Balancing Density Functional Theory Interaction Energies in Charged Dimers Precursors to Organic Semiconductors

This article references 133 other publications.

1. 1

   Goerigk, L.; Hansen, A.; Bauer, C.; Ehrlich, S.; Najibi, A.; Grimme, S. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem. Chem. Phys. 2017, 19, 32184– 32215,  DOI: 10.1039/C7CP04913G

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   A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions

   Goerigk, Lars; Hansen, Andreas; Bauer, Christoph; Ehrlich, Stephan; Najibi, Asim; Grimme, Stefan

   Physical Chemistry Chemical Physics (2017), 19 (48), 32184-32215CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

   We present the GMTKN55 benchmark database for general main group thermochem., kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30, it allows assessment across a larger variety of chem. problems - with 13 new benchmark sets being presented for the first time - and it also provides ref. values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calcns. and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better ref. values, and we re-emphasize the need for London-dispersion corrections in d. functional theory (DFT) treatments of thermochem. problems, including Minnesota methods. We assessed 217 variations of dispersion-cor. and -uncorrected d. functional approxns., and carried out a detailed anal. of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochem. and noncovalent interactions, and they should be used whenever tech. feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalized-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.

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2. 2

   Mardirossian, N.; Head-Gordon, M. Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals. Mol. Phys. 2017, 115, 2315– 2372,  DOI: 10.1080/00268976.2017.1333644

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   Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals

   Mardirossian, Narbe; Head-Gordon, Martin

   Molecular Physics (2017), 115 (19), 2315-2372CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)

   In the past 30 years, Kohn-Sham d. functional theory has emerged as the most popular electronic structure method in computational chem. To assess the ever-increasing no. of approx. exchange-correlation functionals, this review benchmarks a total of 200 d. functionals on a mol. database (MGCDB84) of nearly 5000 data points. The database employed, provided as Supplemental Data, is comprised of 84 data-sets and contains non-covalent interactions, isomerisation energies, thermochem., and barrier heights. In addn., the evolution of non-empirical and semi-empirical d. functional design is reviewed, and guidelines are provided for the proper and effective use of d. functionals. The most promising functional considered is ωB97M-V, a range-sepd. hybrid meta-GGA with VV10 nonlocal correlation, designed using a combinatorial approach. From the local GGAs, B97-D3, revPBE-D3, and BLYP-D3 are recommended, while from the local meta-GGAs, B97M-rV is the leading choice, followed by MS1-D3 and M06-L-D3. The best hybrid GGAs are ωB97X-V, ωB97X-D3, and ωB97X-D, while useful hybrid meta-GGAs (besides ωB97M-V) include ωM05-D, M06-2X-D3, and MN15. Ultimately, today's state-of-the-art functionals are close to achieving the level of accuracy desired for a broad range of chem. applications, and the principal remaining limitations are assocd. with systems that exhibit significant self-interaction/delocalisation errors and/or strong correlation effects.

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3. 3

   Řezáč, J.; Hobza, P. Benchmark Calculations of Interaction Energies in Noncovalent Complexes and Their Applications. Chem. Rev. 2016, 116, 5038– 5071,  DOI: 10.1021/acs.chemrev.5b00526

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   Benchmark Calculations of Interaction Energies in Noncovalent Complexes and Their Applications

   Rezac, Jan; Hobza, Pavel

   Chemical Reviews (Washington, DC, United States) (2016), 116 (9), 5038-5071CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

   A review. Data sets of benchmark interaction energies in noncovalent complexes are an important tool for quantifying the accuracy of computational methods used in this field, as well as for the development of new computational approaches. This review is intended as a guide to conscious use of these data sets. We discuss their construction and accuracy, list the data sets available in the literature, and demonstrate their application to validation and parametrization of quantum-mech. computational methods. In practical model systems, the benchmark interaction energies are usually obtained using composite CCSD(T)/CBS schemes. To use these results as a benchmark, their accuracy should be estd. first. We analyze the errors of this methodol. with respect to both the approxns. involved and the basis set size. We list the most prominent data sets covering various aspects of the field, from general ones to sets focusing on specific types of interactions or systems. The benchmark data are then used to validate more efficient computational approaches, including those based on explicitly correlated methods. Special attention is paid to the transition to large systems, where accurate benchmarking is difficult or impossible, and to the importance of nonequil. geometries in parametrization of more approx. methods.

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   Grimme, S.; Hansen, A.; Brandenburg, J. G.; Bannwarth, C. Dispersion-Corrected Mean-Field Electronic Structure Methods. Chem. Rev. 2016, 116, 5105– 5154,  DOI: 10.1021/acs.chemrev.5b00533

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   Dispersion-Corrected Mean-Field Electronic Structure Methods

   Grimme, Stefan; Hansen, Andreas; Brandenburg, Jan Gerit; Bannwarth, Christoph

   Chemical Reviews (Washington, DC, United States) (2016), 116 (9), 5105-5154CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

   A review. Mean-field electronic structure methods like Hartree-Fock, semilocal d. functional approxns., or semiempirical MO theories do not account for long-range electron correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calcns. on large or condensed chem. systems and for various intramol. phenomena (thermochem.). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, d.-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on mol. complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chem. problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).

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5. 5

   Müller-Dethlefs, K.; Hobza, P. Noncovalent Interactions: A Challenge for Experiment and Theory. Chem. Rev. 2000, 100, 143– 168,  DOI: 10.1021/cr9900331

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   Noncovalent Interactions: A Challenge for Experiment and Theory

   Mueller-Dethlefs, Klaus; Hobza, Pavel

   Chemical Reviews (Washington, D. C.) (2000), 100 (1), 143-167CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

   A review with 291 refs. The topics discussed include: theor. description and exptl. methods for studying noncovalent interactions; hydrogen bond; charge transfer interaction; electrostatic force; dispersion potential; hydrophobic force; and illustrative examples.

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   Stöhr, M.; Van Voorhis, T.; Tkatchenko, A. Theory and practice of modeling van der Waals interactions in electronic-structure calculations. Chem. Soc. Rev. 2019, 48, 4118– 4154,  DOI: 10.1039/C9CS00060G

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   Theory and practice of modeling van der Waals interactions in electronic-structure calculations

   Stohr, Martin; Van Voorhis, Troy; Tkatchenko, Alexandre

   Chemical Society Reviews (2019), 48 (15), 4118-4154CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)

   The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of mols. and materials. vdW forces arise from the interaction of quantum-mech. fluctuations in the electronic charge d. Within (semi-)local d. functional approxns. or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calcns. These methods include vdW-inclusive D. Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of D. Functional Theory, including non-local van der Waals d. functionals, interat. dispersion models within many-body and pairwise formulation, and RPA-based approaches. This review aims to guide the reader through the theor. foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addn., we give an overview of complementary exptl. approaches, and discuss tools for the qual. understanding of non-covalent interactions as well as energy decompn. techniques. Besides representing a ref. for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calcns. for a general and broad audience.

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   Jurečka, P.; Šponer, J.; Černý, J.; Hobza, P. Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. Phys. Chem. Chem. Phys. 2006, 8, 1985– 1993,  DOI: 10.1039/B600027D

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   Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs

   Jurecka, Petr; Sponer, Jiri; Cerny, Jiri; Hobza, Pavel

   Physical Chemistry Chemical Physics (2006), 8 (17), 1985-1993CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

   MP2 and CCSD(T) complete basis set (CBS) limit interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes are for the first time presented together. Extrapolation to the CBS limit is done by using two-point extrapolation methods and different basis sets (aug-cc-pVDZ - aug-cc-pVTZ, aug-cc-pVTZ - aug-cc-pVQZ, cc-pVTZ - cc-pVQZ) are utilized. The CCSD(T) correction term, detd. as a difference between CCSD(T) and MP2 interaction energies, is evaluated with smaller basis sets (6-31G** and cc-pVDZ). Two sets of complex geometries were used, optimized or exptl. ones. The JSCH-2005 benchmark set, which is now available to the chem. community, can be used for testing lower-level computational methods. For the first screening the smaller training set (S22) contg. 22 model complexes can be recommended. In this case larger basis sets were used for extrapolation to the CBS limit and also CCSD(T) and counterpoise-cor. MP2 optimized geometries were sometimes adopted.

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   Podeszwa, R.; Patkowski, K.; Szalewicz, K. Improved interaction energy benchmarks for dimers of biological relevance. Phys. Chem. Chem. Phys. 2010, 12, 5974– 5979,  DOI: 10.1039/b926808a

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   Improved interaction energy benchmarks for dimers of biological relevance

   Podeszwa, Rafal; Patkowski, Konrad; Szalewicz, Krzysztof

   Physical Chemistry Chemical Physics (2010), 12 (23), 5974-5979CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

   The set of interaction energies for 22 systems of biol. importance, developed by P. Jurecka et al. (1985) and called S22, became an often used benchmark for evaluating the performance of various computational methods. As the quality of such methods improves, the uncertainties of the S22 energies are becoming too large to enable meaningful comparisons. The authors therefore improved the benchmarks by performing calcns. in larger basis sets than used by Jurecka et al. The basis extensions included addns. of higher angular momentum, diffuse, and midbond functions. The percentage deviations of the original S22 interaction energies from the authors' values are up to 15.4%. The authors have estd. that the av. (unsigned) uncertainty of the authors' results should be about 1.0%. This est. includes contributions from basis set truncation, frozen-core approxn., and neglected electron excitations.

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   Takatani, T.; Hohenstein, E. G.; Malagoli, M.; Marshall, M. S.; Sherrill, C. D. Basis set consistent revision of the S22 test set of noncovalent interaction energies. J. Chem. Phys. 2010, 132, 144104,  DOI: 10.1063/1.3378024

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   Basis set consistent revision of the S22 test set of noncovalent interaction energies

   Takatani, Tait; Hohenstein, Edward G.; Malagoli, Massimo; Marshall, Michael S.; Sherrill, C. David

   Journal of Chemical Physics (2010), 132 (14), 144104/1-144104/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

   The S22 test set of interaction energies for small model complexes has been very valuable for benchmarking new and existing methods for noncovalent interactions. However, the basis sets utilized to compute the CCSD(T) interaction energies for some of the dimers are insufficient to obtain converged results. Here we consistently extrapolate all CCSD(T)/complete basis set (CBS) interaction energies using larger basis sets for the CCSD(T) component of the computation. The revised values, which we designate S22A, represent the most accurate results to date for this set of dimers. The new values appear to be within a few hundredths of 1 kcal mol-1 of the true CCSD(T)/CBS limit at the given geometries, but the former S22 values are off by as much as 0.6 kcal mol-1 compared to the revised values. Because some of the most promising methods for noncovalent interactions are already achieving this level of agreement (or better) compared to the S22 data, more accurate benchmark values would clearly be helpful. The MP2, SCS-MP2, SCS-CCSD, SCS(MI)-MP2, and B2PLYP-D methods have been tested against the more accurate benchmark set. The B2PLYP-D method outperforms all other methods tested here, with a mean av. deviation of only 0.12 kcal mol-1. However, the consistent, slight underestimation of the interaction energies computed by the SCS-CCSD method (an overall mean abs. deviation and mean deviation of 0.24 and -0.23 kcal mol-1, resp.) suggests that the SCS-CCSD method has the potential to become even more accurate with a reoptimization of its parameters for noncovalent interactions. (c) 2010 American Institute of Physics.

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    Molnar, L. F.; He, X.; Wang, B.; Merz, K. M. Further analysis and comparative study of intermolecular interactions using dimers from the S22 database. J. Chem. Phys. 2009, 131, 065102,  DOI: 10.1063/1.3173809

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    Further analysis and comparative study of intermolecular interactions using dimers from the S22 database

    Molnar, Laszlo Fusti; He, Xiao; Wang, Bing; Merz, Kenneth M., Jr.

    Journal of Chemical Physics (2009), 131 (6), 065102/1-065102/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Accurate MP2 and CCSD(T) complete basis set (CBS) interaction energy curves (14 points for each curve) have been obtained for 20 of the dimers reported in the S22 set and anal. Morse curves have been fitted that can be used in developing updated d. functional theory (DFT) and force field models. The magnitude and the effect of the basis set superposition error (BSSE) were carefully investigated. We found that going up to aug-cc-pVDZ and aug-cc-pVTZ basis sets is enough to obtain accurate CBS MP2 energies when BSSE cor. values are used but aug-cc-pVTZ and aug-cc-pVQZ basis sets are needed when the BSSE uncorrected total energies are used in CBS extrapolations. MP2 interaction energies with smaller basis sets such as 6-31G* are found to have very little dispersion energy and that the true source of dispersion attributed attractive interactions is almost entirely due to BSSE. MP2 and CCSD(T) CBS interaction energies are found to be very close to one another if arom. systems are not involved. Comparative analyses have been performed with semiempirical and ab initio methods utilizing the moderate in size but affordable 6-31G* basis set both of which can be readily applied to macromol. systems. The new M06-2X and M06-L DFT functionals were found to be more accurate than all methods tested herein. Interaction energy curves using the SG1 grid showed discontinuities for several of the dimer systems but this problem disappeared when finer DFT numerical grids were used. (c) 2009 American Institute of Physics.

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    Gráfová, L.; Pitoňák, M.; Řezáč, J.; Hobza, P. Comparative study of selected wave function and density functional methods for noncovalent interaction energy calculations using the extended S22 data set. J. Chem. Theory Comput. 2010, 6, 2365– 2376,  DOI: 10.1021/ct1002253

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    11

    Comparative Study of Selected Wave Function and Density Functional Methods for Noncovalent Interaction Energy Calculations Using the Extended S22 Data Set

    Grafova, Lucie; Pitonak, Michal; Rezac, Jan; Hobza, Pavel

    Journal of Chemical Theory and Computation (2010), 6 (8), 2365-2376CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    In this paper, an extension of the S22 data set of Jurecka et al., the data set of benchmark CCSD(T)/CBS interaction energies of twenty-two noncovalent complexes in equil. geometries, is presented. The S22 data set has been extended by including the stretched (one shortened and three elongated) complex geometries of the S22 data set along the main noncovalent interaction coordinate. The goal of this work is to assess the accuracy of the popular wave function methods (MP2-, MP3- and, CCSD-based) and d. functional methods (with and without empirical correction for the dispersion energy) for noncovalent complexes based on a statistical evaluation not only in equil., but also in nonequil. geometries. The results obtained in this work provide information on whether an accurate and balanced description of the different interaction types and complex geometry distortions can be expected from the tested methods. This information has an important implication in the calcn. of large mol. complexes, where the no. of distant interacting mol. fragments, often in far from equil. geometries, increases rapidly with the system size. The best performing WFT methods were found to be the SCS-CCSD, MP2C, and MP2.5. Since none of the DFT methods fulfilled the required statistical criteria proposed in this work, they cannot be generally recommended for large-scale calcns. The DFT methods still have the potential to deliver accurate results for large mols., but most likely on the basis of an error cancellation.

