (Elsevier Ltd.)
  The thermodn. of the mol. assocn. process between the malvidin-3-O-glucoside and a series of polyphenol derivs. (called copigmentation' in food chem.) were studied in aq. media. The Gibbs free energy, enthalpy and entropy values were detd. by the fluorometric method. A combination of the Job's method with the van't Hoff theory was applied for data evaluation. The results show the exothermic character of the copigmentation process. The change of the enthalpy seems to be the same in every complexation step. However, the decreasing of the entropy term is higher at higher stoichiometries. As a result, the Gibbs free energy changes and, thus, the complex stability decreases quickly with increasing stoichiometry. Quantum-chem. investigation reveals the complexity of mol. interactions between malvidin and polyphenols, which is preferably based on π-π and OH-π interaction moderated by repulsive Coulomb-type interactions.
208. 208
  Kalisz, S.; Oszmiański, J.; Hładyszowski, J.; Mitek, M. Stabilization of Anthocyanin and Skullcap Flavone Complexes – Investigations with Computer Simulation and Experimental Methods Food Chem. 2013, 138 (1) 491– 500 DOI: 10.1016/j.foodchem.2012.10.146
  There is no corresponding record for this reference.
209. 209
  Kunsági-Máté, S.; Ortmann, E.; Kollár, L.; Nikfardjam, M. P. Effect of the Solvatation Shell Exchange on the Formation of Malvidin- 3- O -Glucoside–Ellagic Acid Complexes J. Phys. Chem. B 2007, 111 (40) 11750– 11755 DOI: 10.1021/jp0740144
  There is no corresponding record for this reference.
210. 210
  Sousa, A.; Araújo, P.; Cruz, L.; Brás, N. F.; Mateus, N.; De Freitas, V. Evidence for Copigmentation Interactions between Deoxyanthocyanidin Derivatives (Oaklins) and Common Copigments in Wine Model Solutions J. Agric. Food Chem. 2014, 62 (29) 6995– 7001 DOI: 10.1021/jf404640m
  There is no corresponding record for this reference.
211. 211
  Košinová, P.; Berka, K.; Wykes, M.; Otyepka, M.; Trouillas, P. Positioning of Antioxidant Quercetin and Its Metabolites in Lipid Bilayer Membranes: Implication for Their Lipid-Peroxidation Inhibition J. Phys. Chem. B 2012, 116 (4) 1309– 1318 DOI: 10.1021/jp208731g
  211
  Positioning of Antioxidant Quercetin and Its Metabolites in Lipid Bilayer Membranes: Implication for Their Lipid-Peroxidation Inhibition
  Kosinova, Pavlina; Berka, Karel; Wykes, Michael; Otyepka, Michal; Trouillas, Patrick
  Journal of Physical Chemistry B (2012), 116 (4), 1309-1318CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
  Among numerous biol. activities, natural polyphenols are antioxidants widely distributed in plants capable of inhibiting lipid peroxidn., which belongs to the most serious degenerative cell processes. Positioning of antioxidants in lipid bilayers can provide an insight to the lipid-peroxidn. inhibition at the mol. level. This work aims at detg. the location and orientation of quercetin and its most representative (glucuronidated, methylated, and sulfated) metabolites in lipid bilayer via mol. dynamic simulations. We show that quercetin derivs. penetrate the lipid bilayer and that the depths of penetration depend on mol. charge and substitutional variations. In the presence of charged substituents (sulfates and glucuronidates), the mol. is pulled toward the lipid bilayer surface. The orientation also depends on substitution as H-bonds are formed between the polar head groups of the bilayer and the (i) OH groups, (ii) sugar, and (iii) sulfate moieties of the antioxidants. As flavonoids and their derivs. are preferentially localized in the lipid bilayer membrane or on the bilayer/water interface, they readily conc. in a relatively narrow membrane region. Despite the low concns. of flavonoids in food, their spatial confinement in the membrane greatly enhances their local concn. in this vital region, thus increasing their importance for in vivo biol. activities including oxidative stress defense.
212. 212
  Sirk, T. W.; Brown, E. F.; Sum, A. K.; Friedman, M. Molecular Dynamics Study on the Biophysical Interactions of Seven Green Tea Catechins with Lipid Bilayers of Cell Membranes J. Agric. Food Chem. 2008, 56 (17) 7750– 7758 DOI: 10.1021/jf8013298
  212
  Molecular Dynamics Study on the Biophysical Interactions of Seven Green Tea Catechins with Lipid Bilayers of Cell Membranes
  Sirk, Timothy W.; Brown, Eugene F.; Sum, Amadeu K.; Friedman, Mendel
  Journal of Agricultural and Food Chemistry (2008), 56 (17), 7750-7758CODEN: JAFCAU; ISSN:0021-8561. (American Chemical Society)
  Mol. dynamics simulations were performed to study the interactions of bioactive catechins (flavonoids) commonly found in green tea with lipid bilayers, as a model for cell membranes. Previously, multiple exptl. studies rationalized catechin's anticarcinogenic, antibacterial, and other beneficial effects in terms of physicochem. mol. interactions with the cell membranes. To contribute toward understanding the mol. role of catechins on the structure of cell membranes, we present simulation results for seven green tea catechins in lipid bilayer systems representative of HepG2 cancer cells. Our simulations show that the seven tea catechins evaluated have a strong affinity for the lipid bilayer via hydrogen bonding to the bilayer surface, with some of the smaller catechins able to penetrate underneath the surface. Epigallocatechin-gallate (EGCG) showed the strongest interaction with the lipid bilayer based on the no. of hydrogen bonds formed with lipid headgroups. The simulations also provide insight into the functional characteristics of the catechins that distinguish them as effective compds. to potentially alter the lipid bilayer properties. The results on the hydrogen-bonding effects, described here for the first time, may contribute to a better understanding of proposed multiple mol. mechanisms of the action of catechins in microorganisms, cancer cells, and tissues.
213. 213
  Paloncýová, M.; Fabre, G.; DeVane, R. H.; Trouillas, P.; Berka, K.; Otyepka, M. Benchmarking of Force Fields for Molecule–Membrane Interactions J. Chem. Theory Comput. 2014, 10 (9) 4143– 4151 DOI: 10.1021/ct500419b
  213
  Benchmarking of Force Fields for Molecule-Membrane Interactions
  Paloncyova, Marketa; Fabre, Gabin; DeVane, Russell H.; Trouillas, Patrick; Berka, Karel; Otyepka, Michal
  Journal of Chemical Theory and Computation (2014), 10 (9), 4143-4151CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Free energy profiles of eleven compds. with a model dimyristoylphosphatidylcholine (DMPC) membrane bilayer have been calcd. using five force fields, namely Berger, Slipids, CHARMM36, GAFFlipids, and GROMOS 43A1-S3 via mol. dynamics simulations. For the sake of comparison, the semicontinuous tool COSMOmic was also used. High correlation was obsd. between theor. and exptl. partition coeffs. (log K). Partition coeffs. calcd. by all-at. force fields (Slipids, CHARMM36, and GAFFlipids) and COSMOmic differed by less than 0.75 log units from the expt. and Slipids emerged as the best performing force field. This work provides the following recommendations (i) for a global, systematic and high throughput thermodn. evaluations (e.g., log K) of drugs COSMOmic is a tool of choice due to low computational costs; (ii) for studies of the hydrophilic mols. CHARMM36 should be considered; and (iii) for studies of more complex systems, taking into account all pros and cons, Slipids is the force field of choice.
214. 214
  Podloucká, P.; Berka, K.; Fabre, G.; Paloncýová, M.; Duroux, J.-L.; Otyepka, M.; Trouillas, P. Lipid Bilayer Membrane Affinity Rationalizes Inhibition of Lipid Peroxidation by a Natural Lignan Antioxidant J. Phys. Chem. B 2013, 117 (17) 5043– 5049 DOI: 10.1021/jp3127829
  There is no corresponding record for this reference.
215. 215
  Zhou, H.-X.; Gilson, M. K. Theory of Free Energy and Entropy in Noncovalent Binding Chem. Rev. 2009, 109 (9) 4092– 4107 DOI: 10.1021/cr800551w
  215
  Theory of Free Energy and Entropy in Noncovalent Binding
  Zhou, Huan-Xiang; Gilson, Michael K.
  Chemical Reviews (Washington, DC, United States) (2009), 109 (9), 4092-4107CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Theory of free energy and entropy in noncovalent binding aims to support the development of well-founded models of binding and meaningful interpretation of exptl. data. Discussion includes the statistical thermodn. of binding., changes in translational and other entropy components on binding.
216. 216
  Černỳ, J.; Hobza, P. Non-Covalent Interactions in Biomacromolecules Phys. Chem. Chem. Phys. 2007, 9 (39) 5291– 5303 DOI: 10.1039/b704781a
  There is no corresponding record for this reference.
217. 217
  Grimme, S.; Antony, J.; Schwabe, T.; Mück-Lichtenfeld, C. Density Functional Theory with Dispersion Corrections for Supramolecular Structures, Aggregates, and Complexes of (bio) Organic Molecules Org. Biomol. Chem. 2007, 5 (5) 741– 758 DOI: 10.1039/b615319b
  There is no corresponding record for this reference.
218. 218
  Sherrill, C. D. Computations of Noncovalent N Interactions Rev. Comput. Chem. 2008, 26, 1 DOI: 10.1002/9780470399545.ch1
  There is no corresponding record for this reference.
219. 219
  Tschumper, G. S. Computations for Weak Noncovalent Rev. Comput. Chem. 2008, 26, 39 DOI: 10.1002/9780470399545.ch2
  There is no corresponding record for this reference.
220. 220
  Foster, M. E.; Sohlberg, K. Empirically Corrected DFT and Semi-Empirical Methods for Non-Bonding Interactions Phys. Chem. Chem. Phys. 2010, 12 (2) 307– 322 DOI: 10.1039/B912859J
  There is no corresponding record for this reference.
221. 221
  Riley, K. E.; Pitoňák, M.; Jurečka, P.; Hobza, P. Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories Chem. Rev. 2010, 110 (9) 5023– 5063 DOI: 10.1021/cr1000173
  221
  Stabilization and Structure Calculations for Noncovalent Interactions in Extended Molecular Systems Based on Wave Function and Density Functional Theories
  Riley, Kevin E.; Pitonak, Michal; Jurecka, Petr; Hobza, Pavel
  Chemical Reviews (Washington, DC, United States) (2010), 110 (9), 5023-5063CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. Topics covered include: wave function theory; MP2; methods from MP3 to CCSD; d. functional theories; empirical dispersion corrections; plane wave codes and nonlocal pseudopotentials; symmetry-adapted perturbation theory; and semiempirical quantum chem. theories.
222. 222
  Hobza, P. The Calculation of Intermolecular Interaction Energies Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2011, 107, 148– 168 DOI: 10.1039/c1pc90005f
  222
  The calculation of intermolecular interaction energies
  Hobza, Pavel
  Annual Reports on the Progress of Chemistry, Section C: Physical Chemistry (2011), 107 (), 148-168CODEN: ACPCDW; ISSN:0260-1826. (Royal Society of Chemistry)
  All life on our earth can be viewed as an application of supramol. chem., with noncovalent interactions playing a central role. The knowledge of total interaction energies as well as their components is topical for understanding the nature of these interactions and, in a broader sense, also for understanding the nature of stabilization of noncovalent systems like biomacromols. Accurate data on interaction energies can only be obtained from coupled-cluster with single and double and perturbative triple excitations (CCSD(T)) calcns. performed with extended basis sets. The CCSDD(T) calcns. thus provide benchmark data which can be used for testing and/or parameterizing other, computationally economical techniques. In the present review the applicability and performance of various recently introduced wavefunction and d. functional methods are examd. in detail.
223. 223
  Grimme, S. Density Functional Theory with London Dispersion Corrections Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1 (2) 211– 228 DOI: 10.1002/wcms.30
  223
  Density functional theory with london dispersion corrections
  Grimme, Stefan
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2011), 1 (2), 211-228CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. Dispersion corrections to std. Kohn-Sham d. functional theory (DFT) are reviewed. The focus is on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on sepd. fragments. The recommended approaches (van der Waals d. functional and DFT-D) are asymptotically correct and can be used in combination with std. or slightly modified (short-range) exchange-correlation functionals. The importance of the dispersion energy in intramol. cases (conformational problems and thermochem.) is highlighted.
224. 224
  Klimeš, J.; Michaelides, A. Perspective: Advances and Challenges in Treating van Der Waals Dispersion Forces in Density Functional Theory J. Chem. Phys. 2012, 137 (12) 120901 DOI: 10.1063/1.4754130
  224
  Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
  Klimes, Jiri; Michaelides, Angelos
  Journal of Chemical Physics (2012), 137 (12), 120901/1-120901/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A review. Electron dispersion forces play a crucial role in detg. the structure and properties of biomols., mol. crystals, and many other systems. However, an accurate description of dispersion is highly challenging, with the most widely used electronic structure technique, d. functional theory (DFT), failing to describe them with std. approxns. Therefore, applications of DFT to systems where dispersion is important have traditionally been of questionable accuracy. However, the last decade has seen a surge of enthusiasm in the DFT community to tackle this problem and in so-doing to extend the applicability of DFT-based methods. Here we discuss, classify, and evaluate some of the promising schemes to emerge in recent years. A brief perspective on the outstanding issues that remain to be resolved and some directions for future research are also provided. (c) 2012 American Institute of Physics.
225. 225
  Ehrlich, S.; Moellmann, J.; Grimme, S. Dispersion-Corrected Density Functional Theory for Aromatic Interactions in Complex Systems Acc. Chem. Res. 2013, 46 (4) 916– 926 DOI: 10.1021/ar3000844
  225
  Dispersion-Corrected Density Functional Theory for Aromatic Interactions in Complex Systems
  Ehrlich, Stephan; Moellmann, Jonas; Grimme, Stefan
  Accounts of Chemical Research (2013), 46 (4), 916-926CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  Arom. interactions play a key role in many chem. and biol. systems. However, even if very simple models are chosen, the systems of interest are often too large to be handled with std. wave function theory (WFT). Although d. functional theory (DFT) can easily treat systems of more than 200 atoms, std. semilocal (hybrid) d. functional approxns. fail to describe the London dispersion energy, a factor that is essential for accurate predictions of inter- and intramol. noncovalent interactions. Therefore dispersion-cor. DFT provides a unique tool for the investigation and anal. of a wide range of complex arom. systems. In this Account, we start with an anal. of the noncovalent interactions in simple model dimers of hexafluorobenzene (HFB) and benzene, with a focus on electrostatic and dispersion interactions. The min. for the parallel-displaced dimers of HFB/HFB and HFB/benzene can only be explained when taking into account all contributions to the interaction energy and not by electrostatics alone. By comparison of satd. and arom. model complexes, we show that increased dispersion coeffs. for sp2-hybridized carbon atoms play a major role in arom. stacking. Modern dispersion-cor. DFT yields accurate results (about 5-10% error for the dimerization energy) for the relatively large porphyrin and coronene dimers, systems for which WFT can provide accurate ref. data only with huge computational effort. In this example, it is also demonstrated that new nonlocal, d.-dependent dispersion corrections and atom pairwise schemes mutually agree with each other. The dispersion energy is also important for the complex inter- and intramol. interactions that arise in the mol. crystals of arom. mols. In studies of hexahelicene, dispersion-cor. DFT yields "the right answer for the right reason". By comparison, std. DFT calcns. reproduce intramol. distances quite accurately in single-mol. calcns. while inter- and intramol. distances become too large when dispersion-uncorrected solid-state calcns. are carried out. Dispersion-cor. DFT can fix this problem, and these results are in excellent agreement with exptl. structure and energetic (sublimation) data. Uncorrected treatments do not even yield a bound crystal state. Finally, we present calcns. for the formation of a cationic, quadruply charged dimer of a porphyrin deriv., a case where dispersion is required in order to overcome strong electrostatic repulsion. A combination of dispersion-cor. DFT with an adequate continuum solvation model can accurately reproduce exptl. free assocn. enthalpies in soln. As in the previous examples, consideration of the electrostatic interactions alone does not provide a qual. or quant. correct picture of the interactions of this complex.
226. 226
  DiStasio, R. A., Jr.; Gobre, V. V.; Tkatchenko, A. Many-Body van Der Waals Interactions in Molecules and Condensed Matter J. Phys.: Condens. Matter 2014, 26 (21) 213202 DOI: 10.1088/0953-8984/26/21/213202
  226
  Many-body van der Waals interactions in molecules and condensed matter
  DiStasio, Robert A.; Gobre, Vivekanand V.; Tkatchenko, Alexandre
  Journal of Physics: Condensed Matter (2014), 26 (21), 213202/1-213202/16, 16 pp.CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
  A review. This work reviews the increasing evidence that many-body van der Waals (vdW) or dispersion interactions play a crucial role in the structure, stability and function of a wide variety of systems in biol., chem. and physics. Starting with the exact expression for the electron correlation energy provided by the adiabatic connection fluctuation-dissipation theorem, we derive both pairwise and many-body interat. methods for computing the long-range dispersion energy by considering a model system of coupled quantum harmonic oscillators within the RPA. By coupling this approach to d. functional theory, the resulting many-body dispersion (MBD) method provides an accurate and efficient scheme for computing the frequency-dependent polarizability and many-body vdW energy in mols. and materials with a finite electronic gap. A select collection of applications are presented that ascertain the fundamental importance of these non-bonded interactions across the spectrum of intermol. (the S22 and S66 benchmark databases), intramol. (conformational energies of alanine tetrapeptide) and supramol. (binding energy of the 'buckyball catcher') complexes, as well as mol. crystals (cohesive energies in oligoacenes). These applications demonstrate that electrodynamic response screening and beyond-pairwise many-body vdW interactions - both captured at the MBD level of theory - play a quant., and sometimes even qual., role in describing the properties considered herein. This work is then concluded with an in-depth discussion of the challenges that remain in the future development of reliable (accurate and efficient) methods for treating many-body vdW interactions in complex materials and provides a road-map for navigating many of the research avenues that are yet to be explored.
227. 227
  Casimir, H.; Polder, D. The Influence of Retardation on the London-van Der Waals Forces Phys. Rev. 1948, 73 (4) 360 DOI: 10.1103/PhysRev.73.360
  227
  The influence of retardation on the London-van der Waals forces
  Casimir, H. B. G.; Polder, D.
  Physical Review (1948), 73 (), 360-72CODEN: PHRVAO; ISSN:0031-899X.
  cf. C.A. 41, 1899i. Math.theoretical. The influence of retardation on the energy of interaction between two neutral atoms is investigated by means of quantum electrodynamics. In the interactions between a neutral atom and a perfectly conducting plane, and between two atoms, it is found that the influence of radiation is described by a monotonically decreasing correction factor which is equal to unity for small distances, R, compared with the wave lengths corresponding to the at. frequencies, and proportional to 1/R when R is large compared with these wave lengths.
228. 228
  Starkschall, G.; Gordon, R. G. Calculation of Coefficients in the Power Series Expansion of the Long-Range Dispersion Force between Atoms J. Chem. Phys. 1972, 56 (6) 2801– 2806 DOI: 10.1063/1.1677610
  There is no corresponding record for this reference.
229. 229
  Tang, K.; Toennies, J. P. An Improved Simple Model for the van Der Waals Potential Based on Universal Damping Functions for the Dispersion Coefficients J. Chem. Phys. 1984, 80 (8) 3726– 3741 DOI: 10.1063/1.447150
  229
  An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients
  Tang, K. T.; Toennies, J. Peter
  Journal of Chemical Physics (1984), 80 (8), 3726-41CODEN: JCPSA6; ISSN:0021-9606.
  By using the earlier model (K.T.T. and J.P.T., 1977), a simple expression was derived for the radial-dependent damping functions for the individual dispersion coeffs. C2n for arbitrary even orders 2n. The damping functions are only a function of the Born-Mayer range parameter b, and thus can be applied to all systems for which this is known or can be estd. For H(1S)-H(1S), the results agree with the ab-initio damping functions of A. Koide, et al., (1981). Comparisons with less accurate previous calcns. for other systems also show agreement. By adding a Born-Mayer repulsive term [A exp(-bR)] to the damped dispersion potential, a simple universal expression was obtained for the well region of the atom-atom van der Waals potential with only 5 essential parameters A, b, C6, C8, and C10. The model was tested for the systems: H23Σ, He2, Ar2, NaK3Σ, and LiHg, for which either very precise theor. or exptl. data are available. For each system, the ab-initio dispersion coeffs. together with the parameters ε and Rm were used to det. A and b from the model potential. With these values, the reduced potentials were calcd., and found to agree with the exptl. potentials to better than 1%, and always less than the exptl. uncertainties.