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12. 12

    Řezáč, 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, 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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    Risthaus, T.; Grimme, S. Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes. J. Chem. Theory Comput. 2013, 9, 1580– 91,  DOI: 10.1021/ct301081n

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    Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes

    Risthaus, Tobias; Grimme, Stefan

    Journal of Chemical Theory and Computation (2013), 9 (3), 1580-1591CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    A new test set (S12L) contg. 12 supramol. noncovalently bound complexes is presented and used to evaluate seven different methods to account for dispersion in DFT (DFT-D3, DFT-D2, DFT-NL, XDM, dDsC, TS-vdW, M06-L) at different basis set levels against exptl., back-cor. ref. energies. This allows conclusions about the performance of each method in an explorative research setting on "real-life" problems. Most DFT methods show satisfactory performance but, due to the largeness of the complexes, almost always require an explicit correction for the nonadditive Axilrod-Teller-Muto three-body dispersion interaction to get accurate results. The necessity of using a method capable of accounting for dispersion is clearly demonstrated in that the two-body dispersion contributions are on the order of 20-150% of the total interaction energy. MP2 and some variants thereof are shown to be insufficient for this while a few tested D3-cor. semiempirical MO methods perform reasonably well. Overall, we suggest the use of this benchmark set as a "sanity check" against overfitting to too small mol. cases.

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14. 14

    Burns, L. A.; Vázquez-Mayagoitia, Á.; Sumpter, B. G.; Sherrill, C. D. Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals. J. Chem. Phys. 2011, 134, 084107,  DOI: 10.1063/1.3545971

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    14

    Density-functional approaches to noncovalent interactions: A comparison of dispersion corrections (DFT-D), exchange-hole dipole moment (XDM) theory, and specialized functionals

    Burns, Lori A.; Vazquez-Mayagoitia, Alvaro; Sumpter, Bobby G.; Sherrill, C. David

    Journal of Chemical Physics (2011), 134 (8), 084107/1-084107/25CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    A systematic study of techniques for treating noncovalent interactions within the computationally efficient d. functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for mol. complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT + dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of ref. interaction energies at the CCSD(T) level of theory extrapolated to the estd. complete basis set limit. The established S22 revised in and JSCH test sets of min.-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissocn. curves and a pairwise decompn. of a protein-ligand reaction site (HSG), comprise the chem. systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean abs. deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean abs. deviation of 0.33 - 0.38 kcal/mol. (c) 2011 American Institute of Physics.

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15. 15

    Marshall, M. S.; Burns, L. A.; Sherrill, C. D. Basis set convergence of the coupled-cluster correction, MP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases. J. Chem. Phys. 2011, 135, 194102,  DOI: 10.1063/1.3659142

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    15

    Basis set convergence of the coupled-cluster correction, δCCSD(T)MP2 Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

    Marshall, Michael S.; Burns, Lori A.; Sherrill, C. David

    Journal of Chemical Physics (2011), 135 (19), 194102/1-194102/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    In benchmark-quality studies of non-covalent interactions, it is common to est. interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples CCSD(T) level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δCCSD(T)MP2, evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δCCSD(T)MP2 that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δCCSD(T)MP2 correction, yielding a mean abs. deviation of 0.11 kcal mol-1 for the S22 test set. Examg. the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δCCSD(T)MP2 converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δCCSD(T)MP2 corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, esp. for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The max. differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol-1, resp. (c) 2011 American Institute of Physics.

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16. 16

    Smith, D. G. A.; Burns, L. A.; Patkowski, K.; Sherrill, C. D. Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory. J. Phys. Chem. Lett. 2016, 7, 2197– 2203,  DOI: 10.1021/acs.jpclett.6b00780

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    16

    Revised Damping Parameters for the D3 Dispersion Correction to Density Functional Theory

    Smith, Daniel G. A.; Burns, Lori A.; Patkowski, Konrad; Sherrill, C. David

    Journal of Physical Chemistry Letters (2016), 7 (12), 2197-2203CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)

    Since the original fitting of Grimme's DFT-D3 damping parameters, the no. and quality of benchmark interaction energies has increased significantly. Here, conventional benchmark sets, which focus on min.-orientation radial curves at the expense of angular diversity, are augmented by new databases such as side chain-side chain interactions (SSI), which are composed of interactions gleaned from crystal data and contain no such min.-focused bias. Moreover, some existing databases such as S22×5 are extended to shorter intermol. sepns. This improved DFT-D3 training set provides a balanced description of distances, covers the entire range of interaction types, and at 1526 data points is far larger than the original training set of 130. The results are validated against a new collection of 6773 data points and demonstrate that the effect of refitting the damping parameters ranges from no change in accuracy (LC-ωPBE-D3) to an almost 2-fold decrease in av. error (PBE-D3).

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17. 17

    Goerigk, L.; Grimme, S. A general database for main group thermochemistry, kinetics, and noncovalent interactions - Assessment of common and reparameterized (meta-) GGA density functionals. J. Chem. Theory Comput. 2010, 6, 107– 126,  DOI: 10.1021/ct900489g

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    17

    A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions - Assessment of Common and Reparameterized (meta-)GGA Density Functionals

    Goerigk, Lars; Grimme, Stefan

    Journal of Chemical Theory and Computation (2010), 6 (1), 107-126CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    We present a quantum chem. benchmark database for general main group thermochem., kinetics, and noncovalent interactions (GMTKN24). It is an unprecedented compilation of 24 different, chem. relevant subsets that either are taken from already existing databases or are presented here for the first time. The complete set involves a total of 1.049 at. and mol. single point calcns. and comprises 731 data points (relative chem. energies) based on accurate theor. or exptl. ref. values. The usefulness of the GMTKN24 database is shown by applying common d. functionals on the (meta-)generalized gradient approxn. (GGA), hybrid-GGA, and double-hybrid-GGA levels to it, including an empirical London dispersion correction. Furthermore, we refitted the functional parameters of four (meta-)GGA functionals based on a fit set contg. 143 systems, comprising seven chem. different problems. Validation against the GMTKN24 and the mol. structure (bond lengths) databases shows that the reparameterization does not change bond lengths much, whereas the description of energetic properties is more prone to the parameters' values. The empirical dispersion correction also often improves for conventional thermodn. problems and makes a functional's performance more uniform over the entire database. The refitted functionals typically have a lower mean abs. deviation for the majority of subsets in the proposed GMTKN24 set. This, however, is also often accompanied at the expense of poor performance for a few other important subsets. Thus, creating a broadly applicable (and overall better) functional by just reparameterizing existing ones seems to be difficult. Nevertheless, this benchmark study reveals that a reoptimized (i.e., empirical) version of the TPSS-D functional (oTPSS-D) performs well for a variety of problems and may meet the stds. of an improved functional. We propose validation against this new compilation of benchmark sets as a definitive way to evaluate a new quantum chem. method's true performance.

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18. 18

    Goerigk, L.; Grimme, S. A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions. Phys. Chem. Chem. Phys. 2011, 13, 6670– 6688,  DOI: 10.1039/c0cp02984j

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    18

    A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions

    Goerigk, Lars; Grimme, Stefan

    Physical Chemistry Chemical Physics (2011), 13 (14), 6670-6688CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

    A thorough energy benchmark study of various d. functionals (DFs) is carried out with the new GMTKN30 database for general main group thermochem., kinetics and noncovalent interactions. In total, 47 DFs are investigated: two LDAs, 14 GGAs, three meta-GGAs, 23 hybrids and five double-hybrids. Besides the double-hybrids, also other modern approaches, i.e., the M05 and M06 classes of functionals and range-sepd. hybrids, are tested. For almost all functionals, the new DFT-D3 correction is applied in order to consistently test the performance also for important noncovalent interactions; the parameters are taken from previous works or detd. for the present study. Basis set and quadrature grid issues are also considered. The general aim of the study is to work out which functionals are generally well applicable and robust to describe the energies of mols. In summary, we recommend on the GGA level the B97-D3 and revPBE-D3 functionals. The best meta-GGA is oTPSS-D3 although meta-GGAs represent in general no clear improvement compared to numerically simpler GGAs. Notably, the widely used B3LYP functional performs worse than the av. of all tested hybrids and is also very sensitive to the application of dispersion corrections. We discourage its usage as a std. method without closer inspection of the results, as it still seems to be often done nowadays. Surprisingly, long-range cor. exchange functionals do in general not perform better than the corresponding std. hybrids. However, the ωB97X-D functional seems to be a promising method. The most robust hybrid is Zhao and Truhlar's PW6B95 functional in combination with DFT-D3. If higher accuracy is required, double-hybrids should be applied. The corresponding DSD-BLYP-D3 and PWPB95-D3 variants are the most accurate and robust functionals of the entire study. Addnl. calcns. with MP2 and its spin-scaled variants SCS-MP2, S2-MP2 and SOS-MP2 revealed that double-hybrids in general outperform those. Only SCS-MP2 can be recommended, particularly for reaction energies. We suggest its usage when a large self-interaction error is expected that prohibits usage of double-hybrids. Perdews' metaphoric picture of Jacob's Ladder for the classification of d. functionals' performance could unbiasedly be confirmed with GMTKN30. We also show that there is no statistical correlation between a functional's accuracy for atomization energies and the performance for chem. more relevant reaction energies.

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19. 19

    Zhao, Y.; Truhlar, D. G. Density Functionals with Broad Applicability in Chemistry. Acc. Chem. Res. 2008, 41, 157– 167,  DOI: 10.1021/ar700111a

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    19

    Density Functionals with Broad Applicability in Chemistry

    Zhao, Yan; Truhlar, Donald G.

    Accounts of Chemical Research (2008), 41 (2), 157-167CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)

    A review. Although d. functional theory is widely used in the computational chem. community, the most popular d. functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chem. than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by medium-range correlation energy, such as van der Waals attraction, arom.-arom. stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new d. functionals. We used these data to design new d. functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin d. gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy "across-the-board" for transition metals, main group thermochem., medium-range correlation energy, and barrier heights; (b) M06-2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chem., predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for arom.-arom. stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate functional for transition metals and is the only local functional (no Hartree-Fock exchange) with better across-the-board av. performance than B3LYP; this is very important because only local functionals are affordable for many demanding applications on very large systems; (d) M06-HF has good performance for valence, Rydberg, and charge transfer excited states with minimal sacrifice of ground-state accuracy. In this Account, we compared the performance of the M06-class functionals and one M05-class functional (M05-2X) to that of some popular functionals for diverse databases and their performance on several difficult cases. The tests include barrier heights, conformational energy, and the trend in bond dissocn. energies of Grubbs' ruthenium catalysts for olefin metathesis. Based on these tests, we recommend (1) the M06-2X, BMK, and M05-2X functionals for main-group thermochem. and kinetics, (2) M06-2X and M06 for systems where main-group thermochem., kinetics, and noncovalent interactions are all important, (3) M06-L and M06 for transition metal thermochem., (4) M06 for problems involving multireference rearrangements or reactions where both org. and transition-metal bonds are formed or broken, (5) M06-2X, M05-2X, M06-HF, M06, and M06-L for the study of noncovalent interactions, (6) M06-HF when the use of full Hartree-Fock exchange is important, for example, to avoid the error of self-interaction at long-range, (7) M06-L when a local functional is required, because a local functional has much lower cost for large systems.

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20. 20

    Schneebeli, S. T.; Bochevarov, A. D.; Friesner, R. A. Parameterization of a B3LYP specific correction for noncovalent interactions and basis set superposition error on a gigantic data set of CCSD(T) quality noncovalent interaction energies. J. Chem. Theory Comput. 2011, 7, 658– 668,  DOI: 10.1021/ct100651f

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    20

    Parameterization of a B3LYP Specific Correction for Noncovalent Interactions and Basis Set Superposition Error on a Gigantic Data Set of CCSD(T) Quality Noncovalent Interaction Energies

    Schneebeli, Severin T.; Bochevarov, Arteum D.; Friesner, Richard A.

    Journal of Chemical Theory and Computation (2011), 7 (3), 658-668CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    A vast no. of noncovalent interaction energies at the counterpoise cor. CCSD(T) level have been collected from the literature to build a diverse new data set. The whole data set, which consists of 2027 CCSD(T) energies, includes most of the published data at this level. A large subset of the data was then used to train a novel, B3LYP specific, empirical correction scheme for noncovalent interactions and basis set superposition error (abbreviated as B3LYP-MM). Results obtained with our new correction scheme were directly compared to benchmark results obtained with B3LYP-D3 and M06-2X (two popular d. functionals designed specifically to accurately model noncovalent interactions). For noncovalent complexes dominated by dispersion or dipole-dipole interactions, all three tested methods give accurate results with the medium-sized aug-cc-pVDZ basis set with MUEs of 0.27 (B3LYP-MM), 0.32 (B3LYP-D3), and 0.47 kcal/mol (M06-2X) (with explicit counterpoise corrections). These results validate both B3LYP-D3 and M06-2X for interactions of this type using a much larger data set than was presented in prior work. However, our new dispersion correction scheme shows some clear advantages for dispersion and dipole-dipole dominated complexes with the small LACVP* basis set, which is very popular in use due to its low assocd. computational cost: The MUE for B3LYP-MM with the LACVP* basis set for this subset of complexes (without explicit counterpoise corrections) is only 0.28 kcal/mol, compared to 0.65 kcal/mol for M06-2X or 1.16 kcal/mol for B3LYP-D3. Addnl., our new correction scheme also shows major improvements in accuracy for hydrogen-bonded systems and for systems involving ionic interactions, for example, cation-π interactions. Compared to B3LYP-D3 and M06-2X, we also find that our new B3LYP-MM correction scheme gives results of higher or equal accuracy for a large data set of conformer energies of di- and tripeptides, sugars, and cysteine.