230. 230
  Thakkar, A. J.; Hettema, H.; Wormer, P. E. Abinitio Dispersion Coefficients for Interactions Involving Rare-Gas Atoms J. Chem. Phys. 1992, 97 (5) 3252– 3257 DOI: 10.1063/1.463012
  There is no corresponding record for this reference.
231. 231
  Lein, M.; Dobson, J. F.; Gross, E. K. Toward the Description of van Der Waals Interactions within Density Functional Theory J. Comput. Chem. 1999, 20 (1) 12– 22 DOI: 10.1002/(SICI)1096-987X(19990115)20:1<12::AID-JCC4>3.0.CO;2-U
  There is no corresponding record for this reference.
232. 232
  Kamal, C.; Ghanty, T.; Banerjee, A.; Chakrabarti, A. The van Der Waals Coefficients between Carbon Nanostructures and Small Molecules: A Time-Dependent Density Functional Theory Study J. Chem. Phys. 2009, 131 (16) 164708 DOI: 10.1063/1.3256238
  There is no corresponding record for this reference.
233. 233
  Johnson, E. R.; Becke, A. D. A Post-Hartree–Fock Model of Intermolecular Interactions J. Chem. Phys. 2005, 123 (2) 024101 DOI: 10.1063/1.1949201
  233
  A post-Hartree-Fock model of intermolecular interactions
  Johnson, Erin R.; Becke, Axel D.
  Journal of Chemical Physics (2005), 123 (2), 024101/1-024101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Intermol. interactions are of great importance in chem. but are difficult to model accurately with computational methods. In particular, Hartree-Fock and std. d.-functional approxns. do not include the physics necessary to properly describe dispersion. These methods are sometimes cor. to account for dispersion by adding a pairwise C6/R6 term, with C6 dispersion coeffs. dependent on the atoms involved. We present a post-Hartree-Fock model in which C6 coeffs. are generated by the instantaneous dipole moment of the exchange hole. This model relies on occupied orbitals only, and involves only one, universal, empirical parameter to limit the dispersion energy at small interat. sepns. The model is extensively tested on isotropic C6 coeffs. of 178 intermol. pairs. It is also applied to the calcn. of the geometries and binding energies of 20 intermol. complexes involving dispersion, dipole-induced dipole, dipole-dipole, and hydrogen-bonding interactions, with remarkably good results.
234. 234
  Becke, A. D.; Johnson, E. R. Exchange-Hole Dipole Moment and the Dispersion Interaction J. Chem. Phys. 2005, 122 (15) 154104 DOI: 10.1063/1.1884601
  234
  Exchange-hole dipole moment and the dispersion interaction
  Becke, Axel D.; Johnson, Erin R.
  Journal of Chemical Physics (2005), 122 (15), 154104/1-154104/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A simple model is presented in which the instantaneous dipole moment of the exchange hole is used to generate a dispersion interaction between nonoverlapping systems. The model is easy to implement, requiring no electron correlation (in the usual sense) or time dependence, and has been tested on various at. and mol. pairs. The resulting C6 dispersion coeffs. are remarkably accurate.
235. 235
  Johnson, E. R. Dependence of Dispersion Coefficients on Atomic Environment J. Chem. Phys. 2011, 135 (23) 234109 DOI: 10.1063/1.3670015
  There is no corresponding record for this reference.
236. 236
  Misquitta, A. J. Intermolecular Interactions. In Handbook of Computational Chemistry; Springer, 2012; pp 157– 193.
  There is no corresponding record for this reference.
237. 237
  Wen, S.; Nanda, K.; Huang, Y.; Beran, G. J. Practical Quantum Mechanics-Based Fragment Methods for Predicting Molecular Crystal Properties Phys. Chem. Chem. Phys. 2012, 14 (21) 7578– 7590 DOI: 10.1039/c2cp23949c
  237
  Practical quantum mechanics-based fragment methods for predicting molecular crystal properties
  Wen, Shuhao; Nanda, Kaushik; Huang, Yuanhang; Beran, Gregory J. O.
  Physical Chemistry Chemical Physics (2012), 14 (21), 7578-7590CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  A review. Significant advances in fragment-based electronic structure methods have created a real alternative to force-field and d. functional techniques in condensed-phase problems such as mol. crystals. This perspective article highlights some of the important challenges in modeling mol. crystals and discusses techniques for addressing them. First, we survey recent developments in fragment-based methods for mol. crystals. Second, we use examples from our own recent research on a fragment-based QM/MM method, the hybrid many-body interaction (HMBI) model, to analyze the phys. requirements for a practical and effective mol. crystal model chem. We demonstrate that it is possible to predict mol. crystal lattice energies to within a couple kJ mol-1 and lattice parameters to within a few percent in small-mol. crystals. Fragment methods provide a systematically improvable approach to making predictions in the condensed phase, which is crit. to making robust predictions regarding the subtle energy differences found in mol. crystals.
238. 238
  Wu, Q.; Yang, W. Empirical Correction to Density Functional Theory for van Der Waals Interactions J. Chem. Phys. 2002, 116 (2) 515– 524 DOI: 10.1063/1.1424928
  238
  Empirical correction to density functional theory for van der Waals interactions
  Wu, Qin; Yang, Weitao
  Journal of Chemical Physics (2002), 116 (2), 515-524CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  An empirical method has been designed to account for the van der Waals interactions in practical mol. calcns. with d. functional theory. For each atom pair sepd. at a distance R, the method adds to the d. functional electronic structure calcns. an addnl. attraction energy EvdW = -fd(R)C6R-6, where fd(R) is the damping function which equals to one at large value of R and zero at small value of R. The coeffs. C6 for pair interactions between hydrogen, carbon, nitrogen, and oxygen atoms have been developed in this work by a least-square fitting to the mol. C6 coeffs. obtained from the dipole oscillator strength distribution method by Meath and co-workers. Two forms of the damping functions have been studied, with one dropping to zero at short distances much faster than the other. Four d. functionals have been examd.: Becke's three parameter hybrid functional with the Lee-Yang-Parr correlation functional, Becke's 1988 exchange functional with the LYP correlation functional, Becke's 1988 exchange functional with Perdew and Wang's 1991 (PW91) correlation functional, and PW91 exchange and correlation functional. The method has been applied to three systems where the van der Waals attractions are known to be important: rare-gas diat. mols., stacking of base pairs, and polyalanines' conformation stabilities. The results show that this empirical method, with the damping function dropping to zero smoothly, provides a significant correction to both of the Becke's hybrid functional and the PW91 exchange and correlation functional. Results are comparable with the corresponding second-order Moller-Plesset calcns. in many cases.
239. 239
  Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections Phys. Chem. Chem. Phys. 2008, 10 (44) 6615– 6620 DOI: 10.1039/b810189b
  239
  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
  Chai, Jeng-Da; Head-Gordon, Martin
  Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
240. 240
  Liu, Y.; Goddard, W. A. I. A Universal Damping Function for Empirical Dispersion Correction on Density Functional Theory Mater. Trans. 2009, 50 (7) 1664– 1670 DOI: 10.2320/matertrans.MF200911
  240
  A universal damping function for empirical dispersion correction on density functional theory
  Liu, Yi; Goddard, William A., III
  Materials Transactions (2009), 50 (7), 1664-1670CODEN: MTARCE; ISSN:1345-9678. (Japan Institute of Metals)
  A damped London dispersion interaction is generally adopted in empirical dispersion corrections on d. functional theory (DFT), where dispersion parameters are detd. empirically to reproduce correct dispersive interactions after assuming a damping function. The key to a successful dispersion correction is choosing an appropriate damping function. In this work we propose a single universal damping function that can represent several damping functions used in literatures with a few adjustable parameters. This universal damping function provides a unified formula that allows convenient comparison and flexible optimization in dispersion cor. DFT methods. Using the optimized universal damping functions and dispersion parameters, we develop dispersion correction methods for HF, B3LYP and PBE theories. We calc. the dispersive energies accurately for rare gas diat. mols. and benzene dimers with an averaged error <4.1%.
241. 241
  Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu J. Chem. Phys. 2010, 132 (15) 154104 DOI: 10.1063/1.3382344
  241
  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
  Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
  Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
242. 242
  Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory J. Comput. Chem. 2011, 32 (7) 1456– 1465 DOI: 10.1002/jcc.21759
  242
  Effect of the damping function in dispersion corrected density functional theory
  Grimme, Stefan; Ehrlich, Stephan; Goerigk, Lars
  Journal of Computational Chemistry (2011), 32 (7), 1456-1465CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  It is shown by an extensive benchmark on mol. energy data that the math. form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a std. "zero-damping" formula and rational damping to finite values for small interat. distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coeffs. is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interat. forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramol. dispersion in four representative mol. structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermol. distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of cor. GGAs for non-covalent interactions. According to the thermodn. benchmarks BJ-damping is more accurate esp. for medium-range electron correlation problems and only small and practically insignificant double-counting effects are obsd. It seems to provide a phys. correct short-range behavior of correlation/dispersion even with unmodified std. functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying d. functional. © 2011 Wiley Periodicals, Inc.; J. Comput. Chem., 2011.
243. 243
  Johnson, E. R.; Becke, A. D. A Post-Hartree-Fock Model of Intermolecular Interactions: Inclusion of Higher-Order Corrections J. Chem. Phys. 2006, 124 (17) 174104 DOI: 10.1063/1.2190220
  243
  A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections
  Johnson, Erin R.; Becke, Axel D.
  Journal of Chemical Physics (2006), 124 (17), 174104/1-174104/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermol. C6 dispersion coeffs. [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermol. interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coeffs. C8 and C10. The extended model performs very well for prediction of intermonomer sepns. and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.
244. 244
  Grimme, S. Accurate Description of van Der Waals Complexes by Density Functional Theory Including Empirical Corrections J. Comput. Chem. 2004, 25 (12) 1463– 1473 DOI: 10.1002/jcc.20078
  244
  Accurate description of van der Waals complexes by density functional theory including empirical corrections
  Grimme, Stefan
  Journal of Computational Chemistry (2004), 25 (12), 1463-1473CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  An empirical method to account for van der Waals interactions in practical calcns. in the framework of the d. functional theory (termed DFT-D) was tested for a wide variety of mol. complexes. As in previous schemes, the dispersive energy was described by damped interat. potentials of the form C6R-6. The use of pure, gradient-cor. d. functionals (BLYP and PBE), together with the resoln.-of-the-identity (RI) approxn. for the Coulomb operator, allows very efficient computations for large systems. In contrast to the previous work, extended AO basis sets of polarized TZV or QZV quality were employed, which reduced the basis set superposition error to a negligible extend. By using a global scaling factor for the at. C6 coeffs., the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes was found to be insignificant if steep damping functions were employed. The method was applied to a total of 29 complexes of atoms and small mols. (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene·H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theor. or exptl. results for binding energies and intermol. distances is obtained. For stacked arom. systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to std. MP2 treatments that systematically over-bind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chem. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calcns. of the interaction energies.
245. 245
  Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction J. Comput. Chem. 2006, 27 (15) 1787– 1799 DOI: 10.1002/jcc.20495
  245
  Semiempirical GGA-type density functional constructed with a long-range dispersion correction
  Grimme, Stefan
  Journal of Computational Chemistry (2006), 27 (15), 1787-1799CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A new d. functional (DF) of the generalized gradient approxn. (GGA) type for general chem. applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C6·R-6. A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common d. functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on std. thermochem. benchmark sets, for 40 noncovalently bound complexes, including large stacked arom. mols. and group II element clusters, and for the computation of mol. geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for std. functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean abs. deviation of only 3.8 kcal mol-1. The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the av. CCSD(T) accuracy. The basic strategy in the development to restrict the d. functional description to shorter electron correlation lengths scales and to describe situations with medium to large interat. distances by damped C6·R-6 terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chem. method for large systems where dispersion forces are of general importance.
246. 246
  Jurečka, P.; Černỳ, J.; Hobza, P.; Salahub, D. R. Density Functional Theory Augmented with an Empirical Dispersion Term. Interaction Energies and Geometries of 80 Noncovalent Complexes Compared with Ab Initio Quantum Mechanics Calculations J. Comput. Chem. 2007, 28 (2) 555– 569 DOI: 10.1002/jcc.20570
  There is no corresponding record for this reference.
247. 247
  Tkatchenko, A.; Scheffler, M. Accurate Molecular van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data Phys. Rev. Lett. 2009, 102 (7) 073005 DOI: 10.1103/PhysRevLett.102.073005
  247
  Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data
  Tkatchenko, Alexandre; Scheffler, Matthias
  Physical Review Letters (2009), 102 (7), 073005/1-073005/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  We present a parameter-free method for an accurate detn. of long-range van der Waals interactions from mean-field electronic structure calcns. Our method relies on the summation of interat. C6 coeffs., derived from the electron d. of a mol. or solid and accurate ref. data for the free atoms. The mean abs. error in the C6 coeffs. is 5.5% when compared to accurate exptl. values for 1225 intermol. pairs, irresp. of the employed exchange-correlation functional. We show that the effective at. C6 coeffs. depend strongly on the bonding environment of an atom in a mol. Finally, we analyze the van der Waals radii and the damping function in the C6R-6 correction method for d.-functional theory calcns.
248. 248
  Steinmann, S. N.; Corminboeuf, C. A System-Dependent Density-Based Dispersion Correction J. Chem. Theory Comput. 2010, 6 (7) 1990– 2001 DOI: 10.1021/ct1001494
  248
  A System-Dependent Density-Based Dispersion Correction
  Steinmann, Stephan N.; Corminboeuf, Clemence
  Journal of Chemical Theory and Computation (2010), 6 (7), 1990-2001CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  D. functional approxns. fail to provide a consistent description of weak mol. interactions arising from small electron d. overlaps. A simple remedy to correct for the missing interactions is to add a posteriori an attractive energy term summed over all atom pairs in the system. The d.-dependent energy correction, presented herein, is applicable to all elements of the periodic table and is easily combined with any electronic structure method, which lacks the accurate treatment of weak interactions. Dispersion coeffs. are computed according to Becke and Johnson's exchange-hole dipole moment (XDM) formalism, thereby depending on the chem. environment of an atom (d., oxidn. state). The long-range ∼R-6 potential is supplemented with higher-order correction terms (∼R-8 and ∼R-10) through the universal damping function of Tang and Toennies. A genuine damping factor depending on (iterative) Hirshfeld (overlap) populations, at. ionization energies, and two adjustable parameters specifically fitted to a given DFT functional is also introduced. The proposed correction, dDXDM, dramatically improves the performance of popular d. functionals. The anal. of 30 (dispersion cor.) d. functionals on 145 systems reveals that dDXDM largely reduces the errors of the parent functionals for both inter- and intramol. interactions. With mean abs. deviations (MADs) of 0.74-0.84 kcal mol-1, PBE-dDXDM, PBE0-dDXDM, and B3LYP-dDXDM outperform the computationally more demanding and most recent functionals such as M06-2X and B2PLYP-D (MAD of 1.93 and 1.06 kcal mol-1, resp.).
249. 249
  Steinmann, S. N.; Corminboeuf, C. Comprehensive Benchmarking of a Density-Dependent Dispersion Correction J. Chem. Theory Comput. 2011, 7 (11) 3567– 3577 DOI: 10.1021/ct200602x
  249
  Comprehensive Benchmarking of a Density-Dependent Dispersion Correction
  Steinmann, Stephan N.; Corminboeuf, Clemence
  Journal of Chemical Theory and Computation (2011), 7 (11), 3567-3577CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Std. d. functional approxns. cannot accurately describe interactions between nonoverlapping densities. A simple remedy consists in correcting for the missing interactions a posteriori, adding an attractive energy term summed over all atom pairs. The d.-dependent energy correction, dDsC, presented herein, is constructed from dispersion coeffs. computed on the basis of a generalized gradient approxn. to Becke and Johnson's exchange-hole dipole moment formalism. DDsC also relies on an extended Tang and Toennies damping function accounting for charge-overlap effects. The comprehensive benchmarking on 341 diverse reaction energies divided into 18 illustrative test sets validates the robust performance and general accuracy of dDsC for describing various intra- and intermol. interactions. With a total MAD of 1.3 kcal mol-1, B97-dDsC slightly improves the results of M06-2X and B2PLYP-D3 (MAD = 1.4 kcal mol-1 for both) at a lower computational cost. The d. dependence of both the dispersion coeffs. and the damping function makes the approach esp. valuable for modeling redox reactions and charged species in general.
250. 250
  Steinmann, S. N.; Corminboeuf, C. A Generalized-Gradient Approximation Exchange Hole Model for Dispersion Coefficients J. Chem. Phys. 2011, 134 (4) 044117 DOI: 10.1063/1.3545985
  250
  A generalized-gradient approximation exchange hole model for dispersion coefficients
  Steinmann, Stephan N.; Corminboeuf, Clemence
  Journal of Chemical Physics (2011), 134 (4), 044117/1-044117/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A simple method for computing accurate d.-dependent dispersion coeffs. is presented. The dispersion coeffs. are modeled by a generalized gradient-type approxn. to Becke and Johnson's exchange hole dipole moment formalism. Our most cost-effective variant, based on a disjoint description of atoms in a mol., gives mean abs. errors in the C6 coeffs. for 90 complexes below 10%. The inclusion of the missing long-range van der Waals interactions in d. functionals using the derived coeffs. in a pair wise correction leads to highly accurate typical noncovalent interaction energies. (c) 2011 American Institute of Physics.
251. 251
  Liu, Y.; Goddard, W. A., III First-Principles-Based Dispersion Augmented Density Functional Theory: From Molecules to Crystals J. Phys. Chem. Lett. 2010, 1 (17) 2550– 2555 DOI: 10.1021/jz100615g
  251
  First-Principles-Based Dispersion Augmented Density Functional Theory: From Molecules to Crystals
  Liu, Yi; Goddard, William A., III
  Journal of Physical Chemistry Letters (2010), 1 (17), 2550-2555CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Std. implementations of d. functional theory (DFT) describe well strongly bound mols. and solids but fail to describe long-range van der Waals attractions. We propose here first-principles-based augmentation to DFT that leads to the proper long-range 1/R6 attraction of the London dispersion while leading to low gradients (small forces) at normal valence distances so that it preserves the accurate geometries and thermochem. of std. DFT methods. The DFT-low gradient (DFT-lg) formula differs from previous DFT-D methods by using a purely attractive dispersion correction while not affecting valence bond distances. We demonstrate here that the DFT-lg model leads to good descriptions for graphite, benzene, naphthalene, and anthracene crystals, using just three parameters fitted to reproduce the full potential curves of high-level ab initio quantum mechanics [CCSD(T)] on gas-phase benzene dimers. The addnl. computational costs for this DFT-lg formalism are negligible.
252. 252
  Kim, H.; Choi, J.-M.; Goddard, W. A., III Universal Correction of Density Functional Theory to Include London Dispersion (up to Lr, Element 103) J. Phys. Chem. Lett. 2012, 3 (3) 360– 363 DOI: 10.1021/jz2016395
  252
  Universal Correction of Density Functional Theory to Include London Dispersion (up to Lr, Element 103)
  Kim, Hyungjun; Choi, Jeong-Mo; Goddard, William A., III
  Journal of Physical Chemistry Letters (2012), 3 (3), 360-363CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Conventional d. functional theory (DFT) fails to describe accurately the London dispersion essential for describing mol. interactions in soft matter (biol. systems, polymers, nucleic acids) and mol. crystals. This has led to several methods in which atom-dependent potentials are added into the Kohn-Sham DFT energy. Some of these corrections were fitted to accurate quantum mech. results, but it will be tedious to det. the appropriate parameters to describe all of the atoms of the periodic table. We propose an alternative approach in which a single parameter in the low-gradient (lg) functional form is combined with the rule-based UFF (universal force-field) nonbond parameters developed for the entire periodic table (up to Lr, Z = 103), named as a DFT-ulg method. We show that DFT-ulg method leads to a very accurate description of the properties for mol. complexes and mol. crystals, providing the means for predicting more accurate weak interactions across the periodic table.
253. 253
  Román-Pérez, G.; Soler, J. M. Efficient Implementation of a van Der Waals Density Functional: Application to Double-Wall Carbon Nanotubes Phys. Rev. Lett. 2009, 103 (9) 096102 DOI: 10.1103/PhysRevLett.103.096102
  253
  Efficient Implementation of a van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes
  Roman-Perez, Guillermo; Soler, Jose M.
  Physical Review Letters (2009), 103 (9), 096102/1-096102/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  We present an efficient implementation of the van der Waals d. functional of Dion et al., which expresses the nonlocal correlation energy as a double spatial integral. We factorize the integration kernel and use fast Fourier transforms to evaluate the self-consistent potential, total energy, and at. forces, in O(NlogN) operations. The resulting overhead, for medium and large systems, is a small fraction of the total computational cost, representing a dramatic speedup over the O(N2) evaluation of the double integral. This opens the realm of first-principles simulations to the large systems of interest in soft matter and biomol. problems. We apply the method to calc. the binding energies and the barriers for relative translation and rotation in double-wall carbon nanotubes.
254. 254
  Andersson, Y.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Interactions in Density-Functional Theory Phys. Rev. Lett. 1996, 76 (1) 102– 105 DOI: 10.1103/PhysRevLett.76.102
  There is no corresponding record for this reference.
255. 255
  Dobson, J. F.; Dinte, B. P. Constraint Satisfaction in Local and Gradient Susceptibility Approximations: Application to a van Der Waals Density Functional Phys. Rev. Lett. 1996, 76 (11) 1780 DOI: 10.1103/PhysRevLett.76.1780
  There is no corresponding record for this reference.
256. 256
  Sato, T.; Tsuneda, T.; Hirao, K. Van Der Waals Interactions Studied by Density Functional Theory Mol. Phys. 2005, 103 (6–8) 1151– 1164 DOI: 10.1080/00268970412331333474
  There is no corresponding record for this reference.
257. 257
  Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Density Functional for General Geometries Phys. Rev. Lett. 2004, 92 (24) 246401 DOI: 10.1103/PhysRevLett.92.246401
  257
  Van der Waals Density Functional for General Geometries
  Dion, M.; Rydberg, H.; Schroeder, E.; Langreth, D. C.; Lundqvist, B. I.
  Physical Review Letters (2004), 92 (24), 246401/1-246401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  A scheme within d. functional theory is proposed that provides a practical way to generalize to unrestricted geometries the method applied with some success to layered geometries [H. Rydberg et al., Phys. Rev. Lett. 91, 126402 (2003)]. It includes van der Waals forces in a seamless fashion. By expansion to second order in a carefully chosen quantity contained in the long-range part of the correlation functional, the nonlocal correlations are expressed in terms of a d.-d. interaction formula. It contains a relatively simple parametrized kernel, with parameters detd. by the local d. and its gradient. The proposed functional is applied to rare gas and benzene dimers, where it is shown to give a realistic description.
258. 258
  Pernal, K.; Podeszwa, R.; Patkowski, K.; Szalewicz, K. Dispersionless Density Functional Theory Phys. Rev. Lett. 2009, 103 (26) 263201 DOI: 10.1103/PhysRevLett.103.263201
  There is no corresponding record for this reference.
259. 259
  Klimeš, J.; Bowler, D. R.; Michaelides, A. Chemical Accuracy for the van Der Waals Density Functional J. Phys.: Condens. Matter 2010, 22 (2) 022201 DOI: 10.1088/0953-8984/22/2/022201
  259
  Chemical accuracy for the van der Waals density functional
  Klimes, Jiri; Bowler, David R.; Michaelides, Angelos
  Journal of Physics: Condensed Matter (2010), 22 (2), 022201/1-022201/5CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
  The non-local van der Waals d. functional (vdW-DF) of Dion et al is a very promising scheme for the efficient treatment of dispersion bonded systems. We show here that the accuracy of vdW-DF can be dramatically improved both for dispersion and hydrogen bonded complexes through the judicious selection of its underlying exchange functional. New and published exchange functionals are identified that deliver much better than chem. accuracy from vdW-DF for the S22 benchmark set of weakly interacting dimers and for water clusters. Improved performance for the adsorption of water on salt is also obtained.
260. 260
  Lee, K.; Murray, É. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Higher-Accuracy van Der Waals Density Functional Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82 (8) 081101 DOI: 10.1103/PhysRevB.82.081101
  260
  Higher-accuracy van der Waals density functional
  Lee, Kyuho; Murray, Eamonn D.; Kong, Lingzhu; Lundqvist, Bengt I.; Langreth, David C.
  Physical Review B: Condensed Matter and Materials Physics (2010), 82 (8), 081101/1-081101/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We propose a second version of the van der Waals d. functional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in detg. the vdW kernel. The predicted binding energy, equil. sepn., and potential-energy curve shape are close to those of accurate quantum chem. calcns. on 22 duplexes. We anticipate the enabling of chem. accurate calcns. in sparse materials of importance for condensed matter, surface, chem., and biol. physics.
261. 261
  Hamada, I. Van Der Waals Density Functional Made Accurate Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89 (12) 121103 DOI: 10.1103/PhysRevB.89.121103
  261
  van der Waals density functional made accurate
  Hamada, Ikutaro
  Physical Review B: Condensed Matter and Materials Physics (2014), 89 (12), 121103/1-121103/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  I propose a van der Waals d. functional (vdW-DF) that improves upon the description of energetics and geometries of mols., solids, and adsorption systems over the original vdW-DF. The functional is based on the nonlocal correlation for the second version of the vdW-DF and an exchange functional that recovers the second-order gradient expansion approxn. in the slowly varying limit, while reproducing the large d. gradient behavior proposed by Becke. A systematic assessment of the proposed functional is presented, which demonstrates the applicability of the proposed vdW-DF to a wide range of systems.
262. 262
  Vydrov, O. A.; Van Voorhis, T. Nonlocal van Der Waals Density Functional Made Simple Phys. Rev. Lett. 2009, 103 (6) 063004 DOI: 10.1103/PhysRevLett.103.063004
  262
  Nonlocal van der Waals Density Functional Made Simple
  Vydrov, Oleg A.; Van Voorhis, Troy
  Physical Review Letters (2009), 103 (6), 063004/1-063004/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  We derive a nonlocal correlation functional that adequately describes van der Waals interactions not only in the asymptotic long-range regime but also at short range. Unlike its precursor, developed by Langreth, Lundqvist, and co-workers, the new functional has a simple analytic form, finite for all interelectron sepns., well behaved in the slowly varying d. limit, and generalized to spin-polarized systems.
263. 263
  Vydrov, O. A.; Van Voorhis, T. Improving the Accuracy of the Nonlocal van Der Waals Density Functional with Minimal Empiricism J. Chem. Phys. 2009, 130 (10) 104105 DOI: 10.1063/1.3079684
  There is no corresponding record for this reference.
264. 264
  Vydrov, O. A.; Van Voorhis, T. Implementation and Assessment of a Simple Nonlocal van Der Waals Density Functional J. Chem. Phys. 2010, 132 (16) 164113 DOI: 10.1063/1.3398840
  There is no corresponding record for this reference.
265. 265
  Vydrov, O. A.; Van Voorhis, T. Nonlocal van Der Waals Density Functional: The Simpler the Better J. Chem. Phys. 2010, 133 (24) 244103 DOI: 10.1063/1.3521275
  265
  Nonlocal van der Waals density functional: The simpler the better
  Vydrov, Oleg A.; Van Voorhis, Troy
  Journal of Chemical Physics (2010), 133 (24), 244103/1-244103/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron d. as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy min. but also far from equil. Our model exhibits an outstanding precision at predicting equil. intermonomer sepns. in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability. (c) 2010 American Institute of Physics.
266. 266
  Sabatini, R.; Gorni, T.; de Gironcoli, S. Nonlocal van Der Waals Density Functional Made Simple and Efficient Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (4) 041108 DOI: 10.1103/PhysRevB.87.041108
  266
  Nonlocal van der Waals density functional made simple and efficient
  Sabatini, Riccardo; Gorni, Tommaso; de Gironcoli, Stefano
  Physical Review B: Condensed Matter and Materials Physics (2013), 87 (4), 041108/1-041108/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We present a simple revision of the VV10 nonlocal d. functional by Vydrov and Van Voorhis for dispersion interactions. Unlike the original functional our modification allows nonlocal correlation energy and its derivs. to be efficiently evaluated in a plane wave framework along the lines pioneered by Roman-Perez and Soler. Our revised functional maintains the outstanding precision of the original VV10 in noncovalently bound complexes and performs well in representative covalent, ionic, and metallic solids.
267. 267
  Hujo, W.; Grimme, S. Performance of the van Der Waals Density Functional VV10 and (hybrid) GGA Variants for Thermochemistry and Noncovalent Interactions J. Chem. Theory Comput. 2011, 7 (12) 3866– 3871 DOI: 10.1021/ct200644w
  267
  Performance of the van der Waals Density Functional VV10 and (hybrid)GGA Variants for Thermochemistry and Noncovalent Interactions
  Hujo, Waldemar; Grimme, Stefan
  Journal of Chemical Theory and Computation (2011), 7 (12), 3866-3871CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The nonlocal van der Waals d. functional VV10 (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103) is tested for the thermochem. properties of 1200 + atoms and mols. in the GMTKN30 database in order to assess its global accuracy. Five GGA and hybrid functionals in unmodified form are augmented by the nonlocal (NL) part of the VV10 functional (one parameter adjusted). The addn. of the NL dispersion energy definitely improves the results of all tested functionals. On the basis of little empiricism and basic phys. insight, DFT-NL can be recommended as a fully electronic, robust electronic structure method.
268. 268
  Aragó, J.; Ortí, E.; Sancho-García, J. C. Nonlocal van Der Waals Approach Merged with Double-Hybrid Density Functionals: Toward the Accurate Treatment of Noncovalent Interactions J. Chem. Theory Comput. 2013, 9 (8) 3437– 3443 DOI: 10.1021/ct4003527
  268
  Nonlocal van der Waals Approach Merged with Double-Hybrid Density Functionals: Toward the Accurate Treatment of Noncovalent Interactions
  Arago, Juan; Orti, Enrique; Sancho-Garcia, Juan C.
  Journal of Chemical Theory and Computation (2013), 9 (8), 3437-3443CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Noncovalent interactions drive the self-assembly of weakly interacting mol. systems to form supramol. aggregates, which play a major role in nanotechnol. and biochem. In this work, we present a thorough assessment of the performance of different double-hybrid d. functionals (PBE0-DH-NL, revPBE0-DH-NL, B2PLYP-NL, and TPSS0-DH-NL), as well as their parent hybrid and (meta)GGA functionals, in combination with the most modern version of the nonlocal (NL) van der Waals correction. It is shown that this nonlocal correction can be successfully coupled with double-hybrid d. functionals thanks to the short-range attenuation parameter b, which has been optimized against ref. interaction energies of benchmarking mol. complexes (S22 and S66 databases). Among all the double-hybrid functionals evaluated, revPBE0-DH-NL and B2PLYP-NL behave remarkably accurate with mean unsigned errors (MUE) as small as 0.20 kcal/mol for the training sets and in the 0.25-0.42 kcal/mol range for an independent database (NCCE31). They can be thus seen as appropriate functionals to use in a broad no. of applications where noncovalent interactions play an important role. Overall, the nonlocal van der Waals approach combined with last-generation d. functionals is confirmed as an accurate and affordable computational tool for the modeling of weakly bonded mol. systems.
269. 269
  Cooper, V. R. Van Der Waals Density Functional: An Appropriate Exchange Functional Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (16) 161104 DOI: 10.1103/PhysRevB.81.161104
  269
  Van der Waals density functional: An appropriate exchange functional
  Cooper, Valentino R.
  Physical Review B: Condensed Matter and Materials Physics (2010), 81 (16), 161104/1-161104/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  In this Rapid Communication, an exchange functional which is compatible with the nonlocal Rutgers-Chalmers correlation functional [van der Waals d. functional (vdW-DF)] is presented. This functional, when employed with vdW-DF, demonstrates remarkable improvements on intermol. sepn. distances while further improving the accuracy of vdW-DF interaction energies. The key to the success of this three-parameter functional is its redn. in short-range exchange repulsion through matching to the gradient expansion approxn. in the slowly varying/high-d. limit while recovering the large reduced gradient, s, limit set in the revised Perdew-Burke-Ernzerhof (revPBE) exchange functional. This augmented exchange functional could be a soln. to long-standing issues of vdW-DF lending to further applicability of d.-functional theory to the study of relatively large, dispersion bound (van der Waals) complexes.
270. 270
  Vydrov, O. A.; Van Voorhis, T. Benchmark Assessment of the Accuracy of Several van Der Waals Density Functionals J. Chem. Theory Comput. 2012, 8 (6) 1929– 1934 DOI: 10.1021/ct300081y
  270
  Benchmark Assessment of the Accuracy of Several van der Waals Density Functionals
  Vydrov, Oleg A.; Van Voorhis, Troy
  Journal of Chemical Theory and Computation (2012), 8 (6), 1929-1934CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The nonlocal correlation functional VV10, developed recently in our group, describes the whole range of dispersion interactions in a seamless and general fashion using only the electron d. as input. The VV10 functional has a simple analytic form that can be adjusted for pairing with the exchange functional of choice. In this paper, we use several benchmark data sets of weakly interacting mol. complexes to test the accuracy of two VV10 variants, differing in their treatment of the exchange component. For the sake of comparison, several other d. functionals suitable for noncovalent interactions were also tested against the same benchmarks. We find that the "default" version of VV10 with semilocal exchange gives very accurate geometries and binding energies for most van der Waals complexes but systematically overbinds hydrogen-bonded complexes. The alternative variant of VV10 with long-range cor. hybrid exchange performs exceptionally well for all types of weak bonding sampled in this study, including hydrogen bonds.
271. 271
  Hujo, W.; Grimme, S. Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions J. Chem. Theory Comput. 2013, 9 (1) 308– 315 DOI: 10.1021/ct300813c
  271
  Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions
  Hujo, Waldemar; Grimme, Stefan
  Journal of Chemical Theory and Computation (2013), 9 (1), 308-315CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The nonlocal, electron d. dependent dispersion correction of Vydrov and Van Voorhis (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103), termed VV10 or DFT-NL, was implemented for structural optimizations of mols. It was tested in combination with the four (hybrid)GGA d. functionals TPSS, TPSS0, B3LYP, and revPBE38 for inter- and intramol. noncovalent interactions (NCI) and compared to results from atom-pairwise dispersion cor. DFT-D3. The methods were applied to a wide range of different problems, namely the S22 and S66 test sets, large transition metal complexes, water hexamer clusters, hexahelicene, and four other difficult cases of intramol. NCI. Crit. interat. distances were computed remarkably accurately by both dispersion corrections compared to theor. or exptl. ref. data and inter- and intramol. interactions were treated on equal footing. The methods can be recommended as reliable and robust tools for geometry optimizations of large systems in which long-range dispersion forces are crucial.
272. 272
  Tran, F.; Hutter, J. Nonlocal van Der Waals Functionals: The Case of Rare-Gas Dimers and Solids J. Chem. Phys. 2013, 138 (20) 204103 DOI: 10.1063/1.4807332
  There is no corresponding record for this reference.
273. 273
  Gobre, V. V.; Tkatchenko, A. Scaling Laws for van Der Waals Interactions in Nanostructured Materials Nat. Commun. 2013, 4, 2341 DOI: 10.1038/ncomms3341
  273
  Scaling laws for van der Waals interactions in nanostructured materials
  Gobre Vivekanand V; Tkatchenko Alexandre
  Nature communications (2013), 4 (), 2341 ISSN:.
  Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.
274. 274
  Ambrosetti, A.; Alfè, D.; DiStasio, R. A., Jr.; Tkatchenko, A. Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems J. Phys. Chem. Lett. 2014, 5 (5) 849– 855 DOI: 10.1021/jz402663k
  274
  Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems
  Ambrosetti, Alberto; Alfe, Dario; DiStasio, Robert A.; Tkatchenko, Alexandre
  Journal of Physical Chemistry Letters (2014), 5 (5), 849-855CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Noncovalent interactions are ubiquitous in mol. and condensed-phase environments, and hence a reliable theor. description of these fundamental interactions could pave the way toward a more complete understanding of the microscopic underpinnings for a diverse set of systems in chem. and biol. In this work, we demonstrate that recent algorithmic advances coupled to the availability of large-scale computational resources make the stochastic quantum Monte Carlo approach to solving the Schrodinger equation an optimal contender for attaining "chem. accuracy" (1 kcal/mol) in the binding energies of supramol. complexes of chem. relevance. To illustrate this point, we considered a select set of seven host-guest complexes, representing the spectrum of noncovalent interactions, including dispersion or van der Waals forces, π-π stacking, hydrogen bonding, hydrophobic interactions, and electrostatic (ion-dipole) attraction. A detailed anal. of the interaction energies reveals that a complete theor. description necessitates treatment of terms well beyond the std. London and Axilrod-Teller contributions to the van der Waals dispersion energy.
275. 275
  Šimová, L.; Řezáč, J.; Hobza, P. Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction J. Chem. Theory Comput. 2013, 9 (8) 3420– 3428 DOI: 10.1021/ct4002762
  275
  Convergence of the Interaction Energies in Noncovalent Complexes in the Coupled-Cluster Methods Up to Full Configuration Interaction
  Simova, Lucia; Rezac, Jan; Hobza, Pavel
  Journal of Chemical Theory and Computation (2013), 9 (8), 3420-3428CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The CCSD(T) method stands out among various coupled-cluster (CC) approxns. as the golden std. in computational chem. and is widely and successfully used in the realm of covalent and noncovalent interactions. The CCSD(T) method provides reliable interaction energies, but their surprising accuracy is believed to arise partially from an error compensation. The convergence of the CC expansion has been investigated up to fully iterative pentuple excitations (CCSDTQP); for the smallest eight electron complexes, the full CI calcns. have also been performed. We conclude that the convergence of interaction energy at noncovalent accuracy (0.01 kcal/mol) for the complexes studied is reached already at CCSDTQ or CCSDT(Q) levels. When even higher accuracy (spectroscopic accuracy of 1 cm-1, or 3 cal/mol) is required, then the noniterative CCSDTQ(P) method could be used.