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21. 21

    McGibbon, R. T.; Taube, A. G.; Donchev, A. G.; Siva, K.; Hernández, F.; Hargus, C.; Law, K.-H.; Klepeis, J. L.; Shaw, D. E. Improving the accuracy of Møller-Plesset perturbation theory with neural networks. J. Chem. Phys. 2017, 147, 161725,  DOI: 10.1063/1.4986081

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    21

    Improving the accuracy of Moller-Plesset perturbation theory with neural networks

    McGibbon, Robert T.; Taube, Andrew G.; Donchev, Alexander G.; Siva, Karthik; Hernandez, Felipe; Hargus, Cory; Law, Ka-Hei; Klepeis, John L.; Shaw, David E.

    Journal of Chemical Physics (2017), 147 (16), 161725/1-161725/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Noncovalent interactions are of fundamental importance across the disciplines of chem., materials science, and biol. Quantum chem. calcns. on noncovalently bound complexes, which allow for the quantification of properties such as binding energies and geometries, play an essential role in advancing our understanding of, and building models for, a vast array of complex processes involving mol. assocn. or self-assembly. Because of its relatively modest computational cost, second-order Moller-Plesset perturbation (MP2) theory is one of the most widely used methods in quantum chem. for studying noncovalent interactions. MP2 is, however, plagued by serious errors due to its incomplete treatment of electron correlation, esp. when modeling van der Waals interactions and π-stacked complexes. Here we present spin-network-scaled MP2 (SNS-MP2), a new semiempirical MP2-based method for dimer interaction-energy calcns. To correct for errors in MP2, SNS-MP2 uses quantum chem. features of the complex under study in conjunction with a neural network to reweight terms appearing in the total MP2 interaction energy. The method has been trained on a new data set consisting of over 200 000 complete basis set (CBS)-extrapolated coupled-cluster interaction energies, which are considered the gold std. for chem. accuracy. SNS-MP2 predicts gold-std. binding energies of unseen test compds. with a mean abs. error of 0.04 kcal mol-1 (root-mean-square error 0.09 kcal mol-1), a 6- to 7-fold improvement over MP2. To the best of our knowledge, its accuracy exceeds that of all extant d. functional theory- and wavefunction-based methods of similar computational cost, and is very close to the intrinsic accuracy of our benchmark coupled-cluster methodol. itself. Furthermore, SNS-MP2 provides reliable per-conformation confidence intervals on the predicted interaction energies, a feature not available from any alternative method. (c) 2017 American Institute of Physics.

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22. 22

    Mardirossian, N.; Head-Gordon, M. ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation. J. Chem. Phys. 2016, 144, 214110,  DOI: 10.1063/1.4952647

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    22

    ωB97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation

    Mardirossian, Narbe; Head-Gordon, Martin

    Journal of Chemical Physics (2016), 144 (21), 214110/1-214110/23CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    A combinatorially optimized, range-sepd. hybrid, meta-GGA d. functional with VV10 nonlocal correlation is presented. The final 12-parameter functional form is selected from approx. 10 × 109 candidate fits that are trained on a training set of 870 data points and tested on a primary test set of 2964 data points. The resulting d. functional, ωB97M-V, is further tested for transferability on a secondary test set of 1152 data points. For comparison, ωB97M-V is benchmarked against 11 leading d. functionals including M06-2X, ωB97X-D, M08-HX, M11, ωM05-D, ωB97X-V, and MN15. Encouragingly, the overall performance of ωB97M-V on nearly 5000 data points clearly surpasses that of all of the tested d. functionals. In order to facilitate the use of ωB97M-V, its basis set dependence and integration grid sensitivity are thoroughly assessed, and recommendations that take into account both efficiency and accuracy are provided. (c) 2016 American Institute of Physics.

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23. 23

    Burns, L. A.; Faver, J. C.; Zheng, Z.; Marshall, M. S.; Smith, D. G.; Vanommeslaeghe, K.; MacKerell, A. D.; Merz, K. M.; Sherrill, C. D. The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions. J. Chem. Phys. 2017, 147, 161727,  DOI: 10.1063/1.5001028

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    23

    The BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions

    Burns, Lori A.; Faver, John C.; Zheng, Zheng; Marshall, Michael S.; Smith, Daniel G. A.; Vanommeslaeghe, Kenno; MacKerell, Alexander D.; Merz, Kenneth M.; Sherrill, C. David

    Journal of Chemical Physics (2017), 147 (16), 161727/1-161727/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Accurate potential energy models are necessary for reliable atomistic simulations of chem. phenomena. In the realm of biomol. modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chem. databases of common fragment interactions in biomol. systems as extd. from high-resoln. Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Abs. interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver std." (0.05 kcal/mol av. error) for NCI that demands only a fraction of the cost of the conventional "gold std.," CCSD(T) at the complete basis set limit. By sampling extensively from biol. environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addn. to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), d. functional (244), and wavefunction (45) methods (comprising > 1 M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation. (c) 2017 American Institute of Physics.

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24. 24

    Soydaş, E.; Bozkaya, U. Accurate Open-Shell Noncovalent Interaction Energies from the Orbital-Optimized Møller-Plesset Perturbation Theory: Achieving CCSD Quality at the MP2 Level by Orbital Optimization. J. Chem. Theory Comput. 2013, 9, 4679– 4683,  DOI: 10.1021/ct4008124

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    24

    Accurate Open-Shell Noncovalent Interaction Energies from the Orbital-Optimized Moller-Plesset Perturbation Theory: Achieving CCSD Quality at the MP2 Level by Orbital Optimization

    Soydas, Emine; Bozkaya, Ugur

    Journal of Chemical Theory and Computation (2013), 9 (11), 4679-4683CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    The accurate description of noncovalent interactions is one of the most challenging problems in modern computational chem., esp. those for open-shell systems. In this study, an investigation of open-shell noncovalent interactions with the orbital-optimized MP2 and MP3 (OMP2 and OMP3) is presented. For the considered test set of 23 complexes, mean abs. errors in noncovalent interaction energies (with respect to CCSD-(T) at complete basis set limits) are 0.68 (MP2), 0.37 (OMP2), 0.59 (MP3), 0.23 (OMP3), and 0.38 (CCSD) kcal mol-1 . Hence, with a greatly reduced computational cost, one may achieve CCSD quality at the MP2 level by orbital optimization [scaling formally as O(N6) for CCSD compared to O(N5) for OMP2, where N is the no. of basis functions]. Further, one may obtain a considerably better performance than CCSD using the OMP3 method, which has also a lower cost than CCSD.

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25. 25

    Lochan, R. C.; Head-Gordon, M. Orbital-optimized opposite-spin scaled second-order correlation: An economical method to improve the description of open-shell molecules. J. Chem. Phys. 2007, 126, 164101,  DOI: 10.1063/1.2718952

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    25

    Orbital-optimized opposite-spin scaled second-order correlation: an economical method to improve the description of open-shell molecules

    Lochan, Rohini C.; Head-Gordon, Martin

    Journal of Chemical Physics (2007), 126 (16), 164101/1-164101/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Coupled-cluster methods based on Brueckner orbitals are well known to resolve the problems of symmetry breaking and spin contamination that are often assocd. with Hartree-Fock orbitals. However, their computational cost is large enough to prevent application to large mols. Here the authors present a simple approxn. where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second-order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This "optimized second-order opposite-spin" (abbreviated as O2) method requires fourth-order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed-shell mols. that are very similar to scaled second-order Moller-Plesset methods. However, it yields substantial improvements for open-shell mols., where problems with spin contamination and symmetry breaking are shown to be greatly reduced.

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26. 26

    Neese, F.; Schwabe, T.; Kossmann, S.; Schirmer, B.; Grimme, S. Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics. J. Chem. Theory Comput. 2009, 5, 3060– 3073,  DOI: 10.1021/ct9003299

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    26

    Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics

    Neese, Frank; Schwabe, Tobias; Kossmann, Simone; Schirmer, Birgitta; Grimme, Stefan

    Journal of Chemical Theory and Computation (2009), 5 (11), 3060-3073CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    An efficient implementation of the orbital-optimized second-order Moller-Plesset perturbation theory (OO-MP2) within the resoln. of the identity (RI) approxn. is reported. Both conventional MP2 and spin-component scaled (SCS-MP2) variants are considered, and an extensive numerical investigation of the accuracy of these approaches is presented. This work is closely related to earlier work of Lochan, R. C.; Head-Gordon, M. J. Chem. Phys., 2007, 126. Orbital optimization is achieved by making the Hylleraas functional together with the energy of the ref. determinant stationary with respect to variations of the double excitation amplitudes and the MO rotation parameters. A simple iterative scheme is proposed that usually leads to convergence within 5-15 iterations. The applicability of the method to larger mols. (up to ∼1000-2000 basis functions) is demonstrated. The numerical results show that OO-SCS-MP2 is a major improvement in electronically complicated situations, such as represented by radicals or by transition states where spin contamination often greatly deteriorates the quality of the conventional MP2 and SCS-MP2 methods. The OO-(SCS-)MP2 approach reduces the error by a factor of 3-5 relative to the std. (SCS-)MP2. For closed-shell main group elements, no significant improvement in the accuracy relative to the already excellent SCS-MP2 method is obsd. In addn., the problems of all MP2 variants with 3d transition-metal complexes are not solved by orbital optimization. The close relationship of the OO-MP2 method to the approx. second-order coupled cluster method (CC2) is pointed out. Both methods have comparable computational requirements. Thus, the OO-MP2 method emerges as a very useful tool for computational quantum chem.

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27. 27

    Bozkaya, U.; Turney, J. M.; Yamaguchi, Y.; Schaefer, H. F.; Sherrill, C. D. Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory. J. Chem. Phys. 2011, 135, 104103,  DOI: 10.1063/1.3631129

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    Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Moller-Plesset perturbation theory

    Bozkaya, Ugur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F., III; Sherrill, C. David

    Journal of Chemical Physics (2011), 135 (10), 104103/1-104103/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the MOs for the coupled-cluster doubles (CCD) method and second-order Moller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), resp. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response d. matrixes, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the std. MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O4+ mol. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O4+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle d. matrixes, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides mol. properties that are somewhat different than those of MP2 for most of the test cases considered (although they are similar for H2O). Bond lengths are somewhat longer, and vibrational frequencies somewhat smaller, for OMP2 compared to MP2. In the difficult case of O4+, results for several vibrational frequencies are significantly improved in going from MP2 to OMP2. (c) 2011 American Institute of Physics.

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    Peverati, R.; Head-Gordon, M. Orbital optimized double-hybrid density functionals. J. Chem. Phys. 2013, 139, 024110,  DOI: 10.1063/1.4812689

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    Orbital optimized double-hybrid density functionals

    Peverati, Roberto; Head-Gordon, Martin

    Journal of Chemical Physics (2013), 139 (2), 024110/1-024110/6CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    This paper advocates development of a new class of double-hybrid (DH) d. functionals where the energy is fully orbital optimized (OO) in presence of all correlation, rather than using a final non-iterative second order perturbative correction. The resulting OO-DH functionals resolve a no. of artifacts assocd. with conventional DH functionals, such as first deriv. discontinuities. To illustrate the possibilities, two non-empirical OO-DH functionals are obtained from existing DH functionals based on PBE: OO-PBE0-DH and OO-PBE0-2. Both functionals share the same functional form, with parameters detd. on the basis of different phys. considerations. The new functionals are tested on a variety of bonded, non-bonded and symmetry-breaking problems. (c) 2013 American Institute of Physics.

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29. 29

    Sancho-García, J. C.; Pérez-Jiménez, A. J.; Savarese, M.; Brémond, E.; Adamo, C. Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems. J. Phys. Chem. A 2016, 120, 1756– 1762,  DOI: 10.1021/acs.jpca.6b00994

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    Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems

    Sancho-Garcia, J. C.; Perez-Jimenez, A. J.; Savarese, M.; Bremond, E.; Adamo, C.

    Journal of Physical Chemistry A (2016), 120 (10), 1756-1762CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)

    We assess here the reliability of orbital optimization for modern double-hybrid d. functionals such as the parameter-free PBE-QIDH model. We select for that purpose a set of closed- and open-shell strongly and weakly bound systems, including some std. and widely used data sets, to show that orbital optimization improves the results with respect to std. models, notably for electronically complicated systems, and through first-order properties obtained as derivs. of the energy.

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30. 30

    Najibi, A.; Goerigk, L. A Comprehensive Assessment of the Effectiveness of Orbital Optimization in Double-Hybrid Density Functionals in the Treatment of Thermochemistry, Kinetics, and Noncovalent Interactions. J. Phys. Chem. A 2018, 122, 5610– 5624,  DOI: 10.1021/acs.jpca.8b04058

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    30

    A Comprehensive Assessment of the Effectiveness of Orbital Optimization in Double-Hybrid Density Functionals in the Treatment of Thermochemistry, Kinetics, and Noncovalent Interactions

    Najibi, Asim; Goerigk, Lars

    Journal of Physical Chemistry A (2018), 122 (25), 5610-5624CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)

    Orbital optimization (OO) has been suggested as a way to solve some shortcomings of second-order Moller-Plesset (MP2) variants and double-hybrid d. functionals (DHDFs). A closer inspection of the literature, however, shows that the only two studies on OO-DHDFs were limited to three nonempirical PBE-based functionals, which are known to be of only mediocre accuracy. Herein, we provide a more in-depth anal. of OO-DHDFs with the main focus being on main-group thermochem., kinetics, and noncovalent interactions. We reanalyze two PBE-based OO-DHDFs and present four new OO-DHDF variants, two of which make use of the spin-component-scaling idea in their nonlocal correlation part. We also provide a more thorough anal. of three OO-MP2 variants. After assessing more than 621 ref. points, we come to the conclusion that the benefits of OO are not as straightforward as previously thought. Results heavily depend on the underlying parent method. While OO-SCS/SOS-MP2 usually provide improved results-including for noncovalently bound systems-the opposite is true for OO-MP2. OO-DHDFs, like their nonoptimized counterparts, still require London-dispersion corrections. Among the DHDFs, the largest effect of OO on thermochem. properties is seen for PBE0-2 and the smallest for PBE0-DH. However, results can both worsen and improve with OO. If the latter is the case, the resulting OO-DHDF is still outperformed by the currently most accurate conventional DHDFs, namely DSD-BLYP and DSD-PBEP86. We therefore recommend the OO technique only to be used in specialized cases. For the general method user we re-emphasize using conventional dispersion-cor. DHDFs for robust, reliable results. Our findings also indicate that entirely different strategies seem to be required in order to obtain a substantial improvement over the currently best DHDFs.

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31. 31

    Hains, A. W.; Liang, Z.; Woodhouse, M. A.; Gregg, B. A. Molecular Semiconductors in Organic Photovoltaic Cells. Chem. Rev. 2010, 110, 6689– 6735,  DOI: 10.1021/cr9002984

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    Molecular Semiconductors in Organic Photovoltaic Cells

    Hains, Alexander W.; Liang, Ziqi; Woodhouse, Michael A.; Gregg, Brian A.

    Chemical Reviews (Washington, DC, United States) (2010), 110 (11), 6689-6735CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    A review. Relevant chem., phys., and elec. properties of org. semiconductors are described with comparison to silicon, the prototypical inorg. semiconductor. (poly)cryst. materials illustrate the fundamental properties and the more complex, but popular, disordered materials are also discussed. The understanding of mol. semiconductors is progressing rapidly, as is the field of org. photovoltaics. Major practical issues remain, however, such as minimizing interfacial recombination, preventing both chem. and morphol. instabilities, and learning to employ cleaner, more cryst. materials. New MSCs and new cell designs may be needed to achieve a higher level of performance. Nevertheless, the improvements in OPV cell efficiency in recent years bode well for the future of this exciting field. :.

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32. 32

    Lüssem, B.; Keum, C.-M.; Kasemann, D.; Naab, B.; Bao, Z.; Leo, K. Doped Organic Transistors. Chem. Rev. 2016, 116, 13714– 13751,  DOI: 10.1021/acs.chemrev.6b00329

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    Doped Organic Transistors

    Lussem, Bjorn; Keum, Chang-Min; Kasemann, Daniel; Naab, Ben; Bao, Zhenan; Leo, Karl

    Chemical Reviews (Washington, DC, United States) (2016), 116 (22), 13714-13751CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    Org. field-effect transistors hold the promise of enabling low-cost and flexible electronics. Following its success in org. optoelectronics, the org. doping technol. is also used increasingly in org. field-effect transistors. Doping not only increases device performance, but it also provides a way to fine-control the transistor behavior, to develop new transistor concepts, and even improve the stability of org. transistors. This Review summarizes the latest progress made in the understanding of the doping technol. and its application to org. transistors. It presents the most successful doping models and an overview of the wide variety of materials used as dopants. Further, the influence of doping on charge transport in the most relevant polycryst. org. semiconductors is reviewed, and a concise overview on the influence of doping on transistor behavior and performance is given. In particular, recent progress in the understanding of contact doping and channel doping is summarized.

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    Ostroverkhova, O. Organic Optoelectronic Materials: Mechanisms and Applications. Chem. Rev. 2016, 116, 13279– 13412,  DOI: 10.1021/acs.chemrev.6b00127

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    Organic Optoelectronic Materials: Mechanisms and Applications

    Ostroverkhova, Oksana

    Chemical Reviews (Washington, DC, United States) (2016), 116 (22), 13279-13412CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    A review. Org. (opto)electronic materials have received considerable attention due to their applications in thin-film-transistors, light-emitting diodes, solar cells, sensors, photorefractive devices, and many others. The technol. promises include low cost of these materials and the possibility of their room-temp. deposition from soln. on large-area and/or flexible substrates. The article reviews the current understanding of the phys. mechanisms that det. the (opto)electronic properties of high-performance org. materials. The focus of the review is on photoinduced processes and on electronic properties important for optoelectronic applications relying on charge carrier photogeneration. Addnl., it highlights the capabilities of various exptl. techniques for characterization of these materials, summarizes top-of-the-line device performance, and outlines recent trends in the further development of the field. The properties of materials based both on small mols. and on conjugated polymers are considered, and their applications in org. solar cells, photodetectors, and photorefractive devices are discussed.

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34. 34

    Walzer, K.; Maennig, B.; Pfeiffer, M.; Leo, K. Highly efficient organic devices based on electrically doped transport layers. Chem. Rev. 2007, 107, 1233– 1271,  DOI: 10.1021/cr050156n

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    Highly Efficient Organic Devices Based on Electrically Doped Transport Layers

    Walzer, K.; Maennig, B.; Pfeiffer, M.; Leo, K.

    Chemical Reviews (Washington, DC, United States) (2007), 107 (4), 1233-1271CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    A review. The controlled doping of org. semiconductors by coevaporation with suitable dopant mols. and its application for highly efficient devices, such as org. LED and org. solar cells, is described. The conductivities can be raised many orders of magnitude above the cond. of nominally undoped materials. Due to low mobilities, the cond. of the materials is still much lower than those of inorg. semiconductors but sufficient for many devices that do not need too high current densities, such as org. light- emitting diodes and solar cells. An understanding of the dependence of cond. on doping concn. requires models that take effects like localization and percolation into account.

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35. 35

    Coropceanu, V.; Cornil, J.; da Silva Filho, D. A.; Olivier, Y.; Silbey, R.; Brédas, J.-L. Charge Transport in Organic Semiconductors. Chem. Rev. 2007, 107, 926– 952,  DOI: 10.1021/cr050140x

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    Charge Transport in Organic Semiconductors

    Coropceanu, Veaceslav; Cornil, Jerome; Da Silva Filho, Demetrio A.; Olivier, Yoann; Silbey, Robert; Bredas, Jean-Luc

    Chemical Reviews (Washington, DC, United States) (2007), 107 (4), 926-952CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    A review. Both electron and hole transport in org. semiconductors are discussed.

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36. 36

    Steinmann, S. N.; Corminboeuf, C. Exploring the Limits of Density Functional Approximations for Interaction Energies of Molecular Precursors to Organic Electronics. J. Chem. Theory Comput. 2012, 8, 4305– 4316,  DOI: 10.1021/ct300657h

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    Exploring the Limits of Density Functional Approximations for Interaction Energies of Molecular Precursors to Organic Electronics

    Steinmann, Stephan N.; Corminboeuf, Clemence

    Journal of Chemical Theory and Computation (2012), 8 (11), 4305-4316CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    Neutral and charged assemblies of π-conjugated mols. span the field of org. electronics. Electronic structure computations can provide valuable information regarding the nature of the intermol. interactions within mol. precursors to org. electronics. Here, we introduce a database of neutral (Pi29n) and radical (Orel26rad) dimer complexes that represent binding energies between org. functional units. The new benchmarks are used to test approx. electronic structure methods. Achieving accurate interaction energies for neutral complexes (Pi29n) is straightforward, so long as dispersion interactions are properly taken into account. However, π-dimer radical cations (Orel26rad) are examples of highly challenging situations for d. functional approxns. The role of dispersion corrections is crucial, yet simultaneously long-range cor. exchange schemes are necessary to provide the proper dimer dissocn. behavior. Nevertheless, long-range cor. functionals seriously underestimate the binding energy of Orel26rad at equil. geometries. In fact, only ωB97X-D, an empirical exchange-correlation functional fitted together with an empirical "classical" dispersion correction, leads to suitable results. Valuable alternatives are the more demanding MP2/6-31G*(0.25) level, as well as the most cost-effective combination involving a dispersion cor. long-range functional together with a smaller practical size basis set (e.g., LC-ωPBEB95-dDsC/6-31G*). The Orel26rad test set should serve as an ideal benchmark for assessing the performance of improved schemes.

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37. 37

    Corminboeuf, C. Minimizing density functional failures for non-covalent interactions beyond van der Waals complexes. Acc. Chem. Res. 2014, 47, 3217– 3224,  DOI: 10.1021/ar400303a

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    Minimizing Density Functional Failures for Non-Covalent Interactions Beyond van der Waals Complexes

    Corminboeuf, Clemence

    Accounts of Chemical Research (2014), 47 (11), 3217-3224CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)

    A review. Kohn-Sham d. functional theory offers a powerful and robust formalism for investigating the electronic structure of many-body systems while providing a practical balance of accuracy and computational cost unmatched by other methods. Despite this success, the commonly used semilocal approxns. have difficulties in properly describing attractive dispersion interactions that decay with R-6 at large intermol. distances. Even in the short to medium range, most semilocal d. functionals fail to give an accurate description of weak interactions. The omnipresence of dispersion interactions, which are neglected in the most popular electronic structure framework, has stimulated intense developments during the past decade. In this Account, we summarize our effort to develop and implement dispersion corrections that dramatically reduce the failures of both inter- and intramol. interaction energies. The proposed schemes range from improved variants of empirical atom pairwise dispersion correction (e.g., dD10) to robust formulations dependent upon the electron d. Emphasis has been placed on introducing more physics into a modified Tang and Toennies damping function and deriving accurate dispersion coeffs. Our most sophisticated and established d.-dependent correction, dDsC, is based on a simple generalized gradient approxn. (GGA)-like reformulation of the exchange hole dipole moment introduced by Becke and Johnson. Akin to its empirical precursor, dDsC dramatically improves the interaction energy of a variety of std. d. functionals simultaneously for typical intermol. complexes and shorter-range interactions occurring within mols. The broad applicability and robustness of the dDsC scheme is demonstrated on various representative reaction energies, geometries, and mol. dynamic simulations. The suitability of the a posteriori correction is also established through comparisons with the more computationally demanding self-consistent implementation. The proposed correction is then exploited to identify the key factors at the origin of the errors in thermochem. beyond van der Waals complexes. Particular focus is placed on charge-transfer and mixed-valence complexes, which are relevant to the field of org. electronics. These types of complexes represent insightful examples for which the delocalization error may partially counterbalance the missing dispersion. Our devised methodol. reveals the true performance of std. d. functional approxns. and the subtle interplay between the two types of errors. The anal. presented provides guidance for future functional development that could further improve the modeling of the structures and properties of mol. materials. Overall, the proposed state-of-the-art approaches have contributed to stress the crucial role of dispersion and improve their description in both straightforward van der Waals complexes and more challenging chem. situations. For the treatment of the latter, we have also provided relevant insights into which type of d. functionals to favor.

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38. 38

    Otero-de-la Roza, A.; Johnson, E. R.; DiLabio, G. A. Halogen Bonding from Dispersion-Corrected Density-Functional Theory: The Role of Delocalization Error. J. Chem. Theory Comput. 2014, 10, 5436– 5447,  DOI: 10.1021/ct500899h

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    Halogen Bonding from Dispersion-Corrected Density-Functional Theory: The Role of Delocalization Error

    Otero-de-la-Roza, A.; Johnson, Erin R.; DiLabio, Gino A.

    Journal of Chemical Theory and Computation (2014), 10 (12), 5436-5447CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    Halogen bonds are formed when a Lewis base interacts with a halogen atom in a different mol., which acts as an electron acceptor. Due to its charge transfer component, halogen bonding is difficult to model using many common d.-functional approxns. because they spuriously overstabilize halogen-bonded dimers. It has been suggested that dispersion-cor. d. functionals are inadequate to describe halogen bonding. In this work, we show that the exchange-hole dipole moment (XDM) dispersion correction coupled with functionals that minimize delocalization error (for instance, BH&HLYP, but also other half-and-half functionals) accurately model halogen-bonded interactions, with av. errors similar to other noncovalent dimers with less charge-transfer effects. The performance of XDM is evaluated for three previously proposed benchmarks (XB18 and XB51 by Kozuch and Martin, and the set proposed by Bauza et al.) spanning a range of binding energies up to ∼50 kcal/mol. The good performance of BH&HLYP-XDM is comparable to M06-2X, and extends to the "extreme" cases in the Bauza set. This set contains anionic electron donors where charge transfer occurs even at infinite sepn., as well as other charge transfer dimers belonging to the pnictogen and chalcogen bonding classes. We also show that functional delocalization error results in an overly delocalized electron d. and exact-exchange hole. We propose intermol. Bader delocalization indexes as an indicator of both the donor-acceptor character of an intermol. interaction and the delocalization error coming from the underlying functional.

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39. 39

    Boese, A. D. Density Functional Theory and Hydrogen Bonds: Are We There Yet?. ChemPhysChem 2015, 16, 978– 985,  DOI: 10.1002/cphc.201402786

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    Density Functional Theory and Hydrogen Bonds: Are We There Yet?

    Boese, A. Daniel

    ChemPhysChem (2015), 16 (5), 978-985CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)

    D. functional theory (DFT) has become more successful at introducing dispersion interactions, and can be thus applied to a wide range of systems. Amongst these are systems that contain hydrogen bonds, which are extremely important for the biol. regime. Here, the description of hydrogen-bonded interactions by DFT with and without dispersion corrections is investigated. For small complexes, for which electrostatics are the detg. factor in the intermol. interactions, the inclusion of dispersion with most functionals yields large errors. Only for larger systems, in which van der Waals interactions are more important, do dispersion corrections improve the performance of DFT for hydrogen-bonded systems. None of the studied functionals, including double hybrid functionals (with the exception of DSD-PBEP86 without dispersion corrections), are more accurate than MP2 for the investigated species.