276. 276
  Řezáč, J.; Šimová, L.; Hobza, P. CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods J. Chem. Theory Comput. 2013, 9 (1) 364– 369 DOI: 10.1021/ct3008777
  276
  CCSD[T] Describes Noncovalent Interactions Better than the CCSD(T), CCSD(TQ), and CCSDT Methods
  Rezac, Jan; Simova, Lucia; Hobza, Pavel
  Journal of Chemical Theory and Computation (2013), 9 (1), 364-369CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The CCSD(T) method is often called the "gold std." of computational chem., because it is one of the most accurate methods applicable to reasonably large mols. It is particularly useful for the description of noncovalent interactions where the inclusion of triple excitations is necessary for achieving a satisfactory accuracy. While it is widely used as a benchmark, the accuracy of CCSD(T) interaction energies has not been reliably quantified yet against more accurate calcns. In this work, we compare the CCSD[T], CCSD(T), and CCSD(TQ) noniterative methods with full CCSDTQ and CCSDT(Q) calcns. We investigate various types of noncovalent complexes [hydrogen-bonded (water dimer, ammonia dimer, water ··· ammonia), dispersion-bound (methane dimer, methane ··· ammonia), and π-π stacked (ethene dimer)] using various coupled-clusters schemes up to CCSDTQ in 6-31G*(0.25), 6-31G**(0.25, 0.15), and aug-cc-pVDZ basis sets. We show that CCSDT(Q) reproduces the CCSDTQ results almost exactly and can thus serve as a benchmark in the cases where CCSDTQ calcns. are not feasible. Surprisingly, the CCSD[T] method provides better agreement with the benchmark values than the other noniterative analogs, CCSD(T) and CCSD(TQ), and even than the much more expensive iterative CCSDT scheme. The CCSD[T] interaction energies differ from the benchmark data by less than 5 cal/mol on av. (for all complexes and all basis sets), whereas the error of CCSD(T) is 9 cal/mol. In larger systems, the difference between these two methods can grow by as much as 0.15 kcal/mol. While this effect can be explained only as an error compensation, the CCSD[T] method certainly deserves more attention in accurate calcns. of noncovalent interactions.
277. 277
  Kong, L.; Bischoff, F. A.; Valeev, E. F. Explicitly Correlated R12/F12 Methods for Electronic Structure Chem. Rev. 2012, 112 (1) 75– 107 DOI: 10.1021/cr200204r
  277
  Explicitly Correlated R12/F12 Methods for Electronic Structure
  Kong, Liguo; Bischoff, Florian A.; Valeev, Edward F.
  Chemical Reviews (Washington, DC, United States) (2012), 112 (1), 75-107CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. The following topics are discussed: Electron correlation in atoms and mols.(CI wave functions and their symmetries); Explicitly correlated methods and wave functions; Core technol. of modern R12 methods; Coupled-Cluster R12 methods; Multireference R12 methods (R12-MRCI, MRMP2-F12, [2]R12, CASPT2-F12 and MRCI-F12, G-CASSCF, MR CABS Single correction, comparison of MR-R12 Methods).
278. 278
  Burns, L. A.; Marshall, M. S.; Sherrill, C. D. Appointing Silver and Bronze Standards for Noncovalent Interactions: A Comparison of Spin-Component-Scaled (SCS), Explicitly Correlated (F12), and Specialized Wavefunction Approaches J. Chem. Phys. 2014, 141 (23) 234111 DOI: 10.1063/1.4903765
  278
  Appointing silver and bronze standards for noncovalent interactions: A comparison of spin-component-scaled (SCS), explicitly correlated (F12), and specialized wavefunction approaches
  Burns, Lori A.; Marshall, Michael S.; Sherrill, C. David
  Journal of Chemical Physics (2014), 141 (23), 234111/1-234111/21CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A systematic examn. of noncovalent interactions as modeled by wavefunction theory is presented in comparison to gold-std. quality benchmarks available for 345 interaction energies of 49 bimol. complexes. Quantum chem. techniques examd. include spin-component-scaling (SCS) variations on second-order perturbation theory (MP2) [SCS, SCS(N), SCS(MI)] and coupled cluster singles and doubles (CCSD) [SCS, SCS(MI)]; also, method combinations designed to improve dispersion contacts [DW-MP2, MP2C, MP2.5, DW-CCSD(T)-F12]; where available, explicitly correlated (F12) counterparts are also considered. Dunning basis sets augmented by diffuse functions are employed for all accessible ζ-levels; truncations of the diffuse space are also considered. After examn. of both accuracy and performance for 394 model chemistries, SCS(MI)-MP2/cc-pVQZ can be recommended for general use, having good accuracy at low cost and no ill-effects such as imbalance between hydrogen-bonding and dispersion-dominated systems or non-parallelity across dissocn. curves. Moreover, when benchmarking accuracy is desirable but gold-std. computations are unaffordable, this work recommends silver-std. [DW-CCSD(T**)-F12/aug-cc-pVDZ] and bronze-std. [MP2C-F12/aug-cc-pVDZ] model chemistries, which support accuracies of 0.05 and 0.16 kcal/mol and efficiencies of 97.3 and 5.5 h for adenine·thymine, resp. Choice comparisons of wavefunction results with the best symmetry-adapted perturbation theory [T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys.140, 094106 (2014)] and d. functional theory [L. A. Burns, A. Vazquez-Mayagoitia, B. G. Sumpter, and C. D. Sherrill, J. Chem. Phys.134, 084107 (2011)] methods previously studied for these databases are provided for readers' guidance. (c) 2014 American Institute of Physics.
279. 279
  Austin, B. M.; Zubarev, D. Y.; Lester, W. A., Jr. Quantum Monte Carlo and Related Approaches Chem. Rev. 2012, 112 (1) 263– 288 DOI: 10.1021/cr2001564
  279
  Quantum Monte Carlo and Related Approaches
  Austin, Brian M.; Zubarev, Dmitry Yu.; Lester, William A., Jr.
  Chemical Reviews (Washington, DC, United States) (2012), 112 (1), 263-288CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. The following topics are discussed: Variational Monte Carlo, Fixed-node diffusion Monte Carlo, Self-healing diffusion Monte Carlo, Auxiliary field quantum Monte Carlo, Reptation quantum Monte Carlo, Full CI quantum Monte Carlo, Time-dependent quantum Monte Carlo; Trial electronic wave functions (antisym., backflow transformed, Jastrow), Trial wave function optimization, Effective core potentials; Computational considerations (Linear scaling quantum Monte Carlo, Parallelization and hardware acceleration, Advances in algorithms and software); Applications.
280. 280
  Dubeckỳ, M.; Jurečka, P.; Derian, R.; Hobza, P.; Otyepka, M.; Mitas, L. Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy J. Chem. Theory Comput. 2013, 9 (10) 4287– 4292 DOI: 10.1021/ct4006739
  280
  Quantum Monte Carlo Methods Describe Noncovalent Interactions with Subchemical Accuracy
  Dubecky, Matus; Jurecka, Petr; Derian, Rene; Hobza, Pavel; Otyepka, Michal; Mitas, Lubos
  Journal of Chemical Theory and Computation (2013), 9 (10), 4287-4292CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  An accurate description of noncovalent interaction energies is one of the most challenging tasks in computational chem. To date, nonempirical CCSD-(T)/CBS has been used as a benchmark ref. However, its practical use is limited due to the rapid growth of its computational cost with the system complexity. Here, we show that the fixed-node diffusion Monte Carlo (FN-DMC) method with a more favorable scaling is capable of reaching the CCSD-(T)/CBS within subchem. accuracy (<0.1 kcal/mol) on a testing set of six small noncovalent complexes including the water dimer. In benzene/water, benzene/methane, and the T-shape benzene dimer, FN-DMC provides interaction energies that agree within 0.25 kcal/mol with the best available CCSD-(T)/CBS ests. The demonstrated predictive power of FN-DMC therefore provides new opportunities for studies of the vast and important class of medium/large noncovalent complexes.
281. 281
  Dubeckỳ, M.; Derian, R.; Jurečka, P.; Mitas, L.; Hobza, P.; Otyepka, M. Quantum Monte Carlo for Noncovalent Interactions: An Efficient Protocol Attaining Benchmark Accuracy Phys. Chem. Chem. Phys. 2014, 16 (38) 20915– 20923 DOI: 10.1039/C4CP02093F
  There is no corresponding record for this reference.
282. 282
  Neese, F.; Wennmohs, F.; Hansen, A. Efficient and Accurate Local Approximations to Coupled-Electron Pair Approaches: An Attempt to Revive the Pair Natural Orbital Method J. Chem. Phys. 2009, 130 (11) 114108 DOI: 10.1063/1.3086717
  282
  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method
  Neese, Frank; Wennmohs, Frank; Hansen, Andreas
  Journal of Chemical Physics (2009), 130 (11), 114108/1-114108/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Coupled-electron pair approxns. (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small mols. Recently, interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochem., kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular d. functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient prodn. level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized mols. in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of d. fitting (or resoln. of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the av. no. of PNOs per electron pair, and the no. of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to abs. deviations from the canonical result of only a few kcal mol-1. Extended numerical test calcns. demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochem., kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chem. applications. (c) 2009 American Institute of Physics.
283. 283
  Neese, F.; Hansen, A.; Liakos, D. G. Efficient and Accurate Approximations to the Local Coupled Cluster Singles Doubles Method Using a Truncated Pair Natural Orbital Basis J. Chem. Phys. 2009, 131 (6) 064103 DOI: 10.1063/1.3173827
  283
  Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis
  Neese, Frank; Hansen, Andreas; Liakos, Dimitrios G.
  Journal of Chemical Physics (2009), 131 (6), 064103/1-064103/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A prodn. level implementation of the closed-shell local quadratic CI and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals (local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approxn. (LNPO-CEPA) method and makes extended use of the resoln. of the identity (RI) or d. fitting (DF) approxn. Two variants of each method are compared. The less accurate approxns. (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indexes to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (TCutPNO) has been studied. Extended numerical tests have been performed on abs. and relative correlation energies as function of basis set size and TCutPNO as well as on reaction energies, isomerization energies, and weak intermol. interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calcns. on larger mols. are reported (ranging from 40-86 atoms) and it is shown that for medium sized mols. the total wall clock time required to complete the LPNO-CCSD calcns. is only two to four times that of the preceding SCF. Thus these methods are highly suitable for large-scale computational chem. applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts. (c) 2009 American Institute of Physics.
284. 284
  Huntington, L. M.; Nooijen, M. pCCSD: Parameterized Coupled-Cluster Theory with Single and Double Excitations J. Chem. Phys. 2010, 133 (18) 184109 DOI: 10.1063/1.3494113
  There is no corresponding record for this reference.
285. 285
  Huntington, L. M. J.; Hansen, A.; Neese, F.; Nooijen, M. Accurate Thermochemistry from a Parameterized Coupled-Cluster Singles and Doubles Model and a Local Pair Natural Orbital Based Implementation for Applications to Larger Systems J. Chem. Phys. 2012, 136 (6) 064101 DOI: 10.1063/1.3682325
  There is no corresponding record for this reference.
286. 286
  Hansen, A.; Liakos, D. G.; Neese, F. Efficient and Accurate Local Single Reference Correlation Methods for High-Spin Open-Shell Molecules Using Pair Natural Orbitals J. Chem. Phys. 2011, 135 (21) 214102 DOI: 10.1063/1.3663855
  286
  Efficient and accurate local single reference correlation methods for high-spin open-shell molecules using pair natural orbitals
  Hansen, Andreas; Liakos, Dimitrios G.; Neese, Frank
  Journal of Chemical Physics (2011), 135 (21), 214102/1-214102/20CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A prodn. level implementation of the high-spin open-shell (spin unrestricted) single ref. coupled pair, quadratic CI and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier. The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation assocd. with the large no. of PNOs becomes feasible through the extensive use of d. fitting (resoln. of the identity (RI)) techniques. Tech. complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the ref. determinant are discussed in detail. As in the closed-shell case, only three cutoff parameters control the av. no. of PNOs per electron pair, the size of the significant pair list, and the no. of contributing auxiliary basis functions per PNO. The chosen threshold default values ensure robustness and the results of the parent canonical methods are reproduced to high accuracy. Comprehensive numerical tests on abs. and relative energies as well as timings consistently show that the outstanding performance of the LPNO methods carries over to the open-shell case with minor modifications. Finally, hyperfine couplings calcd. with the variational LPNO-CEPA/1 method, for which a well-defined expectation value type d. exists, indicate the great potential of the LPNO approach for the efficient calcn. of mol. properties. (c) 2011 American Institute of Physics.
287. 287
  Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. Natural Triple Excitations in Local Coupled Cluster Calculations with Pair Natural Orbitals J. Chem. Phys. 2013, 139 (13) 134101 DOI: 10.1063/1.4821834
  287
  Natural triple excitations in local coupled cluster calculations with pair natural orbitals
  Riplinger, Christoph; Sandhoefer, Barbara; Hansen, Andreas; Neese, Frank
  Journal of Chemical Physics (2013), 139 (13), 134101/1-134101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calcn. of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calcns. on alkane chains. The accuracy of the DLPNO-CCSD(T) approxn. relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an av. error of approx. 0.5 kcal/mol for a challenging test set of medium sized org. mols. The triples correction typically adds 30%-50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addn. to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calcn. on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions.
288. 288
  Sparta, M.; Neese, F. Chemical Applications Carried out by Local Pair Natural Orbital Based Coupled-Cluster Methods Chem. Soc. Rev. 2014, 43 (14) 5032– 5041 DOI: 10.1039/c4cs00050a
  There is no corresponding record for this reference.
289. 289
  Liakos, D. G.; Hansen, A.; Neese, F. Weak Molecular Interactions Studied with Parallel Implementations of the Local Pair Natural Orbital Coupled Pair and Coupled Cluster Methods J. Chem. Theory Comput. 2011, 7 (1) 76– 87 DOI: 10.1021/ct100445s
  289
  Weak molecular interactions studied with parallel implementations of the local pair natural orbital coupled pair and coupled cluster methods
  Liakos, Dimitrios G.; Hansen, Andreas; Neese, Frank
  Journal of Chemical Theory and Computation (2011), 7 (1), 76-87CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  A parallel implementation of the recently developed local pair natural orbital CEPA (LPNO-CEPA/n, n = Version 1, 2, or 3) and the corresponding LPNO coupled cluster method with single- and double excitations (LPNO-CCSD) is described. A detailed anal. alongside pseudocode is presented for the most important computational steps. The scaling with respect to the no. of processors is reasonable and speedups of about 10 with 14 processors have been found in benchmark calcns. (wall-clock time). The most important factor limiting the efficiency of the scaling with respect to the no. of processors is probably the limited bandwidth of the presently prevailing multicore machines. The parallel LPNO methods were applied to study weak intermol. interactions. Initially, the well-established S22 set of mols. was studied. The mean abs. error resulting from the use of the LPNO-CEPA/1 method relative to the most recent CCSD(T) ref. data is found to be 0.24 kcal/mol. Thus, LPNO-CEPA/1 holds great promise for the efficient ab initio treatment of weak intermol. interactions. In order to demonstrate the applicability of the methods to real systems, a two-dimensional potential energy surface for a trimer of 2,4-dihydroxy-3-acetyl-6-Me acetophenone [C11H12O4] (81 atoms, 1296 basis functions, 133 single points) has been calcd. with the LPNO-CEPA/1 method. In this system, a clear distinction can be made between hydrogen bonding and π-π interactions. The global min. on the PES obtained from the calcns. agrees excellently with the exptl. detd. crystal structure. By contrast, popular d. functional methods show no discernible min.
290. 290
  Liakos, D. G.; Neese, F. Improved Correlation Energy Extrapolation Schemes Based on Local Pair Natural Orbital Methods J. Phys. Chem. A 2012, 116 (19) 4801– 4816 DOI: 10.1021/jp302096v
  290
  Improved Correlation Energy Extrapolation Schemes Based on Local Pair Natural Orbital Methods
  Liakos, Dimitrios G.; Neese, Frank
  Journal of Physical Chemistry A (2012), 116 (19), 4801-4816CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  It is well-known that the basis set limit is difficult to reach in correlated post Hartree-Fock ab initio calcns. One possible route forward is to employ basis set extrapolation schemes. In order to avoid prohibitively expensive calcns., the highest level calcn. (typically based on the "gold std." coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T)) is only performed with the smallest basis set, and the remaining basis set incompleteness is estd. at a lower level of theory, typically second-order Moeller-Plesset perturbation theory (MP2). In this work, we provide a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approxn., version 1 (CEPA/1) or the local pair natural orbital version of this method (LPNO-CEPA/1). It is shown that the MP2 method achieves apparent accuracy only due to error cancellation. Systematically more accurate results at small addnl. computational cost are obtained if the MP2 step is replaced by LPNO-CEPA/1. The errors of LPNO-CEPA/1 relative to canonical CEPA/1 are negligible. Owing to the highly systematic nature of the deviations between canonical and LPNO methods, basis set extrapolation reduces the LPNO errors in the total energies by 1 order of magnitude (∼0.2 kcal/mol) and errors in energy differences to essentially zero. Using the CCSD(T)/LPNO-CEPA/1-based extrapolation scheme, new ref. values are proposed for the recently published S66 set of interaction energies. The deviations between the new values and the original interactions energies are mostly very small but reach values up to 0.3 kcal/mol.
291. 291
  Schwabe, T. Accurate and Fast Treatment of Large Molecular Systems: Assessment of CEPA and pCCSD within the Local Pair Natural Orbital Approximation J. Comput. Chem. 2012, 33 (26) 2067– 2072 DOI: 10.1002/jcc.23042
  There is no corresponding record for this reference.
292. 292
  Riplinger, C.; Neese, F. An Efficient and near Linear Scaling Pair Natural Orbital Based Local Coupled Cluster Method J. Chem. Phys. 2013, 138 (3) 034106 DOI: 10.1063/1.4773581
  292
  An efficient and near linear scaling pair natural orbital based local coupled cluster method
  Riplinger, Christoph; Neese, Frank
  Journal of Chemical Physics (2013), 138 (3), 034106/1-034106/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In previous publications, it was shown that an efficient local coupled cluster method with single- and double excitations can be based on the concept of pair natural orbitals (PNOs) . The resulting local pair natural orbital-coupled-cluster single double (LPNO-CCSD) method has since been proven to be highly reliable and efficient. For large mols., the no. of amplitudes to be detd. is reduced by a factor of 105-106 relative to a canonical CCSD calcn. on the same system with the same basis set. In the original method, the PNOs were expanded in the set of canonical virtual orbitals and single excitations were not truncated. This led to a no. of fifth order scaling steps that eventually rendered the method computationally expensive for large mols. (e.g., >100 atoms). In the present work, these limitations are overcome by a complete redesign of the LPNO-CCSD method. The new method is based on the combination of the concepts of PNOs and projected AOs (PAOs). Thus, each PNO is expanded in a set of PAOs that in turn belong to a given electron pair specific domain. In this way, it is possible to fully exploit locality while maintaining the extremely high compactness of the original LPNO-CCSD wavefunction. No terms are dropped from the CCSD equations and domains are chosen conservatively. The correlation energy loss due to the domains remains below <0.05%, which implies typically 15-20 but occasionally up to 30 atoms per domain on av. The new method has been given the acronym DLPNO-CCSD ("domain based LPNO-CCSD"). The method is nearly linear scaling with respect to system size. The original LPNO-CCSD method had three adjustable truncation thresholds that were chosen conservatively and do not need to be changed for actual applications. In the present treatment, no addnl. truncation parameters have been introduced. Any addnl. truncation is performed on the basis of the three original thresholds. There are no real-space cutoffs. Single excitations are truncated using singles-specific natural orbitals. Pairs are prescreened according to a multipole expansion of a pair correlation energy est. based on local orbital specific virtual orbitals (LOSVs). Like its LPNO-CCSD predecessor, the method is completely of black box character and does not require any user adjustments. It is shown here that DLPNO-CCSD is as accurate as LPNO-CCSD while leading to computational savings exceeding one order of magnitude for larger systems. The largest calcns. reported here featured >8800 basis functions and >450 atoms. In all larger test calcns. done so far, the LPNO-CCSD step took less time than the preceding Hartree-Fock calcn., provided no approxns. have been introduced in the latter. Thus, based on the present development reliable CCSD calcns. on large mols. with unprecedented efficiency and accuracy are realized. (c) 2013 American Institute of Physics.