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40. 40

    Bauzá, A.; Alkorta, I.; Frontera, A.; Elguero, J. On the Reliability of Pure and Hybrid DFT Methods for the Evaluation of Halogen, Chalcogen, and Pnicogen Bonds Involving Anionic and Neutral Electron Donors. J. Chem. Theory Comput. 2013, 9, 5201– 5210,  DOI: 10.1021/ct400818v

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    On the Reliability of Pure and Hybrid DFT Methods for the Evaluation of Halogen, Chalcogen, and Pnicogen Bonds Involving Anionic and Neutral Electron Donors

    Bauza, Antonio; Alkorta, Ibon; Frontera, Antonio; Elguero, Jose

    Journal of Chemical Theory and Computation (2013), 9 (11), 5201-5210CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    We report a comprehensive theor. study of halogen, chalcogen, and pnicogen bonding interactions using a large set of pure and hybrid functionals and some ab initio methods. We have obsd. that the pure and some hybrid functionals largely overestimate the interaction energies when the donor atom is anionic (Cl- or Br-), esp. in the halogen bonding complexes. To evaluate the reliability of the different DFT (BP86, BP86-D3, BLYP, BLYP-D3, B3LYP, B97-D, B97-D3, PBE0, HSE06, APFD, and M06-2X) and ab initio (MP2, RI-MP2, and HF) methods, we have compared the binding energies and equil. distances to those obtained using the CCSD-(T)/aug-cc-pVTZ level of theory, as ref. The addn. of the latest available correction for dispersion (D3) to pure functionals is not recommended for the calcn. of halogen, chalcogen, and pnicogen complexes with anions, since it further contributes to the overestimation of the binding energies. In addn., in chalcogen bonding interactions, we have studied how the hybridization of the chalcogen atom influences the interaction energies.

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41. 41

    Soniat, M.; Rogers, D. M.; Rempe, S. B. Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration. J. Chem. Theory Comput. 2015, 11, 2958– 2967,  DOI: 10.1021/acs.jctc.5b00357

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    Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration

    Soniat, Marielle; Rogers, David M.; Rempe, Susan B.

    Journal of Chemical Theory and Computation (2015), 11 (7), 2958-2967CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    A challenge in d. functional theory is developing functionals that simultaneously describe intermol. electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-cor. ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decompn. shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amts. of charge transfer and the least polarizable waters of the d. functionals studied, which mimics the lower polarizability of CCSD. When compared with exptl. binding free energies, however, the exchange-cor. CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to exptl. formation enthalpies. For clusters contg. more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with expt.

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42. 42

    Shi, R.; Huang, X.; Su, Y.; Lu, H.-G.; Li, S.-D.; Tang, L.; Zhao, J. Which Density Functional Should Be Used to Describe Protonated Water Clusters?. J. Phys. Chem. A 2017, 121, 3117– 3127,  DOI: 10.1021/acs.jpca.7b00058

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    Which Density Functional Should Be Used to Describe Protonated Water Clusters?

    Shi, Ruili; Huang, Xiaoming; Su, Yan; Lu, Hai-Gang; Li, Si-Dian; Tang, Lingli; Zhao, Jijun

    Journal of Physical Chemistry A (2017), 121 (16), 3117-3127CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)

    Protonated water cluster is one of the most important hydrogen-bond network systems. Finding an appropriate DFT method to study the properties of protonated water clusters can substantially improve the economy in computational resources without sacrificing the accuracy compared to high-level methods. Using high-level MP2 and CCSD(T) methods as well as exptl. results as benchmark, we systematically examd. the effect of seven exchange-correlation GGA functionals (with BLYP, B3LYP, X3LYP, PBE0, PBE1W, M05-2X, and B97-D parametrizations) in describing the geometric parameters, interaction energies, dipole moments, and vibrational properties of protonated water clusters H+(H2O)2-9,12. The overall performance of all these functionals is acceptable, and each of them has its advantage in certain aspects. X3LYP is the best to describe the interaction energies, and PBE0 and M05-2X are also recommended to investigate interaction energies. PBE0 gives the best anharmonic frequencies, followed by PBE1W, B97-D and BLYP methods. PBE1W, B3LYP, B97-D, and X3LYP can yield better geometries. The capability of B97-D to distinguish the relative energies between isomers is the best among all the seven methods, followed by M05-2X and PBE0.

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43. 43

    Schreiner, P. R. Relative Energy Computations with Approximate Density Functional Theory-A Caveat!. Angew. Chem., Int. Ed. 2007, 46, 4217– 4219,  DOI: 10.1002/anie.200700386

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    Relative energy computations with approximate density functional theory - a caveat!

    Schreiner, Peter R.

    Angewandte Chemie, International Edition (2007), 46 (23), 4217-4219CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)

    A review. Not so simple: Common and broadly used d. functional theory (DFT) implementations do not properly account for medium-range electron correlation. The resultant errors in energy calcns., for example, for simple hydrocarbon isomers, can be large and increase with increasingly larger structures.

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44. 44

    Grimme, S.; Steinmetz, M.; Korth, M. Stereoelectronic Substituent Effects in Saturated Main Group Molecules: Severe Problems of Current Kohn-Sham Density Functional Theory. J. Chem. Theory Comput. 2007, 3, 42– 45,  DOI: 10.1021/ct600224b

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    Stereoelectronic Substituent Effects in Saturated Main Group Molecules: Severe Problems of Current Kohn-Sham Density Functional Theory

    Grimme, S.; Steinmetz, M.; Korth, M.

    Journal of Chemical Theory and Computation (2007), 3 (1), 42-45CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    The Hartree-Fock method, two common d. functionals (PBE and B3LYP), and two new functionals (B97-D and B2PLYP) together with very large AO basis sets are used to compute the isomerization energies for substituted (R:H, F, Cl) branched to linear alkanes and silanes. The results of accurate SCS-MP2 computations are taken as ref. These reactions are an important test of how nonlocal electron correlation effects on medium-range lengths scales in satd. mols. are treated by approx. quantum chem. methods. It is found that the unacceptably large errors obsd. previously for hydrocarbons persist also for the here considered more polar systems. Although the B97-D and B2PLYP functionals provide improved energetics, the problem is not fully solved, and thus these systems are suggested as mandatory benchmarks for future d. functionals.

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45. 45

    Chai, J.-D. D.; Head-Gordon, M. Systematic optimization of long-range corrected hybrid density functionals. J. Chem. Phys. 2008, 128, 084106,  DOI: 10.1063/1.2834918

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    Systematic optimization of long-range corrected hybrid density functionals

    Chai, Jeng-Da; Head-Gordon, Martin

    Journal of Chemical Physics (2008), 128 (8), 084106/1-084106/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    A general scheme for systematically modeling long-range cor. (LC) hybrid d. functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochem., kinetics, and noncovalent interactions, when compared with common hybrid d. functionals. The qual. failures of the commonly used hybrid d. functionals in some "difficult problems," such as dissocn. of sym. radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid d. functionals. (c) 2008 American Institute of Physics.

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    Facchetti, A. π-conjugated polymers for organic electronics and photovoltaic cell applications. Chem. Mater. 2011, 23, 733– 758,  DOI: 10.1021/cm102419z

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    π-Conjugated Polymers for Organic Electronics and Photovoltaic Cell Applications

    Facchetti, Antonio

    Chemistry of Materials (2011), 23 (3), 733-758CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)

    A review. The optoelectronic properties of polymeric semiconductor materials can be used for the fabrication of org. electronic and photonic devices. When key structural requirements are met, these materials exhibit unique properties such as soln. processability, large charge transporting capabilities, and/or broad optical absorption. In this review recent developments in the area of π-conjugated polymeric semiconductors for org. thin-film (or field-effect) transistors (OTFTs or OFETs) and bulk-heterojunction photovoltaic (or solar) cell (BHJ-OPV or OSC) applications are summarized and analyzed.

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47. 47

    Wang, C.; Dong, H.; Hu, W.; Liu, Y.; Zhu, D. Semiconducting π-conjugated systems in field-effect transistors: A material odyssey of organic electronics. Chem. Rev. 2012, 112, 2208– 2267,  DOI: 10.1021/cr100380z

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    Semiconducting π-Conjugated Systems in Field-Effect Transistors: A Material Odyssey of Organic Electronics

    Wang, Chengliang; Dong, Huanli; Hu, Wenping; Liu, Yunqi; Zhu, Daoben

    Chemical Reviews (Washington, DC, United States) (2012), 112 (4), 2208-2267CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)

    A review.

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48. 48

    Wang, C.; Dong, H.; Jiang, L.; Hu, W. Organic semiconductor crystals. Chem. Soc. Rev. 2018, 47, 422– 500,  DOI: 10.1039/C7CS00490G

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    Organic semiconductor crystals

    Wang, Chengliang; Dong, Huanli; Jiang, Lang; Hu, Wenping

    Chemical Society Reviews (2018), 47 (2), 422-500CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)

    Org. semiconductors have attracted a lot of attention since the discovery of highly doped conductive polymers, due to the potential application in field-effect transistors (OFETs), light-emitting diodes (OLEDs) and photovoltaic cells (OPVs). Single crystals of org. semiconductors are particularly intriguing because they are free of grain boundaries and have long-range periodic order as well as minimal traps and defects. Hence, org. semiconductor crystals provide a powerful tool for revealing the intrinsic properties, examg. the structure-property relationships, demonstrating the important factors for high performance devices and uncovering fundamental physics in org. semiconductors. This review provides a comprehensive overview of the mol. packing, morphol. and charge transport features of org. semiconductor crystals, the control of crystn. for achieving high quality crystals and the device physics in the three main applications. We hope that this comprehensive summary can give a clear picture of the state-of-art status and guide future work in this area.

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49. 49

    Pederson, M. R.; Ruzsinszky, A.; Perdew, J. P. Communication: Self-interaction correction with unitary invariance in density functional theory. J. Chem. Phys. 2014, 140, 121103,  DOI: 10.1063/1.4869581

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    Communication: Self-interaction correction with unitary invariance in density functional theory

    Pederson, Mark R.; Ruzsinszky, Adrienn; Perdew, John P.

    Journal of Chemical Physics (2014), 140 (12), 121103/1-121103/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Std. spin-d. functionals for the exchange-correlation energy of a many-electron ground state make serious self-interaction errors which can be cor. by the Perdew-Zunger self-interaction correction (SIC). We propose a size-extensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spin-d. functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the non-interacting one-particle d. matrix. When this SIC is applied to the local spin-d. approxn., improvements are found for the atomization energies of mols. (c) 2014 American Institute of Physics.

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50. 50

    Gryn’ova, G.; Nicolaï, A.; Prlj, A.; Ollitrault, P.; Andrienko, D.; Corminboeuf, C. Charge transport in highly ordered organic nanofibrils: lessons from modelling. J. Mater. Chem. C 2017, 5, 350– 361,  DOI: 10.1039/C6TC04463H

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    Charge transport in highly ordered organic nanofibrils: lessons from modelling

    Gryn'ova, Ganna; Nicolai, Adrien; Prlj, Antonio; Ollitrault, Pauline; Andrienko, Denis; Corminboeuf, Clemence

    Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2017), 5 (2), 350-361CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)

    H-Aggregates featuring tight π-stacks of the conjugated heterocyclic cores represent ideal morphologies for 1D org. semiconductors. Such nanofibrils have larger electronic couplings between the adjacent cores compared to the herringbone crystal or amorphous assemblies. In this work, we show that for a set of seven structurally and electronically distinct cores, including quaterthiophene and oligothienoacenes, the co-planar dimer model captures the impact of the monomer's electronic structure on charge transport, but more advanced multiscale modeling, featuring mol. dynamics and kinetic Monte-Carlo simulations, is needed to account for the packing and disorder effects. The differences in the results between these two computational approaches arise from the sensitivity of the electronic coupling strength to the relative alignment of adjacent cores, in particular the long-axis shift between them, imposed by the oligopeptide side chains. Our results demonstrate the dependence of the performance of H-aggregates on the chem. nature of the cores and the presence of the side chains, as well as the limitations in using the simple dimer model for a rapid computational pre-screening of the conjugated cores.

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51. 51

    Steinmann, S. N.; Corminboeuf, C. A System-Dependent Density-Based Dispersion Correction. J. Chem. Theory Comput. 2010, 6, 1990– 2001,  DOI: 10.1021/ct1001494

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    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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52. 52

    Steinmann, S. N.; Corminboeuf, C. A generalized-gradient approximation exchange hole model for dispersion coefficients. J. Chem. Phys. 2011, 134, 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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53. 53

    Steinmann, S. N.; Corminboeuf, C. Comprehensive Benchmarking of a Density-Dependent Dispersion Correction. J. Chem. Theory Comput. 2011, 7, 3567– 3577,  DOI: 10.1021/ct200602x

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    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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54. 54

    Lin, Y.-S.; Li, G.-D.; Mao, S.-P.; Chai, J.-D. Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. J. Chem. Theory Comput. 2013, 9, 263– 272,  DOI: 10.1021/ct300715s

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    Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections

    Lin, You-Sheng; Li, Guan-De; Mao, Shan-Ping; Chai, Jeng-Da

    Journal of Chemical Theory and Computation (2013), 9 (1), 263-272CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    By incorporating the improved empirical atom-atom dispersion corrections from DFT-D3 [Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys.2010, 132, 154104], two long-range cor. (LC) hybrid d. functionals are proposed. Our resulting LC hybrid functionals, ωM06-D3 and ωB97X-D3, are shown to be accurate for a very wide range of applications, such as thermochem., kinetics, noncovalent interactions, frontier orbital energies, fundamental gaps, and long-range charge-transfer excitations, when compared with common global and LC hybrid functionals. Relative to ωB97X-D [Chai, J.-D.; Head-Gordon, M. Phys. Chem. Chem. Phys.2008, 10, 6615], ωB97X-D3 (reoptimization of ωB97X-D with improved dispersion corrections) is shown to be superior for nonbonded interactions, and similar in performance for bonded interactions, while ωM06-D3 is shown to be superior for general applications.

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55. 55

    Mardirossian, N.; Head-Gordon, M. ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy. Phys. Chem. Chem. Phys. 2014, 16, 9904,  DOI: 10.1039/c3cp54374a

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    ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy

    Mardirossian, Narbe; Head-Gordon, Martin

    Physical Chemistry Chemical Physics (2014), 16 (21), 9904-9924CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

    A 10-parameter, range-sepd. hybrid (RSH), generalized gradient approxn. (GGA) d. functional with nonlocal correlation (VV10) is presented. Instead of truncating the B97-type power series inhomogeneity correction factors (ICF) for the exchange, same-spin correlation, and opposite-spin correlation functionals uniformly, all 16 383 combinations of the linear parameters up to fourth order (m = 4) are considered. These functionals are individually fit to a training set and the resulting parameters are validated on a primary test set in order to identify the 3 optimal ICF expansions. Through this procedure, it is discovered that the functional that performs best on the training and primary test sets has 7 linear parameters, with 3 addnl. nonlinear parameters from range-sepn. and nonlocal correlation. The resulting d. functional, ωB97X-V, is further assessed on a secondary test set, the parallel-displaced coronene dimer, as well as several geometry datasets. Furthermore, the basis set dependence and integration grid sensitivity of ωB97X-V are analyzed and documented in order to facilitate the use of the functional.

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56. 56

    Mardirossian, N.; Head-Gordon, M. Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ωB97M(2) double hybrid density functional. J. Chem. Phys. 2018, 148, 241736,  DOI: 10.1063/1.5025226

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    Survival of the most transferable at the top of Jacob's ladder: Defining and testing the ωB97M(2) double hybrid density functional

    Mardirossian, Narbe; Head-Gordon, Martin

    Journal of Chemical Physics (2018), 148 (24), 241736/1-241736/14CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    A meta-generalized gradient approxn., range-sepd. double hybrid (DH) d. functional with VV10 non-local correlation is presented. The final 14-parameter functional form is detd. by screening trillions of candidate fits through a combination of best subset selection, forward stepwise selection, and random sample consensus (RANSAC) outlier detection. The MGCDB84 database of 4986 data points is employed in this work, contg. a training set of 870 data points, a validation set of 2964 data points, and a test set of 1152 data points. Following an xDH approach, orbitals from the ωB97M-V d. functional are used to compute the second-order perturbation theory correction. The resulting functional, ωB97M(2), is benchmarked against a variety of leading double hybrid d. functionals, including B2PLYP-D3(BJ), B2GPPLYP-D3(BJ), ωB97X-2(TQZ), XYG3, PTPSS-D3(0), XYGJ-OS, DSD-PBEP86-D3(BJ), and DSD-PBEPBE-D3(BJ). Encouragingly, the overall performance of ωB97M(2) on nearly 5000 data points clearly surpasses that of all of the tested d. functionals. As a Rung 5 d. functional, ωB97M(2) completes our family of combinatorially optimized functionals, complementing B97M-V on Rung 3, and ωB97X-V and ωB97M-V on Rung 4. The results suggest that ωB97M(2) has the potential to serve as a powerful predictive tool for accurate and efficient electronic structure calcns. of main-group chem. (c) 2018 American Institute of Physics.

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    Anthony, J. E.; Eaton, D. L.; Parkin, S. R. A Road Map to Stable, Soluble, Easily Crystallized Pentacene Derivatives. Org. Lett. 2002, 4, 15– 18,  DOI: 10.1021/ol0167356

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    A Road Map to Stable, Soluble, Easily Crystallized Pentacene Derivatives

    Anthony, John E.; Eaton, David L.; Parkin, Sean R.

    Organic Letters (2002), 4 (1), 15-18CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)

    A series of 6,13-disubstituted pentacenes, e.g., I, in which the substituents are functionalized ethyne units, were synthesized and analyzed by X-ray crystallog. The resulting pentacene derivs. were highly sol. and oxidatively stable and exhibited a significant amt. of π-stacking in the crystal.

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    Herwig, P.; Kayser, C. W.; Müllen, K.; Spiess, H. W. Columnar mesophases of alkylated hexa-peri-hexabenzocoronenes with remarkably large phase widths. Adv. Mater. 1996, 8, 510– 513,  DOI: 10.1002/adma.19960080613

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    Columnar mesophases of alkylated hexa-peri-hexabenzocoronenes with remarkably large phase widths

    Herwig, Peter; Kayser, Christoph W.; Muellen, Klaus; Spiess, Hans Wolfgang

    Advanced Materials (Weinheim, Germany) (1996), 8 (6), 510-513CODEN: ADVMEW; ISSN:0935-9648. (VCH)

    The prepn. and preliminary characterization of liq-cryst. behavior of the alkylated hexa-peri-hexabenzocoronenes (alkyl n = 11, 13, 15) are described. They exhibit hexagonal columnar mesophases with remarkably large widths, e.g., 339 K for R = dodecyl.

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59. 59

    Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785– 789,  DOI: 10.1103/PhysRevB.37.785

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    Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density

    Lee, Chengteh; Yang, Weitao; Parr, Robert G.

    Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.

    A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

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    Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648,  DOI: 10.1063/1.464913

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    Density-functional thermochemistry. III. The role of exact exchange

    Becke, Axel D.

    Journal of Chemical Physics (1993), 98 (7), 5648-52CODEN: JCPSA6; ISSN:0021-9606.

    Despite the remarkable thermochem. accuracy of Kohn-Sham d.-functional theories with gradient corrections for exchange-correlation, the author believes that further improvements are unlikely unless exact-exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange-correlation functional (contg. local-spin-d., gradient, and exact-exchange terms) is tested for 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total at. energies of first- and second-row systems. This functional performs better than previous functionals with gradient corrections only, and fits expt. atomization energies with an impressively small av. abs. deviation of 2.4 kcal/mol.

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61. 61

    Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623– 11627,  DOI: 10.1021/j100096a001

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    Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields

    Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J.

    Journal of Physical Chemistry (1994), 98 (45), 11623-7CODEN: JPCHAX; ISSN:0022-3654.

    The unpolarized absorption and CD spectra of the fundamental vibrational transitions of the chiral mol. 4-methyl-2-oxetanone are calcd. ab initio. Harmonic force fields are obtained using d. functional theory (DFT), MP2 and SCF methodologies, and a [5s4p2d/3s2p] (TZ2P) basis set. DFT calcns. use the LSDA, BLYP, and Becke3LYP (B3LYP) d. functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with expt. The MP2 force field yields spectra in slightly worse agreement with expt. than the B3LYP force field. The SCF force field yields spectra in poor agreement with expt. The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreement with expt.

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    Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H.; Li, X.; Caricato, M.; Marenich, A. V.; Bloino, J.; Janesko, B. G.; Gomperts, R.; Mennucci, B.; Hratchian, H. P.; Ortiz, J. V.; Izmaylov, A. F.; Sonnenberg, J. L.; Williams-Young, D.; Ding, F.; Lipparini, F.; Egidi, F.; Goings, J.; Peng, B.; Petrone, A.; Henderson, T.; Ranasinghe, D.; Zakrzewski, V. G.; Gao, J.; Rega, N.; Zheng, G.; Liang, W.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Throssell, K.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M. J.; Heyd, J. J.; Brothers, E. N.; Kudin, K. N.; Staroverov, V. N.; Keith, T. A.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A. P.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Millam, J. M.; Klene, M.; Adamo, C.; Cammi, R.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Farkas, O.; Foresman, J. B.; Fox, D. J. Gaussian16, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2016.

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    Mas-Torrent, M.; Hadley, P.; Bromley, S. T.; Ribas, X.; Tarrés, J.; Mas, M.; Molins, E.; Veciana, J.; Rovira, C. Correlation between crystal structure and mobility in organic field-effect transistors based on single crystals of tetrathiafulvalene derivatives. J. Am. Chem. Soc. 2004, 126, 8546– 8553,  DOI: 10.1021/ja048342i

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    Correlation between Crystal Structure and Mobility in Organic Field-Effect Transistors Based on Single Crystals of Tetrathiafulvalene Derivatives

    Mas-Torrent, Marta; Hadley, Peter; Bromley, Stefan T.; Ribas, Xavi; Tarres, Judit; Mas, Montserrat; Molins, Elies; Veciana, Jaume; Rovira, Concepcio

    Journal of the American Chemical Society (2004), 126 (27), 8546-8553CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)

    Recently, it was reported that crystals of the org. material dithiophene-tetrathiafulvalene (DT-TTF) have a high field-effect charge carrier mobility of 1.4 cm2/(V·s). These crystals were formed by a simple drop-casting method, making this material interesting to study for possible applications in low-cost electronics. Here, org. single-crystal field-effect transistors based on materials related to DT-TTF are presented and a clear correlation between the crystal structure and the elec. characteristics is obsd. The obsd. relation between the mobilities in the different crystal structures is strongly corroborated by calcns. of both the mol. reorganization energies and the max. intermol. transfer integrals. The most suitable materials described here exhibit mobilities that are among the highest reported for org. field-effect transistors and that are the highest reported for soln.-processed materials.

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64. 64

    Li, X.-C.; Sirringhaus, H.; Garnier, F.; Holmes, A. B.; Moratti, S. C.; Feeder, N.; Clegg, W.; Teat, S. J.; Friend, R. H. A highly π-stacked organic semiconductor for thin-film transistors based on fused thiophenes. J. Am. Chem. Soc. 1998, 120, 2206– 2207,  DOI: 10.1021/ja9735968

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    A highly π-stacked organic semiconductor for thin-film transistors based on fused thiophenes

    Li, Xiao-Chang; Sirringhaus, Henning; Garnier, Francis; Holmes, Andrew B.; Moratti, Stephen C.; Feeder, Neil; Clegg, William; Teat, Simon J.; Friend, Richard H.

    Journal of the American Chemical Society (1998), 120 (9), 2206-2207CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)

    A new org. semiconductor, α,α'-bis(dithieno[3,2-b:2',3'-d]thiophene) was synthesized and identified as a promising material for a thin-film transistor. The crystal structure was detd. using synchrotron radiation microcrystal diffraction facilities, and exhibited a compressed π-stacking. It is a material which can conveniently be used to fabricate the device configurations shown below which exhibit high mobility (0.05/cm2 V-s) and high ON/OFF ratio (108).

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65. 65

    Groom, C. R.; Bruno, I. J.; Lightfoot, M. P.; Ward, S. C. The Cambridge structural database. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2016, 72, 171– 179,  DOI: 10.1107/S2052520616003954

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    The Cambridge Structural Database

    Groom, Colin R.; Bruno, Ian J.; Lightfoot, Matthew P.; Ward, Suzanna C.

    Acta Crystallographica, Section B: Structural Science, Crystal Engineering and Materials (2016), 72 (2), 171-179CODEN: ACSBDA; ISSN:2052-5206. (International Union of Crystallography)

    The Cambridge Structural Database (CSD) contains a complete record of all published org. and metal-org. small-mol. crystal structures. The database has been in operation for over 50 years and continues to be the primary means of sharing structural chem. data and knowledge across disciplines. As well as structures that are made public to support scientific articles, it includes many structures published directly as CSD Communications. All structures are processed both computationally and by expert structural chem. editors prior to entering the database. A key component of this processing is the reliable assocn. of the chem. identity of the structure studied with the exptl. data. This important step helps ensure that data is widely discoverable and readily reusable. Content is further enriched through selective inclusion of addnl. exptl. data. Entries are available to anyone through free CSD community web services. Linking services developed and maintained by the CCDC, combined with the use of std. identifiers, facilitate discovery from other resources. Data can also be accessed through CCDC and third party software applications and through an application programming interface.

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66. 66

    Afonina, I.; Skabara, P. J.; Vilela, F.; Kanibolotsky, A. L.; Forgie, J. C.; Bansal, A. K.; Turnbull, G. A.; Samuel, I. D.; Labram, J. G.; Anthopoulos, T. D.; Coles, S. J.; Hursthouse, M. B. Synthesis and characterisation of new diindenodithienothiophene (DITT) based materials. J. Mater. Chem. 2010, 20, 1112– 1116,  DOI: 10.1039/B919574B

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    Synthesis and characterization of new diindenodithienothiophene (DITT) based materials

    Afonina, Irina; Skabara, Peter J.; Vilela, Filipe; Kanibolotsky, Alexander L.; Forgie, John C.; Bansal, Ashu K.; Turnbull, Graham A.; Samuel, Ifor D. W.; Labram, John G.; Anthopoulos, Thomas D.; Coles, Simon J.; Hursthouse, Michael B.

    Journal of Materials Chemistry (2010), 20 (6), 1112-1116CODEN: JMACEP; ISSN:0959-9428. (Royal Society of Chemistry)

    Three new diindenodithienothiophene (DITT) based materials were synthesized and their electrochem. properties investigated. The HOMO-LUMO gaps were obsd. to be 3.33, 3.48 and 2.81 eV, resp. Cyclic voltammetry results indicate increased stability for the alkylated derivs. The dioxide exhibits strong photoluminescence, giving a photoluminescence quantum yield of 0.72 in soln. and 0.14 in the solid state. Hole mobility measurements were carried out on the non-alkylated deriv. and the corresponding values were ∼10-4 cm2 V-1 s-1.

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67. 67

    Chen, M.-C.; Vegiraju, S.; Huang, C.-M.; Huang, P.-Y.; Prabakaran, K.; Yau, S. L.; Chen, W.-C.; Peng, W.-T.; Chao, I.; Kim, C.; Tao, Y.-T. Asymmetric fused thiophenes for field-effect transistors: crystal structure-film microstructure-transistor performance correlations. J. Mater. Chem. C 2014, 2, 8892– 8902,  DOI: 10.1039/C4TC01454E

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    Asymmetric fused thiophenes for field-effect transistors: crystal structure-film microstructure-transistor performance correlations

    Chen, Ming-Chou; Vegiraju, Sureshraju; Huang, Chi-Ming; Huang, Peng-Yi; Prabakaran, Kumaresan; Yau, Shueh Lin; Chen, Wei-Chih; Peng, Wei-Tao; Chao, Ito; Kim, Choongik; Tao, Yu-Tai

    Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2014), 2 (42), 8892-8902CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)

    New asym. Ph and perfluorophenyl end-functionalized dithienothiophene (DTT)- and bisdithienothiophene (BDTT)-based fused-thiophene derivs. (FPP-DTT; 1 and FPP-BDTT; 3) were synthesized and characterized for org. thin-film transistor (OTFT) applications. For comparison, sym. Ph end-capped dithienothiophene and bisdithienothiophene derivs. DP-DTT (2) and DP-BDTT (4) were also explored in parallel. The crystal structures of all four mols. were detd. via single-crystal X-ray diffraction. Asym. compds. 1 and 3 exhibit face-to-face π-π stacking, while sym. 2 and 4 show herringbone stacking. Single-crystal and thin-film transistors based on these four materials were fabricated. For single-crystal transistors, asym. FPP-DTT and FPP-BDTT gave high p-channel mobilities of 0.74 and 0.73 cm2 V-1 s-1, resp., as well as current on/off ratios of ∼105. Sym. DP-DTT and DP-BDTT gave relatively lower p-channel mobilities of 0.36 and 0.41 cm2 V-1 s-1, resp. For thin-film transistors, FPP-DTT and DP-DTT films deposited at 25 °C exhibited decent p-channel characteristics with a carrier mobility as high as 0.15 and 0.20 cm2 V-1 s-1, resp. for top-contact/bottom-gate OTFT devices. The device characteristics on various gate dielecs. have been correlated with the film morphologies and microstructures of the corresponding compds.