293. 293
  Sancho-García, J. C.; Aragó, J.; Ortí, E.; Olivier, Y. Obtaining the Lattice Energy of the Anthracene Crystal by Modern yet Affordable First-Principles Methods J. Chem. Phys. 2013, 138 (20) 204304 DOI: 10.1063/1.4806436
  There is no corresponding record for this reference.
294. 294
  Grimme, S. Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory Chem. - Eur. J. 2012, 18 (32) 9955– 9964 DOI: 10.1002/chem.201200497
  294
  Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory
  Grimme, Stefan
  Chemistry - A European Journal (2012), 18 (32), 9955-9964, S9955/1-S9955/53CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  The equil. assocn. free enthalpies ΔGa for typical supramol. complexes in soln. are calcd. by ab initio quantum chem. methods. Ten neutral and three pos. charged complexes with exptl. ΔGa values in the range 0 to -21 kcal mol-1 (on av. -6 kcal mol-1) are investigated. The theor. approach employs a (non-dynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion cor. d. functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to det. structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calcns. Low-lying vibrational modes are treated by a free-rotor approxn. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60 kcal mol-1 (up to 200% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semi-local (TPSS) and a hybrid d. functional (PW6B95) have been tested. Although the ΔGa values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔGa values with errors of only 2 kcal mol-1 on av. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramol. chem. and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.
295. 295
  Calbo, J.; Ortí, E.; Sancho-García, J. C.; Aragó, J. Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van Der Waals Corrections J. Chem. Theory Comput. 2015, 11 (3) 932– 939 DOI: 10.1021/acs.jctc.5b00002
  295
  Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections
  Calbo, Joaquin; Orti, Enrique; Sancho-Garcia, Juan C.; Arago, Juan
  Journal of Chemical Theory and Computation (2015), 11 (3), 932-939CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We present a thorough assessment of the performance of some representative double-hybrid d. functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting mol. systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of ref. interaction energies was computed for the supramol. complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the d. functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate assocn. energies very close to the chem. accuracy. Overall, the NL van der Waals approach combined with proper d. functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramol. systems.
296. 296
  Pitoňák, M.; Řezáč, J.; Hobza, P. Spin-Component Scaled Coupled-Clusters Singles and Doubles Optimized towards Calculation of Noncovalent Interactions Phys. Chem. Chem. Phys. 2010, 12 (33) 9611– 9614 DOI: 10.1039/c0cp00158a
  There is no corresponding record for this reference.
297. 297
  Grimme, S. Improved Second-Order Møller–Plesset Perturbation Theory by Separate Scaling of Parallel-and Antiparallel-Spin Pair Correlation Energies J. Chem. Phys. 2003, 118 (20) 9095– 9102 DOI: 10.1063/1.1569242
  There is no corresponding record for this reference.
298. 298
  Szabados, Á. Theoretical Interpretation of Grimme’s Spin-Component-Scaled Second Order Møller-Plesset Theory J. Chem. Phys. 2006, 125 (21) 214105 DOI: 10.1063/1.2404660
  298
  Theoretical interpretation of Grimme's spin-component-scaled second order Moller-Plesset theory
  Szabados, Agnes
  Journal of Chemical Physics (2006), 125 (21), 214105/1-214105/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  It is shown that spin-component-scaled second order Moller-Plesset theory proposed by Grimme [J. Chem. Phys. 118, 9095 (2003)] can be interpreted as a two-parameter scaling of the zero order Hamiltonian, a generalization of the approach reported by Feenberg [Phys. Rev. 103, 1116 (1956)].
299. 299
  Fink, R. F. Spin-Component-Scaled Møller–Plesset (SCS-MP) Perturbation Theory: A Generalization of the MP Approach with Improved Properties J. Chem. Phys. 2010, 133 (17) 174113 DOI: 10.1063/1.3503041
  There is no corresponding record for this reference.
300. 300
  Hill, J. G.; Platts, J. A. Spin-Component Scaling Methods for Weak and Stacking Interactions J. Chem. Theory Comput. 2007, 3 (1) 80– 85 DOI: 10.1021/ct6002737
  300
  Spin-Component Scaling Methods for Weak and Stacking Interactions
  Hill, J. Grant; Platts, James A.
  Journal of Chemical Theory and Computation (2007), 3 (1), 80-85CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  New scaling parameters are presented for use in the spin-component scaled (SCS) variant of d. fitted local second-order Moller-Plesset perturbation theory (DF-LMP2) that have been optimized for use in evaluating the interaction energy between nucleic acid base pairs. The optimal set of parameters completely neglects the contribution from antiparallel-spin electron pairs to the MP2 energy while scaling the parallel contribution by 1.76. These spin-component scaled for nucleobases (SCSN) parameters are obtained by minimizing, with respect to SCS parameters, the rms interaction energy error relative to the best available literature values, over a set of ten stacked nucleic acid base pairs. The applicability of this scaling to a wide variety of noncovalent interactions is verified through evaluation of a larger set of model complexes, including those dominated by dispersion and electrostatics.
301. 301
  Hill, J. G.; Platts, J. A. Calculating Stacking Interactions in Nucleic Acid Base-Pair Steps Using Spin-Component Scaling and Local Second Order Møller–Plesset Perturbation Theory Phys. Chem. Chem. Phys. 2008, 10 (19) 2785– 2791 DOI: 10.1039/b718691f
  There is no corresponding record for this reference.
302. 302
  Karton, A.; Tarnopolsky, A.; Lamere, J.-F.; Schatz, G. C.; Martin, J. M. Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics J. Phys. Chem. A 2008, 112 (50) 12868– 12886 DOI: 10.1021/jp801805p
  302
  Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics
  Karton, Amir; Tarnopolsky, Alex; Lamere, Jean-Francois; Schatz, George C.; Martin, Jan M. L.
  Journal of Physical Chemistry A (2008), 112 (50), 12868-12886CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  We present a no. of near-exact, nonrelativistic, Born-Oppenheimer ref. data sets for the parametrization of more approx. methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochem. protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small mols. that cover varying degrees of non-dynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calcd. DFT values with exptl. atomization energies is hampered by comparatively large exptl. uncertainties in many exptl. values and compds. errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. The optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimol. and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x,y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochem. and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochem. and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochem., B2GP-PLYP appears to be the more robust toward non-dynamical correlation and strongly polar character. We addnl. find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.
303. 303
  Distasio, R. A., Jr.; Head-Gordon, M. Optimized Spin-Component Scaled Second-Order Møller-Plesset Perturbation Theory for Intermolecular Interaction Energies Mol. Phys. 2007, 105 (8) 1073– 1083 DOI: 10.1080/00268970701283781
  There is no corresponding record for this reference.
304. 304
  Marchetti, O.; Werner, H.-J. Accurate Calculations of Intermolecular Interaction Energies Using Explicitly Correlated Coupled Cluster Wave Functions and a Dispersion-Weighted MP2 Method J. Phys. Chem. A 2009, 113 (43) 11580– 11585 DOI: 10.1021/jp9059467
  There is no corresponding record for this reference.
305. 305
  Riley, K. E.; Platts, J. A.; Řezáč, J.; Hobza, P.; Hill, J. G. Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions J. Phys. Chem. A 2012, 116 (16) 4159– 4169 DOI: 10.1021/jp211997b
  There is no corresponding record for this reference.
306. 306
  Takatani, T.; Hohenstein, E. G.; Sherrill, C. D. Improvement of the Coupled-Cluster Singles and Doubles Method via Scaling Same-and Opposite-Spin Components of the Double Excitation Correlation Energy J. Chem. Phys. 2008, 128 (12) 124111 DOI: 10.1063/1.2883974
  There is no corresponding record for this reference.
307. 307
  Jung, Y.; Lochan, R. C.; Dutoi, A. D.; Head-Gordon, M. Scaled Opposite-Spin Second Order Møller–Plesset Correlation Energy: An Economical Electronic Structure Method J. Chem. Phys. 2004, 121 (20) 9793– 9802 DOI: 10.1063/1.1809602
  There is no corresponding record for this reference.
308. 308
  Lochan, R. C.; Jung, Y.; Head-Gordon, M. Scaled Opposite Spin Second Order Møller-Plesset Theory with Improved Physical Description of Long-Range Dispersion Interactions J. Phys. Chem. A 2005, 109 (33) 7598– 7605 DOI: 10.1021/jp0514426
  There is no corresponding record for this reference.
309. 309
  Takatani, T.; Sherrill, C. D. Performance of Spin-Component-Scaled Møller–Plesset Theory (SCS-MP2) for Potential Energy Curves of Noncovalent Interactions Phys. Chem. Chem. Phys. 2007, 9 (46) 6106– 6114 DOI: 10.1039/b709669k
  There is no corresponding record for this reference.
310. 310
  Antony, J.; Grimme, S. Is Spin-Component Scaled Second-Order Møller-Plesset Perturbation Theory an Appropriate Method for the Study of Noncovalent Interactions in Molecules? J. Phys. Chem. A 2007, 111 (22) 4862– 4868 DOI: 10.1021/jp070589p
  There is no corresponding record for this reference.
311. 311
  Bachorz, R. A.; Bischoff, F. A.; Höfener, S.; Klopper, W.; Ottiger, P.; Leist, R.; Frey, J. A.; Leutwyler, S. Scope and Limitations of the SCS-MP2 Method for Stacking and Hydrogen Bonding Interactions Phys. Chem. Chem. Phys. 2008, 10 (19) 2758– 2766 DOI: 10.1039/b718494h
  There is no corresponding record for this reference.
312. 312
  King, R. A. On the Accuracy of Spin-Component-Scaled Perturbation Theory (SCS-MP2) for the Potential Energy Surface of the Ethylene Dimer Mol. Phys. 2009, 107 (8–12) 789– 795 DOI: 10.1080/00268970802641242
  There is no corresponding record for this reference.
313. 313
  Grabowski, I.; Fabiano, E.; Sala, F. D. A Simple Non-Empirical Procedure for Spin-Component-Scaled MP2 Methods Applied to the Calculation of the Dissociation Energy Curve of Noncovalently-Interacting Systems Phys. Chem. Chem. Phys. 2013, 15 (37) 15485– 15493 DOI: 10.1039/c3cp51431e
  There is no corresponding record for this reference.
314. 314
  Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van Der Waals Complexes Chem. Rev. 1994, 94 (7) 1887– 1930 DOI: 10.1021/cr00031a008
  314
  Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes
  Jeziorski, Bogumil; Moszynski, Robert; Szalewicz, Krzysztof
  Chemical Reviews (Washington, DC, United States) (1994), 94 (7), 1887-930CODEN: CHREAY; ISSN:0009-2665.
  The topics reviewed with 445 refs. include: polarization theory; exchange effects; multipole expansion of the interaction energy; charge-overlap effects and bipolar expansion of polarization energies; the intramonomer electron correlation problem and many-body formulation of symmetry-adapted perturbation theory; and applications.
315. 315
  Misquitta, A. J.; Podeszwa, R.; Jeziorski, B.; Szalewicz, K. Intermolecular Potentials Based on Symmetry-Adapted Perturbation Theory with Dispersion Energies from Time-Dependent Density-Functional Calculations J. Chem. Phys. 2005, 123 (21) 214103 DOI: 10.1063/1.2135288
  315
  Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations
  Misquitta, Alston J.; Podeszwa, Rafal; Jeziorski, Bogumil; Szalewicz, Krzysztof
  Journal of Chemical Physics (2005), 123 (21), 214103/1-214103/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Recently, three of us have proposed a method [Phys. Rev. Lett. 91, 33201 (2003)] for an accurate calcn. of the dispersion energy utilizing frequency-dependent d. susceptibilities of monomers obtained from time-dependent d.-functional theory (DFT). In the present paper, we report numerical calcns. for the helium, neon, water, and carbon dioxide dimers and show that for a wide range of intermonomer sepns., including the van der Waals and short-range repulsion regions, the method provides dispersion energies with accuracies comparable to those that can be achieved using the current most sophisticated wave-function methods. If the dispersion energy is combined with (i) the electrostatic and first-order exchange interaction energies as defined in symmetry-adapted perturbation theory (SAPT) but computed using monomer Kohn-Sham (KS) determinants, and (ii) the induction energy computed using the coupled KS static response theory, (iii) the exchange-induction and exchange-dispersion energies computed using KS orbitals and orbital energies, the resulting method, denoted by SAPT(DFT), produces very accurate total interaction potentials. For the helium dimer, the only system with nearly exact benchmark values, SAPT(DFT) reproduces the interaction energy to within about 2% at the min. and to a similar accuracy for all other distances ranging from the strongly repulsive to the asymptotic region. For the remaining systems investigated by us, the quality of the SAPT(DFT) interaction energies is so high that these energies may actually be more accurate than the best available results obtained with wave-function techniques. At the same time, SAPT(DFT) is much more computationally efficient than any method previously used for calcg. the dispersion and other interaction energy components at this level of accuracy.
316. 316
  Hesselmann, A.; Jansen, G.; Schütz, M. Interaction Energy Contributions of H-Bonded and Stacked Structures of the AT and GC DNA Base Pairs from the Combined Density Functional Theory and Intermolecular Perturbation Theory Approach J. Am. Chem. Soc. 2006, 128 (36) 11730– 11731 DOI: 10.1021/ja0633363
  There is no corresponding record for this reference.
317. 317
  Rezáč, J.; Riley, K. E.; Hobza, P. S66: A Well-Balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures J. Chem. Theory Comput. 2011, 7 (8) 2427– 2438 DOI: 10.1021/ct2002946
  317
  S66: A Well-balanced Database of Benchmark Interaction Energies Relevant to Biomolecular Structures
  Rezac, Jan; Riley, Kevin E.; Hobza, Pavel
  Journal of Chemical Theory and Computation (2011), 7 (8), 2427-2438CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  With numerous new quantum chem. methods being developed in recent years and the promise of even more new methods to be developed in the near future, it is clearly crit. that highly accurate, well-balanced, ref. data for many different at. and mol. properties be available for the parametrization and validation of these methods. One area of research that is of particular importance in many areas of chem., biol., and material science is the study of noncovalent interactions. Because these interactions are often strongly influenced by correlation effects, it is necessary to use computationally expensive high-order wave function methods to describe them accurately. Here, the authors present a large new database of interaction energies calcd. using an accurate CCSD(T)/CBS scheme. Data are presented for 66 mol. complexes, at their ref. equil. geometries and at 8 points systematically exploring their dissocn. curves; in total, the database contains 594 points: 66 at equil. geometries, and 528 in dissocn. curves. The data set is designed to cover the most common types of noncovalent interactions in biomols., while keeping a balanced representation of dispersion and electrostatic contributions. The data set is therefore well suited for testing and development of methods applicable to bioorg. systems. In addn. to the benchmark CCSD(T) results, the authors also provide decompns. of the interaction energies by DFT-SAPT calcns. The data set was used to test several correlated QM methods, including those parametrized specifically for noncovalent interactions. Among these, the SCS-MI-CCSD method outperforms all other tested methods, with a root-mean-square error of 0.08 kcal/mol for the S66 data set.
318. 318
  Sinnokrot, M. O.; Sherrill, C. D. Substituent Effects in Π–π Interactions: Sandwich and T-Shaped Configurations J. Am. Chem. Soc. 2004, 126 (24) 7690– 7697 DOI: 10.1021/ja049434a
  318
  Substituent Effects in π-π Interactions: Sandwich and T-Shaped Configurations
  Sinnokrot, Mutasem Omar; Sherrill, C. David
  Journal of the American Chemical Society (2004), 126 (24), 7690-7697CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Sandwich and T-shaped configurations of benzene dimer, benzene-phenol, benzene-toluene, benzene-fluorobenzene, and benzene-benzonitrile are studied by coupled-cluster theory to elucidate how substituents tune π-π interactions. All substituted sandwich dimers bind more strongly than benzene dimer, whereas the T-shaped configurations bind more or less favorably depending on the substituent. Symmetry-adapted perturbation theory (SAPT) indicates that electrostatic, dispersion, induction, and exchange-repulsion contributions are all significant to the overall binding energies, and all but induction are important in detg. relative energies. Models of π-π interactions based solely on electrostatics, such as the Hunter-Sanders rules, do not seem capable of explaining the energetic ordering of the dimers considered.
319. 319
  Sure, R.; Grimme, S. Corrected Small Basis Set Hartree-Fock Method for Large Systems J. Comput. Chem. 2013, 34 (19) 1672– 1685 DOI: 10.1002/jcc.23317
  319
  Corrected small basis set Hartree-Fock method for large systems
  Sure, Rebecca; Grimme, Stefan
  Journal of Computational Chemistry (2013), 34 (19), 1672-1685CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  A quantum chem. method based on a Hartree-Fock calcn. with a small Gaussian AO basis set is presented. Its main area of application is the computation of structures, vibrational frequencies, and noncovalent interaction energies in huge mol. systems. The method is suggested as a partial replacement of semiempirical approaches or d. functional theory (DFT) in particular when self-interaction errors are acute. In order to get accurate results three phys. plausible atom pair-wise correction terms are applied for London dispersion interactions (D3 scheme), basis set superposition error (gCP scheme), and short-ranged basis set incompleteness effects. In total nine global empirical parameters are used. This so-called Hartee-Fock-3c (HF-3c) method is tested for geometries of small org. mols., interaction energies and geometries of noncovalently bound complexes, for supramol. systems, and protein structures. In the majority of realistic test cases good results approaching large basis set DFT quality are obtained at a tiny fraction of computational cost. © 2013 Wiley Periodicals, Inc.
320. 320
  Goerigk, L.; Collyer, C. A.; Reimers, J. R. Recommending Hartree–Fock Theory with London-Dispersion and Basis-Set-Superposition Corrections for the Optimization or Quantum Refinement of Protein Structures J. Phys. Chem. B 2014, 118 (50) 14612– 14626 DOI: 10.1021/jp510148h
  There is no corresponding record for this reference.
321. 321
  Brandenburg, J.; Grimme, S. Dispersion Corrected Hartree-Fock and Density Functional Theory for Organic Crystal Structure Prediction Top. Curr. Chem. 2013, 345, 1 DOI: 10.1007/128_2013_488
  There is no corresponding record for this reference.
322. 322
  Brandenburg, J. G.; Hochheim, M.; Bredow, T.; Grimme, S. Low-Cost Quantum Chemical Methods for Noncovalent Interactions J. Phys. Chem. Lett. 2014, 5 (24) 4275– 4284 DOI: 10.1021/jz5021313
  322
  Low-Cost Quantum Chemical Methods for Noncovalent Interactions
  Brandenburg, Jan Gerit; Hochheim, Manuel; Bredow, Thomas; Grimme, Stefan