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68. 68

    Ebata, H.; Miyazaki, E.; Yamamoto, T.; Takimiya, K. Synthesis, properties, and structures of benzo[1,2-b:4,5-b’) bis[b) benzothiophene and benzo[1,2-b:4,5-b’) bis[b) benzoselenophene. Org. Lett. 2007, 9, 4499– 4502,  DOI: 10.1021/ol701815j

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    Synthesis, Properties, and Structures of Benzo[1,2-b:4,5-b']bis[1]benzothiophene and Benzo[1,2-b:4,5-b']bis[b]benzoselenophene

    Ebata, Hideaki; Miyazaki, Eigo; Yamamoto, Tatsuya; Takimiya, Kazuo

    Organic Letters (2007), 9 (22), 4499-4502CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)

    Employing two consecutive cyclization reactions, benzo[1,2-b:4,5-b']bis[b]benzochalcogenophenes, which are π-extended heteroarenes, were efficiently synthesized. Their electronic and crystal structures were elucidated on the basis of UV-vis spectra, electrochem. measurements, and X-ray structural analyses.

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69. 69

    Wang, C.; Dong, H.; Li, H.; Zhao, H.; Meng, Q.; Hu, W. Dibenzothiophene derivatives: From herringbone to lamellar packing motif. Cryst. Growth Des. 2010, 10, 4155– 4160,  DOI: 10.1021/cg100863q

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    Dibenzothiophene Derivatives: From Herringbone to Lamellar Packing Motif

    Wang, Chengliang; Dong, Huanli; Li, Hongxiang; Zhao, Huaping; Meng, Qing; Hu, Wenping

    Crystal Growth & Design (2010), 10 (9), 4155-4160CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)

    It is generally believed that π-π stacking would be much more efficient than herringbone stacking for the transporting of charge carriers. The electron-withdrawing group sulfone unit was introduced into dibenzothiophene (DBT) derivs., and lamellar structures were obsd. in the single crystals of the products along with strong, long-range π-π intermol. interactions. As a contrast, the reduced materials adopted herringbone packing. The authors contributed this change of packing motif to the polarity of the sulfone unit. These results are meaningful to the mol. design to obtain π-π stacking.

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70. 70

    Antolini, L.; Horowitz, G.; Kouki, F.; Garnier, F. Polymorphism in oligothiophenes with an even number of thiophene subunits. Adv. Mater. 1998, 10, 382– 385,  DOI: 10.1002/(SICI)1521-4095(199803)10:5<382::AID-ADMA382>3.0.CO;2-Y

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    Polymorphism in oligothiophenes with an even number of thiophene subunits

    Antolini, Luciano; Horowitz, Gilles; Kouki, Faycal; Garnier, Francis

    Advanced Materials (Weinheim, Germany) (1998), 10 (5), 382-385CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH)

    The growth of single crystals of quarterthiophene from the vapor phase and their characterization by single-crystal x-ray diffraction spectroscopy is reported. The structure is monoclinic, space group P21/a, a = 8.936(3), b = 5.7504(9), c = 14.341(3) Å , β = 97.22(2)°, V = 731.1(3) Å3, Z = 2, ρc = 1.501 g/cm3, μ(MoKα) = 0.634 mm-1, F(000) = 340, 1644 obsd. reflections, 104 refined parameters, R1 = 0.0431, wR2 = 0.1417 for I > 2σ(I). The structure resembles that of bithiophene and the high-temp. form of sexithiophene grown from the melt.

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71. 71

    Yamazaki, D.; Nishinaga, T.; Komatsu, K. Radical Cation of Dibenzothiophene Fully Annelated with Bicyclo[2.2.2) octene Units: X-ray Crystal Structure and Electronic Properties. Org. Lett. 2004, 6, 4179– 4182,  DOI: 10.1021/ol0483605

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    Radical Cation of Dibenzothiophene Fully Annelated with Bicyclo[2.2.2]octene Units: X-ray Crystal Structure and Electronic Properties

    Yamazaki, Daisuke; Nishinaga, Tohru; Komatsu, Koichi

    Organic Letters (2004), 6 (23), 4179-4182CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)

    New dibenzothiophene 2 fully annelated with bicyclo[2.2.2]octene units was synthesized and oxidized to stable radical cation salt 2•+SbCl6-, whose structure was detd. by X-ray crystallog. Although the intrinsic electronic structure of 2•+ is predicted to be close to structure A, an interaction with the counter anion makes structure B contribute significantly. A part of the salt 2•+SbCl6- underwent rearrangement to arenium ion 6+, the structure of which was also clarified by X-ray crystallog.

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72. 72

    Zhang, X.; Johnson, J. P.; Kampf, J. W.; Matzger, A. J. Ring fusion effects on the solid-state properties of α- oligothiophenes. Chem. Mater. 2006, 18, 3470– 3476,  DOI: 10.1021/cm0609348

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    Ring Fusion Effects on the Solid-State Properties of α-Oligothiophenes

    Zhang, Xinnan; Johnson, James P.; Kampf, Jeff W.; Matzger, Adam J.

    Chemistry of Materials (2006), 18 (15), 3470-3476CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)

    The solid-state properties of a series of fused-ring oligothiophenes were studied by UV-visible absorption spectroscopy and single crystal X-ray diffraction. Although the degree of ring fusion has little effect on the soln. absorption spectra, the solid-state spectra are dramatically different. Three thieno[3,2-b]thiophene-contg. oligomers display spectral blue shifts when comparing the solid state to soln. because they adopt a herringbone packing motif that leads to H aggregation. The solid-state structure of a dithieno[3,2-b:2',3'-d]thiophene-based oligomer contains both herringbone and slipped π-π interactions, and the overlap of transitions from these different interaction modes results in a broad absorption spectrum in the solid state. The fully fused pentathienoacene adopts a π-stacked packing motif and displays a small blue shift in the solid-state spectrum compared to soln. Time-dependent d. functional theory calcns. of the electronic transitions of isolated mols. and interacting dimers provide support that the different behavior in the solid-state spectra is due to the unique intermol. interactions arising in each packing motif.

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73. 73

    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, 134101,  DOI: 10.1063/1.4821834

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    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.

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74. 74

    Riplinger, C.; Neese, F. An efficient and near linear scaling pair natural orbital based local coupled cluster method. J. Chem. Phys. 2013, 138, 034106,  DOI: 10.1063/1.4773581

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    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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75. 75

    Neese, F. The ORCA program system. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 73– 78,  DOI: 10.1002/wcms.81

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    The ORCA program system

    Neese, Frank

    Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 73-78CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)

    A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.

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76. 76

    Zhang, J.; Dolg, M. Dispersion Interaction Stabilizes Sterically Hindered Double Fullerenes. Chem. - Eur. J. 2014, 20, 13909– 13912,  DOI: 10.1002/chem.201404106

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    Dispersion Interaction Stabilizes Sterically Hindered Double Fullerenes

    Zhang, Jun; Dolg, Michael

    Chemistry - A European Journal (2014), 20 (43), 13909-13912CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)

    By state-of-the-art quantum chem. methods, we show that for bulky functional groups like cyclohexane, [20]fullerene, dodecahedrane, and C60, the attractive dispersion interaction can have a greater impact on stereochem. than the repulsive steric effect, making the compact isomer the more stable one. In particular, for the double C60 adduct of pentacene 1, the syn isomer should be the main product instead of the anti one inferred in the original synthesis expt. (Y. Murata et al., J. Org. Chem. 1999, 64, 3483). With and without dispersion interactions taken into account, the Gibbs energy difference ΔG(syn-anti) is -6.36 and +1.15 kcal mol-1, resp. This study reminds us that dispersion interactions as well as electrostatic or hyperconjugation effects, etc. can lead to some unusual stereochem. phenomena.

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77. 77

    Minenkov, Y.; Chermak, E.; Cavallo, L. Accuracy of DLPNO-CCSD(T) Method for Noncovalent Bond Dissociation Enthalpies from Coinage Metal Cation Complexes. J. Chem. Theory Comput. 2015, 11, 4664– 4676,  DOI: 10.1021/acs.jctc.5b00584

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    Accuracy of DLPNO-CCSD(T) Method for Noncovalent Bond Dissociation Enthalpies from Coinage Metal Cation Complexes

    Minenkov, Yury; Chermak, Edrisse; Cavallo, Luigi

    Journal of Chemical Theory and Computation (2015), 11 (10), 4664-4676CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    The performance of the domain based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) method has been tested to reproduce the exptl. gas phase ligand dissocn. enthalpy in a series of Cu+, Ag+, and Au+ complexes. For 33 Cu+-noncovalent ligand dissocn. enthalpies, all-electron calcns. with the same method result in MUE below 2.2 kcal/mol, although an MSE of 1.4 kcal/mol indicates systematic underestimation of the exptl. values. Inclusion of scalar relativistic effects for Cu either via effective core potential (ECP) or Douglass-Kroll-Hess Hamiltonian, reduces the MUE below 1.7 kcal/mol and the MSE to -1.0 kcal/mol. For 24 Ag+-noncovalent ligand dissocn. enthalpies, the DLPNO-CCSD(T) method results in a mean unsigned error (MUE) below 2.1 kcal/mol and vanishing mean signed error (MSE). For 15 Au+-noncovalent ligand dissocn. enthalpies, the DLPNO-CCSD(T) methods provides larger MUE and MSE, equal to 3.2 and 1.7 kcal/mol, which might be related to poor precision of the exptl. measurements. Overall, for the combined data set of 72 coinage metal ion complexes, DLPNO-CCSD(T) results in a MUE below 2.2 kcal/mol and an almost vanishing MSE. As for a comparison with computationally cheaper d. functional theory (DFT) methods, the routinely used M06 functional results in MUE and MSE equal to 3.6 and -1.7 kcal/mol. Results converge already at CC-PVTZ quality basis set, making highly accurate DLPNO-CCSD(T) ests. affordable for routine calcns. (single-point) on large transition metal complexes of >100 atoms.

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78. 78

    Neese, F.; Valeev, E. F. Revisiting the atomic natural orbital approach for basis sets: Robust systematic basis sets for explicitly correlated and conventional correlated ab initio methods. J. Chem. Theory Comput. 2011, 7, 33– 43,  DOI: 10.1021/ct100396y

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    Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods?

    Neese, Frank; Valeev, Edward F.

    Journal of Chemical Theory and Computation (2011), 7 (1), 33-43CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    The performance of several families of basis sets for correlated wave function calcns. on mols. is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of at. natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in at. multireference av. coupled pair functional (MR-ACPF) calcns. Segmented basis sets optimized for SCF calcns. (def2-SVP, def2-TZVPP, and def2-QZVPP as well as "pc-n", n = 1, 2, 3) were also tested. Ref. Hartree-Fock energies are detd. with the uncontracted aug-cc-pV6Z basis set for a set of 21 small mols. built from H, B, C, N, O, and F. Ref. coupled cluster CCSD(T) correlation energies were detd. from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3 at each cardinal no. In addn., the ano-pVXZ consistently recovers more correlation energy than their competitors at each cardinal no. The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated. A conclusion by Truhlar is confirmed that the optimum exponent for correlation energy extrapolations at the DZ/TZ level is ∼2.4. All TZ/QZ basis set pairs lead to an optimum exponent close to the expected value of 3. The SCF energy extrapolation proposed by Petersson and co-workers is found to be effective. At the DZ/TZ level, errors in total energies of less than 2 mEh are found for the test set, while at the TZ/QZ level one obtains the total energies within ∼0.3 mEh of the basis set limit. For extrapolation, the "cc" and "ano" bases are found to be similarly successful. Extrapolation results were compared to explicitly correlated calcns. with dedicated basis sets (cc-pVXZ-F12) as well as the ano-pVXZ bases. It is found that the ano-pVXZ + basis sets perform as well as the cc-pVXZ-F12 family (both are of comparable size); addnl. improvement should be possible by reoptimizing the ANO basis sets for explicitly correlated calcns. The error of the extrapolated energies is about 2-3 times smaller than what was found in the explicitly correlated calcns. However, the error in the explicitly correlated calcns. is more systematic, and hence the same conclusion may not hold for the computation of energy differences.

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79. 79

    Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007– 1023,  DOI: 10.1063/1.456153

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    Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen

    Dunning, Thom H., Jr.

    Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.

    Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.

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80. 80

    Boys, S. F.; Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 1970, 19, 553– 566,  DOI: 10.1080/00268977000101561

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    The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors

    Boys, S. F.; Bernardi, F.

    Molecular Physics (1970), 19 (4), 553-566CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)

    A new direct difference method for the computation of mol. interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors. It appears that these new features can give a strong redn. in the error of the interaction energy, and they seem to be particularly suitable for computations in the important region near the min. energy. It has been generally accepted that this problem is dominated by unresolved difficulties and the relation of the new methods of these apparent difficulties is analyzed here.

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81. 81

    Saitow, M.; Becker, U.; Riplinger, C.; Valeev, E. F.; Neese, F. A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. J. Chem. Phys. 2017, 146, 164105,  DOI: 10.1063/1.4981521

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    A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory

    Saitow, Masaaki; Becker, Ute; Riplinger, Christoph; Valeev, Edward F.; Neese, Frank

    Journal of Chemical Physics (2017), 146 (16), 164105/1-164105/31CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable mol. electronic wave functions and energies for many mol. systems around their equil. geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approx. 20-30 atoms. To overcome these limitations, low-order scaling approxns. to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The prodn. level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell UHF ref. wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approxns. have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approx. 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set. (c) 2017 American Institute of Physics.