  Journal of Physical Chemistry Letters (2014), 5 (24), 4275-4284CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  A review. The efficient and reasonably accurate description of noncovalent interactions is important for various areas of chem., ranging from supramol. host-guest complexes and biomol. applications to the challenging task of crystal structure prediction. While London dispersion inclusive d. functional theory (DFT-D) can be applied, faster "low-cost" methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical mol.-orbital-based methods. Various levels of approxns. are discussed based either on canonical Hartree-Fock or on semilocal d. functionals. The performance for intermol. interactions is examd. on various small to large mol. complexes and org. solids covering many different chem. groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle d. functional theory results. The mean unsigned deviations of binding energies from ref. data are typically 10-30%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.
323. 323
  Grimme, S.; Brandenburg, J. G.; Bannwarth, C.; Hansen, A. Consistent Structures and Interactions by Density Functional Theory with Small Atomic Orbital Basis Sets J. Chem. Phys. 2015, 143 (5) 054107 DOI: 10.1063/1.4927476
  323
  Consistent structures and interactions by density functional theory with small atomic orbital basis sets
  Grimme, Stefan; Brandenburg, Jan Gerit; Bannwarth, Christoph; Hansen, Andreas
  Journal of Chemical Physics (2015), 143 (5), 054107/1-054107/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A d. functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chem. systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approxn. in a modified global hybrid functional with a relatively large amt. of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta AO Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold cor. (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a phys. sound and asymptotically correct manner. PBEh-3c yields good results for thermochem. properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equil. structures, a new compilation of std. test sets is suggested. These consist of small (light) mols., partially flexible, medium-sized org. mols., mols. comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate ref. data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calcns. conducted for mol. crystals to test structures (including cell vols.) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calcns. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theor. chem. and physics. (c) 2015 American Institute of Physics.
324. 324
  Stewart, J. J. Optimization of Parameters for Semiempirical Methods I. Method J. Comput. Chem. 1989, 10 (2) 209– 220 DOI: 10.1002/jcc.540100208
  324
  Optimization of parameters for semiempirical methods. I. Method
  Stewart, James J. P.
  Journal of Computational Chemistry (1989), 10 (2), 209-20CODEN: JCCHDD; ISSN:0192-8651.
  A new method for obtaining optimized parameters for semiempirical methods is developed and applied to the MNDO method. The method uses derivs. of calcd. values for properties with respect to adjustable parameters to obtain the optimized values of parameters. The large increase in speed is a result of using a simple series expression for calcd. values of properties rather than employing full semiempirical calcns. With this optimization procedure, the rate-detg. step for parameterizing elements changes from the mechanics of parameterization to the assembling of exptl. ref. data.
325. 325
  Weber, W.; Thiel, W. Orthogonalization Corrections for Semiempirical Methods Theor. Chem. Acc. 2000, 103 (6) 495– 506 DOI: 10.1007/s002149900083
  325
  Orthogonalization corrections for semiempirical methods
  Weber, Wolfgang; Thiel, Walter
  Theoretical Chemistry Accounts (2000), 103 (6), 495-506CODEN: TCACFW; ISSN:1432-881X. (Springer-Verlag)
  Based on a general discussion of orthogonalization effects, two new one-electron orthogonalization corrections are derived to improve existing semiempirical models at the NDDO level. The first one accounts for valence-shell orthogonalization effects on the resonance integrals, while the second one includes the dominant repulsive core-valence interactions through an effective core potential. The corrections for the resonance integrals consist of three-center terms which incorporate stereodiscriminating properties into the two-center matrix elements of the core Hamiltonian. They provide a better description of conformational properties, which is rationalized qual. and demonstrated through numerical calcns. on small model systems. The proposed corrections are part of a new general-purpose semiempirical method which will be described elsewhere.
326. 326
  Stewart, J. J. Optimization of Parameters for Semiempirical Methods VI: More Modifications to the NDDO Approximations and Re-Optimization of Parameters J. Mol. Model. 2013, 19 (1) 1– 32 DOI: 10.1007/s00894-012-1667-x
  326
  Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters
  Stewart, James J. P.
  Journal of Molecular Modeling (2013), 19 (1), 1-32CODEN: JMMOFK; ISSN:0948-5023. (Springer)
  Modern semiempirical methods are of sufficient accuracy when used in the modeling of mols. of the same type as used as ref. data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using exptl. and high-level ab initio ref. data, augmented by a new type of ref. data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approxns.: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Av. unsigned errors (AUEs) in geometry and ΔH f for PM7 were reduced relative to PM6; for simple gas-phase org. systems, the AUE in bond lengths decreased by about 5 % and the AUE in ΔH f decreased by about 10 %; for org. solids, the AUE in ΔH f dropped by 60 % and the redn. was 33.3 % for geometries. A two-step process (PM7-TS) for calcg. the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple org. reactions was decreased from values of 12.6 kcal/mol-1 in PM6 and 10.8 kcal/mol-1 in PM7 to 3.8 kcal/mol-1. The origins of the errors in NDDO methods have been examd., and were found to be attributable to inadequate and inaccurate ref. data. This conclusion provides insight into how these methods can be improved.
327. 327
  Tuttle, T.; Thiel, W. OM X-D: Semiempirical Methods with Orthogonalization and Dispersion Corrections. Implementation and Biochemical Application Phys. Chem. Chem. Phys. 2008, 10 (16) 2159– 2166 DOI: 10.1039/b718795e
  There is no corresponding record for this reference.
328. 328
  Thiel, W. Semiempirical Quantum–chemical Methods Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4 (2) 145– 157 DOI: 10.1002/wcms.1161
  328
  Semiempirical quantum-chemical methods
  Thiel, Walter
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (2), 145-157CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  The semiempirical methods of quantum chem. are reviewed, with emphasis on established NDDO-based methods (MNDO, AM1, PM3) and on the more recent orthogonalization-cor. methods (OM1, OM2, OM3). After a brief historical overview, the methodol. is presented in nontech. terms, covering the underlying concepts, parameterization strategies, and computational aspects, as well as linear scaling and hybrid approaches. The application section addresses selected recent benchmarks and surveys ground-state and excited-state studies, including recent OM2-based excited-state dynamics investigations.
329. 329
  Řezáč, J.; Fanfrlík, J.; Salahub, D.; Hobza, P. Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes J. Chem. Theory Comput. 2009, 5 (7) 1749– 1760 DOI: 10.1021/ct9000922
  329
  Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes
  Rezac, Jan; Fanfrlik, Jindrich; Salahub, Dennis; Hobza, Pavel
  Journal of Chemical Theory and Computation (2009), 5 (7), 1749-1760CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Because of its construction and parametrization for more than 80 elements, the semiempirical quantum chem. PM6 method is superior to other similar methods. Despite its advantages, however, the PM6 method fails for the description of noncovalent interactions, specifically the dispersion energy and H-bonding. Upon inclusion of correction terms for dispersion and H-bonding, the performance of the method was found to be dramatically improved. The former correction included two parameters in the damping function that were parametrized to reproduce the benchmark interaction energies [CCSD(T)/complete basis set (CBS) limit] of the dispersion-bonded complexes from the S22 data set. The latter correction was parametrized on an extended set of H-bonded stabilization energies detd. at the MP2/cc-pVTZ level. The resulting PM6-DH method was tested on the S22 data set, for which chem. accuracy (error < 1 kcal/mol) was achieved, and also on the JSCH2005 set, for which significant improvement over the original PM6 method was also obtained. Implementation of anal. gradients allows very efficient geometry optimization, which, for all complexes, provides better agreement with the benchmark data. Excellent results were also achieved for small peptides, and here again, chem. accuracy was obtained (i.e., the error with respect to CCSD(T)/CBS results was smaller than 1 kcal/mol). The performance of the technique was finally demonstrated on extended complexes, namely, the porphine dimer and various graphene models with DNA bases and base pairs, where the PM6-DH stabilization energies agree very well with available benchmark data obtained with DFT-D, SCS-MP2, and MP2.5 methods. The PM6-DH calcns. are very efficient and can be routinely applied for systems of up to 1000 atoms. For nonarom. systems, the use of a linear scaling version of the SCF procedure based on localized orbitals speeds up the method significantly and allows one to investigate systems with several thousand atoms. The method can thus replace force fields, which face basic problems for the description of quantum effects, in many applications.
330. 330
  Korth, M.; Pitoňák, M.; Řezáč, J.; Hobza, P. A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods J. Chem. Theory Comput. 2010, 6 (1) 344– 352 DOI: 10.1021/ct900541n
  330
  A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods
  Korth, Martin; Pitonak, Michal; Rezac, Jan; Hobza, Pavel
  Journal of Chemical Theory and Computation (2010), 6 (1), 344-352CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Semiempirical methods could offer a feasible compromise between ab initio and empirical approaches for the calcn. of large mols. with biol. relevance. A key problem for attempts in this direction is the rather bad performance of current semiempirical methods for noncovalent interactions, esp. hydrogen-bonding. On the basis of the recently introduced PM6-DH method, which includes empirical corrections for dispersion (D) and hydrogen-bond (H) interactions, we have developed an improved and transferable H-bonding correction for semiempirical quantum chem. methods. The performance of the improved correction is evaluated for PM6, AM1, OM3, and SCC-DFTB (enhanced by std. empirical dispersion corrections) with several test sets for noncovalent interactions and is shown to reach the quality of current DFT-D approaches for these types of problems.
331. 331
  Porezag, D.; Frauenheim, T.; Köhler, T.; Seifert, G.; Kaschner, R. Construction of Tight-Binding-like Potentials on the Basis of Density-Functional Theory: Application to Carbon Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51 (19) 12947 DOI: 10.1103/PhysRevB.51.12947
  331
  Construction of tight-binding-like potentials on the basis of density-functional theory: application to carbon
  Porezag, D.; Frauenheim, Th.; Koehler, Th.; Seifert, G.; Kaschner, R.
  Physical Review B: Condensed Matter (1995), 51 (19), 12947-57CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The authors present a d.-functional-based scheme for detg. the necessary parameters of common nonorthogonal tight-binding (TB) models within the framework of the LCAO formalism using the local-d. approxn. (LDA). By only considering two-center integrals the Hamiltonian and overlap matrix elements are calcd. out of suitable input densities and potentials rather than fitted to exptl. data. Anal. functions can be derived for the C-C, C-H, and H-H Hamiltonians and overlap matrix elements. The usual short-range repulsive potential appearing in most TB models is fitted to self-consistent calcns. performed within the LDA. The calcn. of forces is easy and allows an application of the method to mol.-dynamics simulations. Despite its extreme simplicity, the method is transferable to complex carbon and hydrocarbon systems. The detn. of equil. geometries, total energies, and vibrational modes of carbon clusters, hydrocarbon mols., and solid-state modifications of carbon yield results showing an overall good agreement with more sophisticated methods.
332. 332
  Seifert, G.; Porezag, D.; Frauenheim, T. Calculations of Molecules, Clusters, and Solids with a Simplified LCAO-DFT-LDA Scheme Int. J. Quantum Chem. 1996, 58 (2) 185– 192 DOI: 10.1002/(SICI)1097-461X(1996)58:2<185::AID-QUA7>3.3.CO;2-B
  There is no corresponding record for this reference.
333. 333
  Elstner, M.; Hobza, P.; Frauenheim, T.; Suhai, S.; Kaxiras, E. Hydrogen Bonding and Stacking Interactions of Nucleic Acid Base Pairs: A Density-Functional-Theory Based Treatment J. Chem. Phys. 2001, 114 (12) 5149– 5155 DOI: 10.1063/1.1329889
  333
  Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment
  Elstner, Marcus; Hobza, Pavel; Frauenheim, Thomas; Suhai, Sandor; Kaxiras, Efthimios
  Journal of Chemical Physics (2001), 114 (12), 5149-5155CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We extend an approx. d. functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irresp. of the correlation function applied. An empirical formula, consisting of an R-6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coeff., which is calcd. from exptl. at. polarizabilities, can be consistently added to the total energy expression of the method. We apply this approx. DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.
334. 334
  Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, T.; Suhai, S.; Seifert, G. Self-Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Complex Materials Properties Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58 (11) 7260 DOI: 10.1103/PhysRevB.58.7260
  334
  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties
  Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.
  Physical Review B: Condensed Matter and Materials Physics (1998), 58 (11), 7260-7268CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  We outline details about an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability. The method is based on a second-order expansion of the Kohn-Sham total energy in d.-functional theory (DFT) with respect to charge-d. fluctuations. The zeroth-order approach is equiv. to a common std. non-self-consistent (TB) scheme, while at second-order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual "band structure" and short-range repulsive terms the final approx. Kohn-Sham energy addnl. includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approx. includes self-interaction contributions of a given atom if the charges are located at one and the same atom. We apply the new SCC scheme to problems where deficiencies within the non-SCC std. TB approach become obvious. We thus considerably improve transferability.
335. 335
  Kunsági-Máté, S.; Ortmann, E.; Kollár, L.; Szabó, K.; Nikfardjam, M. P. Effect of Ferrous and Ferric Ions on Copigmentation in Model Solutions J. Mol. Struct. 2008, 891 (1–3) 471– 474 DOI: 10.1016/j.molstruc.2008.04.036
  There is no corresponding record for this reference.
336. 336
  Bondi, A. J. Van Der Waals Volumes and Radii J. Phys. Chem. 1964, 68 (3) 441– 451 DOI: 10.1021/j100785a001
  336
  van der Waals volumes and radii
  Bondi, A.
  Journal of Physical Chemistry (1964), 68 (3), 441-51CODEN: JPCHAX; ISSN:0022-3654.
  Intermol. van der Waals radii of the nonmetallic elements were assembled into a list of recommended values for vol. calcns. These values were arrived at by selecting from the most reliable x-ray diffraction data those which could be reconciled with crystal d. at 0°K. (to give reasonable packing d.), gas kinetic collision cross section, crit. d., and with liquid state properties. A qual. understanding of the nature of van der Waals radii is provided by correlation with the de Broglie wavelength of the outermost valence electron. Tentative values for the van der Waals radii of metallic elements in organometallic compds. are proposed. A list of increments for the vol. of mols. impenetrable to thermal collision, the so-called van der Waals vol., and of the corresponding increments in area per mol. is given.
337. 337
  As seen in previous sections, we are aware that in principle, CCSD(T), or other methods such as QMC, are more desirable. However, such methods are currently too computationally demanding to be applied to real-world copigmentation systems.
  There is no corresponding record for this reference.
338. 338
  Freitas, A. A.; Shimizu, K.; Dias, L. G.; Quina, F. H. A Computational Study of Substituted Flavylium Salts and Their Quinonoidal Conjugate-Bases: S0→S1 Electronic Transition, Absolute pKa and Reduction Potential Calculations by DFT and Semiempirical Methods J. Braz. Chem. Soc. 2007, 18 (8) 1537– 1546 DOI: 10.1590/S0103-50532007000800014
  338
  A computational study of substituted flavylium salts and their quinonoidal conjugate-bases: S0→S1 electronic transition, absolute pKa and reduction potential calculations by DFT and semiempirical methods
  Freitas, Adilson A.; Shimizu, K.; Dias, Luis G.; Quina, Frank H.
  Journal of the Brazilian Chemical Society (2007), 18 (8), 1537-1546CODEN: JOCSET; ISSN:0103-5053. (Sociedade Brasileira de Quimica)
  The electronic transitions for flavylium cations and quinonoidal bases of 17 substituted flavylium salts have been studied at semiempirical and DFT (d. functional theory) levels. Solvent effect on electronic spectra was included by Polarizable Continuum Model, PCM. We assigned longest-wavelength absorption maxima to HOMO→LUMO transition. Both levels of theory gave good results for electronic transitions of flavylium cations whereas only TDDFT-PCM calcns. could be used for electronic transitions of their quinonoidal bases. We also performed abs. pKa calcns. of nine flavylium salts at DFT level. The pKa calcd. values by our PCM parameterization gave excellent results with mean abs. deviation less than a half of one pKa unit. One-electron redn. potentials were carried out for 5 flavylium cations at DFT level. The theor. results found were in good agreement with exptl. values after adjustment for a systematic deviation.
339. 339
  Sakata, K.; Saito, N.; Honda, T. Ab Initio Study of Molecular Structures and Excited States in Anthocyanidins Tetrahedron 2006, 62 (15) 3721– 3731 DOI: 10.1016/j.tet.2006.01.081
  339
  Ab initio study of molecular structures and excited states in anthocyanidins
  Sakata, Ken; Saito, Norio; Honda, Toshio
  Tetrahedron (2006), 62 (15), 3721-3731CODEN: TETRAB; ISSN:0040-4020. (Elsevier B.V.)
  The structural and electronic characters of four types of hydroxyl group-substituted anthocyanidins (pelargonidin, cyanidin, delphinidin, and aurantinidin) were examd. using quantum chem. calcns. For these cationic mols., both the planar and non-planar structures in the electronic ground state were detd. at the B3LYP/D95 level of theory. We revealed that the planar structure is slightly more stable than the non-planar structure for each mol. For the optimized planar structures, single excitation-CI (SE-CI) based on the RHF (RHF) wave function was evaluated and the electronic character in the low-excited states was discussed in terms of the MO theory. Symmetry adapted cluster (SAC)/SAC-CI calcns. were also carried out to est. the excitation energies precisely. The results showed that hydroxylation of the Ph group causes a change in the excitation energies without taking the solvent effects into account. The results are in agreement with spectral expts. and previous MO calcns.
340. 340
  Anouar, E. H.; Gierschner, J.; Duroux, J.-L.; Trouillas, P. UV/Visible Spectra of Natural Polyphenols: A Time-Dependent Density Functional Theory Study Food Chem. 2012, 131 (1) 79– 89 DOI: 10.1016/j.foodchem.2011.08.034
  340
  UV/Visible spectra of natural polyphenols: A time-dependent density functional theory study
  Anouar, El Hassane; Gierschner, Johannes; Duroux, Jean-Luc; Trouillas, Patrick
  Food Chemistry (2012), 131 (1), 79-89CODEN: FOCHDJ; ISSN:0308-8146. (Elsevier Ltd.)
  In addn. to their numerous biol. activities, natural and hemisynthetic polyphenols contribute to the large variety of colors (from red to violet) in nature (e.g., fruit, vegetables, leaves and petals). In order to understand the color variation attributed to the multitude of chem. structures of this wide class of compds., time-dependent d. functional quantum-chem. calcns. at the B3P86/6-311+G(d,p) level of theory appears as a relevant and efficient tool. The UV/Vis properties of 33 polyphenols were systematically investigated, including mainly flavonoids, isoflavonoids and flavonolignans. On the basis of MO anal. we established the structure-property relationship, inter alia showing the role of π orbital (de-)localization, mesomeric (+M) effects of hydroxyl groups and structural modification of the mol. backbone. The results might help in the future, for example, for the prediction of novel hemisynthetic compds.
341. 341
  Millot, M.; Di Meo, F.; Tomasi, S.; Boustie, J.; Trouillas, P. Photoprotective Capacities of Lichen Metabolites: A Joint Theoretical and Experimental Study. J. Photochem. Photobiol., B 111, 17– 26. DOI: 10.1016/j.jphotobiol.2012.03.005
  There is no corresponding record for this reference.
342. 342
  Carvalho, A. R. F.; Oliveira, J.; De Freitas, V.; Mateus, N.; Melo, A. Unusual Color Change of Vinylpyranoanthocyanin–Phenolic Pigments J. Agric. Food Chem. 2010, 58 (7) 4292– 4297 DOI: 10.1021/jf904246g
  There is no corresponding record for this reference.
343. 343
  Quartarolo, A. D.; Russo, N. A Computational Study (TDDFT and RICC2) of the Electronic Spectra of Pyranoanthocyanins in the Gas Phase and Solution J. Chem. Theory Comput. 2011, 7 (4) 1073– 1081 DOI: 10.1021/ct2000974
  343
  A Computational Study (TDDFT and RICC2) of the Electronic Spectra of Pyranoanthocyanins in the Gas Phase and Solution
  Quartarolo, Angelo Domenico; Russo, Nino
  Journal of Chemical Theory and Computation (2011), 7 (4), 1073-1081CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The conformational structures and UV-vis absorption electronic spectra of a class of derived anthocyanin mols. (pyranoanthocyanins) have been investigated mainly by means of d. functional (DFT) and time-dependent DFT methods. Pyranoanthocyanins are natural pigments present in aged wines and absorb at shorter wavelengths (around 500 nm) than the parent anthocyanin compds., giving an orange-brown colored soln. The investigated mols. are derived from the reaction of glycosylated malvidin, peonidin, and petunidin with enolizable mols. (acetaldehyde and pyruvic acid) and vinyl derivs. During wine storage, the concn. of pyranoanthocyanins increases with time, and anal. measurements (e.g., UV-vis spectroscopy) can characterize aged wines by color anal. The prediction of absorption electronic spectra from TDDFT results, with the inclusion of water bulk solvation effects through the conductor-like polarizable continuum model, gives an abs. mean deviation from exptl. absorption maxima of 0.1 eV and a good reprodn. of the spectra line shape over the visible range of the spectrum. TDDFT calcd. excitation energies agree with those obtained from ab initio multireference coupled cluster with the resoln. of identity approxn. (RICC2) methods, calcd. at DFT gas-phase geometries.
344. 344
  Milián-Medina, B.; Gierschner, J. Computational Design of Low Singlet–triplet Gap All-Organic Molecules for OLED Application Org. Electron. 2012, 13 (6) 985– 991 DOI: 10.1016/j.orgel.2012.02.010
  344
  Computational design of low singlet-triplet gap all-organic molecules for OLED application
  Milian-Medina, Begona; Gierschner, Johannes
  Organic Electronics (2012), 13 (6), 985-991CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
  It was recently reported that external quantum efficiency in org. LEDs can be substantially enhanced when triplet excitons are harvested through upconversion by E-type delayed fluorescence in materials with small singlet-triplet energy gap ΔEST, based on donor-acceptor (DA) chromophores. Furthermore, org. solar cells (OSCs) might profit from such materials in order to reduce recombination losses. However, targeted design rules for such materials are missing up to now. In this paper, we follow a facile (TD-)DFT-based computational design concept by engineering the fragment frontier orbitals in DA systems. The calcns. show that optimized systems with very small ΔEST in the range of kT can be achieved by balancing the energetic offset between fragment MOs as well as through the nature of the DA connector. Application in OLED will addnl. require small non-radiative rates, which recommends large bandgap materials. Utilization in polymeric DA systems with small ΔEST in OSCs requires the full exploration of the chain length dependence of the resp. oligomers.
345. 345
  Dreuw, A.; Weisman, J. L.; Head-Gordon, M. Long-Range Charge-Transfer Excited States in Time-Dependent Density Functional Theory Require Non-Local Exchange J. Chem. Phys. 2003, 119 (6) 2943– 2946 DOI: 10.1063/1.1590951
  345
  Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange
  Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin
  Journal of Chemical Physics (2003), 119 (6), 2943-2946CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The electrostatic attraction between the sepd. charges in long-range excited charge-transfer states originates from the non-local Hartree-Fock exchange potential and is, thus, a non-local property. Present-day time-dependent d. functional theory employing local exchange-correlation functionals does not capture this effect and therefore fails to describe charge-transfer excited states correctly. A hybrid method that is qual. correct is described.
346. 346
  Dreuw, A.; Head-Gordon, M. Single-Reference Ab Initio Methods for the Calculation of Excited States of Large Molecules Chem. Rev. 2005, 105 (11) 4009– 4037 DOI: 10.1021/cr0505627
  346
  Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules
  Dreuw, Andreas; Head-Gordon, Martin
  Chemical Reviews (Washington, DC, United States) (2005), 105 (11), 4009-4037CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review of single-ref. ab initio excited state methods, which are applicable to large mols. and do not explicitly include correlation through the ground-state wave function. CIS, TDHF, and TDDFT are rigorously introduced by outlining their derivations and theor. footing, where special emphasis is put on their relations to each other. Different methods for the anal. of complicated electronically excited states are reviewed and comparatively discussed. The applicability of the presented methods is outlined, their limitations are show, and out their strengths and weaknesses are pointed out.
347. 347
  Casida, M. E.; Gutierrez, F.; Guan, J.; Gadea, F.-X.; Salahub, D.; Daudey, J.-P. Charge-Transfer Correction for Improved Time-Dependent Local Density Approximation Excited-State Potential Energy Curves: Analysis within the Two-Level Model with Illustration for H2 and LiH J. Chem. Phys. 2000, 113 (17) 7062– 7071 DOI: 10.1063/1.1313558
  347
  Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 and LiH
  Casida, Mark E.; Gutierrez, Fabien; Guan, Jingang; Gadea, Florent-Xavier; Salahub, Dennis; Daudey, Jean-Pierre
  Journal of Chemical Physics (2000), 113 (17), 7062-7071CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Time-dependent d.-functional theory (TDDFT) is an increasingly popular approach for calcg. mol. excitation energies. However, the TDDFT lowest triplet excitation energy, ωT, of a closed-shell mol. often falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphys. behavior occurs because ωT2 must become neg. wherever symmetry breaking lowers the energy of the ground state soln. below that of the symmetry unbroken soln. We use the fact that the ΔSCF method gives a qual. correct first triplet excited state to derive a "charge-transfer correction" (CTC) for the time-dependent local d. approxn. (TDLDA) within the two-level model and the Tamm-Dancoff approxn. (TDA). Although this correction would not be needed for the exact exchange-correlation functional, it is evidently important for a correct description of mol. excited state potential energy surfaces in the TDLDA. As a byproduct of our anal., we show why TDLDA and LDA ΔSCF excitation energies are often very similar near the equil. geometries. The reasoning given here is fairly general and it is expected that similar corrections will be needed in the case of generalized gradient approxns. and hybrid functionals.
348. 348
  Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid Exchange–correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP) Chem. Phys. Lett. 2004, 393 (1–3) 51– 57 DOI: 10.1016/j.cplett.2004.06.011
  348
  A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
  Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
  Chemical Physics Letters (2004), 393 (1-3), 51-57CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
  A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the std. error function with parameter 0.33.
349. 349
  Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped Atom–atom Dispersion Corrections Phys. Chem. Chem. Phys. 2008, 10 (44) 6615– 6620 DOI: 10.1039/b810189b
  349
  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
  Chai, Jeng-Da; Head-Gordon, Martin
  Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
350. 350
  Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Double-Hybrid Density Functionals J. Chem. Phys. 2009, 131 (17) 174105 DOI: 10.1063/1.3244209
  350
  Long-range corrected double-hybrid density functionals
  Chai, Jeng-Da; Head-Gordon, Martin
  Journal of Chemical Physics (2009), 131 (17), 174105/1-174105/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We extend the range of applicability of our previous long-range cor. (LC) hybrid functional, ωB97X, with a nonlocal description of electron correlation, inspired by second-order Moller-Plesset (many-body) perturbation theory. This LC "double-hybrid" d. functional, denoted as ωB97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calcns. using triple and quadruple zeta basis sets), and also sep. using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calcns. (as well as training set results), ωB97X-2 yields high accuracy for thermochem., kinetics, and noncovalent interactions. In addn., owing to its high fraction of exact Hartree-Fock exchange, ωB97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as sym. homonuclear radical cations. (c) 2009 American Institute of Physics.
351. 351
  Caricato, M.; Trucks, G. W.; Frisch, M. J.; Wiberg, K. B. Oscillator Strength: How Does TDDFT Compare to EOM-CCSD? J. Chem. Theory Comput. 2011, 7 (2) 456– 466 DOI: 10.1021/ct100662n
  351
  Oscillator Strength: How Does TDDFT Compare to EOM-CCSD?
  Caricato, Marco; Trucks, Gary W.; Frisch, Michael J.; Wiberg, Kenneth B.
  Journal of Chemical Theory and Computation (2011), 7 (2), 456-466CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We compare a large variety of d. functionals against the equation of motion coupled cluster singles and doubles (EOM-CCSD) method for the calcn. of oscillator strengths. Valence and Rydberg states are considered for a test set composed of 11 small org. mols. In our previous work, the same systems and methods were tested against exptl. results for the excitation energies. The results from this investigation confirm our previous findings, i.e., that there is a large difference between the functionals. For the oscillator strength, the av. best agreement with EOM-CCSD is provided by CAM-B3LYP followed by LC-ωPBE and, to a lesser extent, B3P86 and LC-BLYP.
352. 352
  Beyhan, S. M.; Götz, A. W.; Ariese, F.; Visscher, L.; Gooijer, C. Computational Study on the Anomalous Fluorescence Behavior of Isoflavones J. Phys. Chem. A 2011, 115 (9) 1493– 1499 DOI: 10.1021/jp109059e
  There is no corresponding record for this reference.
353. 353
  Malcıoğlu, O. B.; Calzolari, A.; Gebauer, R.; Varsano, D.; Baroni, S. Dielectric and Thermal Effects on the Optical Properties of Natural Dyes: A Case Study on Solvated Cyanin J. Am. Chem. Soc. 2011, 133 (39) 15425– 15433 DOI: 10.1021/ja201733v
  There is no corresponding record for this reference.
354. 354
  Petrone, A.; Cerezo, J.; Ferrer, F. J. A.; Donati, G.; Improta, R.; Rega, N.; Santoro, F. Absorption and Emission Spectral Shapes of a Prototype Dye in Water by Combining Classical/Dynamical and Quantum/Static Approaches J. Phys. Chem. A 2015, 119 (21) 5426– 5438 DOI: 10.1021/jp510838m
  There is no corresponding record for this reference.
355. 355
  Sinnecker, S.; Rajendran, A.; Klamt, A.; Diedenhofen, M.; Neese, F. Calculation of Solvent Shifts on Electronic G-Tensors with the Conductor-Like Screening Model (COSMO) and Its Self-Consistent Generalization to Real Solvents (Direct COSMO-RS) J. Phys. Chem. A 2006, 110, 2235– 2245 DOI: 10.1021/jp056016z
  355
  Calculation of Solvent Shifts on Electronic g-Tensors with the Conductor-Like Screening Model (COSMO) and Its Self-Consistent Generalization to Real Solvents (Direct COSMO-RS)
  Sinnecker, Sebastian; Rajendran, Arivazhagan; Klamt, Andreas; Diedenhofen, Michael; Neese, Frank
  Journal of Physical Chemistry A (2006), 110 (6), 2235-2245CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  The conductor-like screening model (COSMO) was used to investigate the solvent influence on electronic g-values of org. radicals. The previously studied di-Ph nitric oxide and di-tert-Bu nitric oxide radicals were taken as test cases. The calcns. employed spin-unrestricted d. functional theory and the BP and B3LYP d. functionals. The g-tensors were calcd. as mixed second deriv. properties with respect to the external magnetic field and the electron magnetic moment. The first-order response of the Kohn-Sham orbitals with respect to the external magnetic field was detd. through the coupled-perturbed DFT approach. The spin-orbit coupling operator was treated using an accurate multicenter spin-orbit mean-field (SOMF) approach. Provided that important hydrogen bonds are explicitly modeled by a supermol. approach and that the basis set is sufficiently satd., the COSMO calcns. lead to accurate predictions of isotropic g-shifts with deviations of not more than 100 ppm relative to expt. Very accurate results were obtained by employing a recently developed self-consistent modification of the COSMO method to real solvents (COSMO-RS), which we briefly introduce in this paper as direct COSMO-RS (D-COSMO-RS). This model gives isotropic g-shifts of similar high accuracy for water without using the supermol. approach. This is an important result because it solves many of the problems assocd. with the supermol. approach such as local min. and the choice of a suitable model system. Thus, the self-consistent D-COSMO-RS incorporates some specific solvation effects into continuum models, in particular it appears to successfully model the effects of hydrogen bonding. Although not yet widely validated, this opens a novel approach for the calcn. of properties which so far only could be calcd. by the inclusion of explicit solvent mols. in continuum solvation methods.
356. 356
  Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models Chem. Rev. 2005, 105, 2999– 3093 DOI: 10.1021/cr9904009
  356
  Quantum Mechanical Continuum Solvation Models
  Tomasi, Jacopo; Mennucci, Benedetta; Cammi, Roberto
  Chemical Reviews (Washington, DC, United States) (2005), 105 (8), 2999-3093CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review.
357. 357
  Ge, X.; Timrov, I.; Binnie, S.; Biancardi, A.; Calzolari, A.; Baroni, S. Accurate and Inexpensive Prediction of the Color Optical Properties of Anthocyanins in Solution J. Phys. Chem. A 2015, 119 (16) 3816– 3822 DOI: 10.1021/acs.jpca.5b01272
  There is no corresponding record for this reference.
358. 358
  Pedersen, M. N.; Hedegård, E. D.; Olsen, J. M. H.; Kauczor, J.; Norman, P.; Kongsted, J. Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method J. Chem. Theory Comput. 2014, 10 (3) 1164– 1171 DOI: 10.1021/ct400946k
  358
  Damped Response Theory in Combination with Polarizable Environments: The Polarizable Embedding Complex Polarization Propagator Method
  Pedersen, Morten N.; Hedegaard, Erik D.; Olsen, Jogvan Magnus H.; Kauczor, Joanna; Norman, Patrick; Kongsted, Jacob
  Journal of Chemical Theory and Computation (2014), 10 (3), 1164-1171CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We present a combination of the polarizable embedding (PE) scheme with the complex polarization propagator (CPP) method with the aim of calcg. response properties including relaxation for large and complex systems. This new approach, termed PE-CPP, will benefit from the highly advanced description of the environmental electrostatic potential and polarization in the PE method as well as the treatment of near-resonant effects in the CPP approach. The PE-CPP model has been implemented in a Kohn-Sham d. functional theory approach, and we present pilot calcns. exemplifying the implementation for the UV/vis and carbon K-edge X-ray absorption spectra of the protein plastocyanin. Furthermore, tech. details assocd. with a PE-CPP calcn. are discussed.
359. 359
  Olsen, J. M.; Aidas, K.; Kongsted, J. Excited States in Solution through Polarizable Embedding J. Chem. Theory Comput. 2010, 6 (12) 3721– 3734 DOI: 10.1021/ct1003803
  359
  Excited States in Solution through Polarizable Embedding
  Olsen, Jogvan Magnus; Aidas, Kestutis; Kongsted, Jacob
  Journal of Chemical Theory and Computation (2010), 6 (12), 3721-3734CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We present theory and implementation of an advanced quantum mechanics/mol. mechanics (QM/MM) approach using a fully self-consistent polarizable embedding (PE) scheme. It is a polarizable layered model designed for effective yet accurate inclusion of an anisotropic medium in a quantum mech. calcn. The polarizable embedding potential is described by an atomistic representation including terms up to localized octupoles and anisotropic polarizabilities. It is generally applicable to any quantum chem. description but is here implemented for the case of Kohn-Sham d. functional theory which we denote the PE-DFT method. It has been implemented in combination with time-dependent quantum mech. linear and nonlinear response techniques, thus allowing for assessment of electronic excitation processes and dynamic ground- and excited-state mol. properties using a nonequil. formulation of the environmental response. In our formulation of polarizable embedding we explicitly take into account the full self-consistent many-body environmental response from both ground and excited states. The PE-DFT method can be applied to any mol. system, e.g., proteins, nanoparticles and solute-solvent systems. Here, we present numerical examples of solvent shifts and excited-state properties related to a set of org. mols. in aq. soln.
360. 360
  Sjöqvist, J.; Linares, M.; Mikkelsen, K. V.; Norman, P. QM/MM-MD Simulations of Conjugated Polyelectrolytes: A Study on Luminescent Conjugated Oligothiophenes for Use as Bio-Physical Probes J. Phys. Chem. A 2014, 118 (19) 3419– 3428 DOI: 10.1021/jp5009835
  There is no corresponding record for this reference.
361. 361
  Avila Ferrer, F. J.; Cerezo, J.; Stendardo, E.; Improta, R.; Santoro, F. Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation J. Chem. Theory Comput. 2013, 9 (4) 2072– 2082 DOI: 10.1021/ct301107m
  361
  Insights for an Accurate Comparison of Computational Data to Experimental Absorption and Emission Spectra: Beyond the Vertical Transition Approximation
  Avila Ferrer, Francisco J.; Cerezo, Javier; Stendardo, Emiliano; Improta, Roberto; Santoro, Fabrizio
  Journal of Chemical Theory and Computation (2013), 9 (4), 2072-2082CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The authors carefully study the relation between computed data and exptl. electronic spectra. To that end, the authors compare both vertical transition energies, EV, and characteristic frequencies of the spectrum like the max., νmax, and the center of gravity, M1, taking advantage of an anal. expression of M1 in terms of the parameters of the initial- and final-state potential energy surfaces. After pointing out that, for an accurate comparison, exptl. spectra should be preliminarily mapped from wavelength to frequency domain and transformed to normalized lineshapes, the authors simulate the absorption and emission spectra of several prototypical chromophores, obtaining lineshapes in very good agreement with exptl. data. Results indicate that the customary comparison of exptl. νmax and computational EV, without taking into account vibrational effects, is not an adequate measure of the performance of an electronic method. In fact, it introduces systematic errors that, in the studied systems, are ∼0.1-0.3 eV, i.e., values comparable to the expected accuracy of the most accurate computational methods. On the contrary, a comparison of exptl. and computed M1 and/or 0-0 transition frequencies provides more robust results. Some rules of thumbs probably help rationalize which kind of correction 1 should expect when comparing EV, M1, and νmax.
362. 362
  Avila Ferrer, F. J.; Cerezo, J.; Soto, J.; Improta, R.; Santoro, F. First-Principle Computation of Absorption and Fluorescence Spectra in Solution Accounting for Vibronic Structure, Temperature Effects and Solvent Inhomogenous Broadening Comput. Theor. Chem. 2014, 1040–1041, 328– 337 DOI: 10.1016/j.comptc.2014.03.003
  362
  First-principle computation of absorption and fluorescence spectra in solution accounting for vibronic structure, temperature effects and solvent inhomogeneous broadening
  Avila Ferrer, Francisco Jose; Cerezo, Javier; Soto, Juan; Improta, Roberto; Santoro, Fabrizio
  Computational & Theoretical Chemistry (2014), 1040-1041 (), 328-337CODEN: CTCOA5; ISSN:2210-271X. (Elsevier B.V.)
  We compute the line shape of absorption and emission electronic spectra of two different dyes, coumarin C153 and N-methyl-6-quinolinium betaine accounting for the vibronic structure, temp. effects and polar solvent inhomogeneous broadening, without using any phenomenol. parameter. We exploit a no. of recent developments including a time-dependent (TD) approach to the computation of vibronic spectra that provides fully converged line shapes at finite temp. accounting for both Duschinsky and Herzberg-Teller effects, and the state-specific (SS) implementation of Polarizable Continuum Model (PCM). This latter is adopted to compute the solvent reorganization energy connected to inhomogeneous broadening. We compute the absorption and fluorescence spectra in the gas-phase, non-polar and polar solvents analyzing the relative importance of different sources of broadening. To this end we investigate the performance of time-dependent d. functional theory, complete active space self consistent field (CASSCF), and complete active space 2nd-order perturbation theory (CASPT2) methods in the computation of inhomogeneous broadening.

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and ExperimentClick to copy article linkArticle link copied!

Chemical Reviews

Abstract

SPECIAL ISSUE

1 Introduction

Scheme 1

2 Pigments and Copigments

2.1 Pigments

2.1.1 (Proto)typical Pigments

Figure 1

Figure 2

2.1.2 Chemistry of Anthocyanins

Figure 3

Figure 4

2.2 Copigmentation

2.2.1 Types of Copigments

Figure 5

2.2.2 Key Historical Milestones

Scheme 2

3 Pigment···Copigment Complexes in Nature

3.1 Copigmentation in Blue Flowers

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

3.2 Copigmentation in Wine

3.3 Copigmentation in Food and Beverages

4 Experimental Techniques to Analyze Copigmentation

4.1 UV–vis Absorption

Figure 13

Figure 14

Figure 15

4.2 Other Analytical Tools

5 Stability in Intermolecular Copigmentation

5.1 Structure–Affinity Relationships

5.2 Environmental Effects

5.3 Self-Association

5.4 Metal–Anthocyanin Complexes

6 Stability in Intramolecular Copigmentation

6.1 Conformational Folding of Acylated Anthocyanins

Figure 16

Figure 17

6.2 Improving the Chemical Stability of Anthocyanins by Copigmentation

7 Driving Forces of Copigmentation

8 Conformation and Thermodynamics in Copigmentation from Molecular Dynamics

8.1 Molecular Dynamics Challenges

8.1.1 Exploring Conformational Space

Figure 18

8.1.2 Biased vs Unbiased Molecular Dynamics

8.1.3 Estimation of ΔGbinding

Scheme 3

8.2 Molecular Picture of Copigmentation

8.2.1 Molecular Dynamics Based Studies: Early Stages

Figure 19

Figure 20

8.2.2 Challenges in the Theoretical Description of Copigmentation Complexes

9 Conformation and Thermodynamics in Copigmentation from Quantum Chemistry

9.1 Computing Copigmentation with DFT

Figure 21

Figure 22

9.2 Other Methods to Compute Copigmentation

9.3 Quantum Chemistry Studies on Copigmentation: Failures and Successes

9.3.1 Conformational Analysis

Figure 23

Figure 24

9.3.2 Association Energies

10 Underlying Concepts of Spectral Shifts in Copigmentation

10.1 Charge Transfer and Underlying Theory

Scheme 4

10.2 Theoretical Investigations of Spectral Shifts in Copigmentation

Figure 25

10.3 Environmental Effects and Peak Broadening

11 Concluding Remarks, Future Needs, and Applications

Author Information

Biographies

Patrick Trouillas

Juan C. Sancho-García

Stabilizing and Modulating Color by Copigmentation: Insights from Theory and Experiment
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8.1.3 Estimation of ΔG_binding