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82. 82

    Weigend, F.; Ahlrichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297– 305,  DOI: 10.1039/b508541a

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    Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy

    Weigend, Florian; Ahlrichs, Reinhart

    Physical Chemistry Chemical Physics (2005), 7 (18), 3297-3305CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)

    Gaussian basis sets of quadruple zeta valence quality for Rb-Rn are presented, as well as bases of split valence and triple zeta valence quality for H-Rn. The latter were obtained by (partly) modifying bases developed previously. A large set of more than 300 mols. representing (nearly) all elements-except lanthanides-in their common oxidn. states was used to assess the quality of the bases all across the periodic table. Quantities investigated were atomization energies, dipole moments and structure parameters for Hartree-Fock, d. functional theory and correlated methods, for which we had chosen Moller-Plesset perturbation theory as an example. Finally recommendations are given which type of basis set is used best for a certain level of theory and a desired quality of results.

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83. 83

    Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14, 1347– 1363,  DOI: 10.1002/jcc.540141112

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    General atomic and molecular electronic structure system

    Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A.; Elbert, Steven T.; Gordon, Mark S.; Jensen, Jan H.; Koseki, Shiro; Matsunaga, Nikita; Nguyen, Kiet A.; et al.

    Journal of Computational Chemistry (1993), 14 (11), 1347-63CODEN: JCCHDD; ISSN:0192-8651.

    A description of the ab initio quantum chem. package GAMESS is presented. Chem. systems contg. atoms through Rn can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calcns. at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speedup results are given. Parallel calcns. can be run on ordinary workstations as well as dedicated parallel machines.

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84. 84

    Gordon, M. S.; Schmidt, M. W. In Theory and Applications of Computational Chemistry; Dykstra, C., Frenking, G., Kim, K., Scuseria, G., Eds.; Elsevier: Amsterdam, 2005; pp 1167– 1189.

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    Dasgupta, S.; Herbert, J. M. Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3. J. Comput. Chem. 2017, 38, 869– 882,  DOI: 10.1002/jcc.24761

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    Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3

    Dasgupta, Saswata; Herbert, John M.

    Journal of Computational Chemistry (2017), 38 (12), 869-882CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)

    D.-functional approxns. developed in the past decade necessitate the use of quadrature grids that are far more dense than those required to integrate older generations of functionals. This category of difficult-to-integrate functionals includes meta-generalized gradient approxns., which depend on orbital gradients and/or the Laplacian of the d., as well as functionals based on B97 and the popular "Minnesota" class of functionals, each of which contain complicated and/or oscillatory expressions for the exchange inhomogeneity factor. Following a strategy introduced previously by Gill and co-workers to develop the relatively sparse "SG-0" and "SG-1" std. quadrature grids, we introduce two higher-quality grids that we designate SG-2 and SG-3, obtained by systematically "pruning" medium- and high-quality atom-centered grids. The pruning procedure affords computational speedups approaching a factor of two for hybrid functionals applied to systems of ∼100 atoms, without significant loss of accuracy. The grid dependence of several popular d. functionals is characterized for various properties. © 2017 Wiley Periodicals, Inc.

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86. 86

    Shao, Y.; Gan, Z.; Epifanovsky, E.; Gilbert, A. T.; Wormit, M.; Kussmann, J.; Lange, A. W.; Behn, A.; Deng, J.; Feng, X.; Ghosh, D.; Goldey, M.; Horn, P. R.; Jacobson, L. D.; Kaliman, I.; Khaliullin, R. Z.; Kuś, T.; Landau, A.; Liu, J.; Proynov, E. I.; Rhee, Y. M.; Richard, R. M.; Rohrdanz, M. A.; Steele, R. P.; Sundstrom, E. J.; Woodcock, H. L.; Zimmerman, P. M.; Zuev, D.; Albrecht, B.; Alguire, E.; Austin, B.; Beran, G. J. O.; Bernard, Y. A.; Berquist, E.; Brandhorst, K.; Bravaya, K. B.; Brown, S. T.; Casanova, D.; Chang, C.-M.; Chen, Y.; Chien, S. H.; Closser, K. D.; Crittenden, D. L.; Diedenhofen, M.; DiStasio, R. A.; Do, H.; Dutoi, A. D.; Edgar, R. G.; Fatehi, S.; Fusti-Molnar, L.; Ghysels, A.; Golubeva-Zadorozhnaya, A.; Gomes, J.; Hanson-Heine, M. W.; Harbach, P. H.; Hauser, A. W.; Hohenstein, E. G.; Holden, Z. C.; Jagau, T.-C.; Ji, H.; Kaduk, B.; Khistyaev, K.; Kim, J.; Kim, J.; King, R. A.; Klunzinger, P.; Kosenkov, D.; Kowalczyk, T.; Krauter, C. M.; Lao, K. U.; Laurent, A. D.; Lawler, K. V.; Levchenko, S. V.; Lin, C. Y.; Liu, F.; Livshits, E.; Lochan, R. C.; Luenser, A.; Manohar, P.; Manzer, S. F.; Mao, S.-P.; Mardirossian, N.; Marenich, A. V.; Maurer, S. A.; Mayhall, N. J.; Neuscamman, E.; Oana, C. M.; Olivares-Amaya, R.; O’Neill, D. P.; Parkhill, J. A.; Perrine, T. M.; Peverati, R.; Prociuk, A.; Rehn, D. R.; Rosta, E.; Russ, N. J.; Sharada, S. M.; Sharma, S.; Small, D. W.; Sodt, A.; Stein, T.; Stück, D.; Su, Y.-C.; Thom, A. J.; Tsuchimochi, T.; Vanovschi, V.; Vogt, L.; Vydrov, O.; Wang, T.; Watson, M. A.; Wenzel, J.; White, A.; Williams, C. F.; Yang, J.; Yeganeh, S.; Yost, S. R.; You, Z.-Q.; Zhang, I. Y.; Zhang, X.; Zhao, Y.; Brooks, B. R.; Chan, G. K.; Chipman, D. M.; Cramer, C. J.; Goddard, W. A.; Gordon, M. S.; Hehre, W. J.; Klamt, A.; Schaefer, H. F.; Schmidt, M. W.; Sherrill, C. D.; Truhlar, D. G.; Warshel, A.; Xu, X.; Aspuru-Guzik, A.; Baer, R.; Bell, A. T.; Besley, N. A.; Chai, J.-D.; Dreuw, A.; Dunietz, B. D.; Furlani, T. R.; Gwaltney, S. R.; Hsu, C.-P.; Jung, Y.; Kong, J.; Lambrecht, D. S.; Liang, W.; Ochsenfeld, C.; Rassolov, V. A.; Slipchenko, L. V.; Subotnik, J. E.; Van Voorhis, T.; Herbert, J. M.; Krylov, A. I.; Gill, P. M.; Head-Gordon, M. Advances in molecular quantum chemistry contained in the Q-Chem 4 program package. Mol. Phys. 2015, 113, 184– 215,  DOI: 10.1080/00268976.2014.952696

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    86

    Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

    Shao, Yihan; Gan, Zhengting; Epifanovsky, Evgeny; Gilbert, Andrew T. B.; Wormit, Michael; Kussmann, Joerg; Lange, Adrian W.; Behn, Andrew; Deng, Jia; Feng, Xintian; Ghosh, Debashree; Goldey, Matthew; Horn, Paul R.; Jacobson, Leif D.; Kaliman, Ilya; Khaliullin, Rustam Z.; Kus, Tomasz; Landau, Arie; Liu, Jie; Proynov, Emil I.; Rhee, Young Min; Richard, Ryan M.; Rohrdanz, Mary A.; Steele, Ryan P.; Sundstrom, Eric J.; Woodcock, H. Lee, III; Zimmerman, Paul M.; Zuev, Dmitry; Albrecht, Ben; Alguire, Ethan; Austin, Brian; Beran, Gregory J. O.; Bernard, Yves A.; Berquist, Eric; Brandhorst, Kai; Bravaya, Ksenia B.; Brown, Shawn T.; Casanova, David; Chang, Chung-Min; Chen, Yunquing; Chien, Siu Hung; Closser, Kristina D.; Crittenden, Deborah L.; Diedenhofen, Michael; DiStasio, Robert A., Jr.; Do, Hainam; Dutoi, Anthony D.; Edgar, Richard G.; Fatehi, Shervin; Fusti-Molnar, Laszlo; Ghysels, An; Golubeva-Zadorozhnaya, Anna; Gomes, Joseph; Hanson-Heine, Magnus W. D.; Harbach, Philipp H. P.; Hauser, Andreas W.; Hohenstein, Edward G.; Holden, Zachary C.; Jagau, Thomas-C.; Ji, Hyunjun; Kaduk, Ben; Khistyaev, Kirill; Kim, Jaehoon; Kim, Jihan; King, Rollin A.; Klunzinger, Phil; Kosenkov, Dmytro; Kowalczyk, Tim; Krauter, Caroline M.; Lao, Ka Un; Laurent, Adele; Lawler, Keith V.; Levchenko, Sergey V.; Lin, Ching Yeh; Liu, Fenglai; Livshits, Ester; Lochan, Rohini C.; Luenser, Arne; Manohar, Prashant; Manzer, Samuel F.; Mao, Shan-Ping; Mardirossian, Narbe; Marenich, Aleksandr V.; Maurer, Simon A.; Mayhall, Nicholas J.; Neuscamman, Eric; Oana, C. Melania; Olivares-Amaya, Roberto; O'Neill, Darragh P.; Parkhill, John A.; Perrine, Trilisa M.; Peverati, Roberto; Prociuk, Alexander; Rehn, Dirk R.; Rosta, Edina; Russ, Nicholas J.; Sharada, Shaama M.; Sharma, Sandeep; Small, David W.; Sodt, Alexander; Stein, Tamar; Stuck, David; Su, Yu-Chuan; Thom, Alex J. W.; Tsuchimochi, Takashi; Vanovschi, Vitalii; Vogt, Leslie; Vydrov, Oleg; Wang, Tao; Watson, Mark A.; Wenzel, Jan; White, Alec; Williams, Christopher F.; Yang, Jun; Yeganeh, Sina; Yost, Shane R.; You, Zhi-Qiang; Zhang, Igor Ying; Zhang, Xing; Zhao, Yan; Brooks, Bernard R.; Chan, Garnet K. L.; Chipman, Daniel M.; Cramer, Christopher J.; Goddard, William A., III; Gordon, Mark S.; Hehre, Warren J.; Klamt, Andreas; Schaefer, Henry F., III; Schmidt, Michael W.; Sherrill, C. David; Truhlar, Donald G.; Warshel, Arieh; Xu, Xin; Aspuru-Guzik, Alan; Baer, Roi; Bell, Alexis T.; Besley, Nicholas A.; Chai, Jeng-Da; Dreuw, Andreas; Dunietz, Barry D.; Furlani, Thomas R.; Gwaltney, Steven R.; Hsu, Chao-Ping; Jung, Yousung; Kong, Jing; Lambrecht, Daniel S.; Liang, WanZhen; Ochsenfeld, Christian; Rassolov, Vitaly A.; Slipchenko, Lyudmila V.; Subotnik, Joseph E.; Van Voorhis, Troy; Herbert, John M.; Krylov, Anna I.; Gill, Peter M. W.; Head-Gordon, Martin

    Molecular Physics (2015), 113 (2), 184-215CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)

    A review. A summary of the tech. advances that are incorporated in the fourth major release of the Q-Chem quantum chem. program is provided, covering approx. the last seven years. These include developments in d. functional theory methods and algorithms, NMR (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, anal. tools, energy and electron transfer modeling, parallel computing capabilities, and graphical user interfaces. In addn., a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern d. functionals for bonded and non-bonded interactions, tests of attenuated second order Moller-Plesset (MP2) methods for intermol. interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chem. examples include calcns. on the strongly correlated Cr2 dimer, exploring zeolite-catalyzed ethane dehydrogenation, energy decompn. anal. of a charged ter-mol. complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

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87. 87

    Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401,  DOI: 10.1103/PhysRevLett.91.146401

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    87

    Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids

    Tao, Jianmin; Perdew, John P.; Staroverov, Viktor N.; Scuseria, Gustavo E.

    Physical Review Letters (2003), 91 (14), 146401/1-146401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    The electron d., its gradient, and the Kohn-Sham orbital kinetic energy d. are the local ingredients of a meta-generalized gradient approxn. (meta-GGA). We construct a meta-GGA d. functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect two paradigms: one- or two-electron densities and slowly varying densities, and so describe both mols. and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of "Jacob's ladder" of approxns., above the local spin d. and GGA rungs.

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88. 88

    Ren, X.; Rinke, P.; Joas, C.; Scheffler, M. Random-phase approximation and its applications in computational chemistry and materials science. J. Mater. Sci. 2012, 47, 7447– 7471,  DOI: 10.1007/s10853-012-6570-4

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    88

    Random-phase approximation and its applications in computational chemistry and materials science

    Ren, Xinguo; Rinke, Patrick; Joas, Christian; Scheffler, Matthias

    Journal of Materials Science (2012), 47 (21), 7447-7471CODEN: JMTSAS; ISSN:0022-2461. (Springer)

    A review. The RPA (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theor. formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chem. and materials science. The computational cost of RPA is also addressed which is crit. for its widespread use in future applications. In addn., current correction schemes going beyond RPA and directions of further development will be discussed.

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89. 89

    Eshuis, H.; Bates, J. E.; Furche, F. Electron correlation methods based on the random phase approximation. Theor. Chem. Acc. 2012, 131, 1084,  DOI: 10.1007/s00214-011-1084-8

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90. 90

    Eshuis, H.; Yarkony, J.; Furche, F. Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. J. Chem. Phys. 2010, 132, 234114,  DOI: 10.1063/1.3442749

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    90

    Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration

    Eshuis, Henk; Yarkony, Julian; Furche, Filipp

    Journal of Chemical Physics (2010), 132 (23), 234114/1-234114/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    The RPA is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited mol. applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resoln. of the identity (RI) and imaginary frequency integration techniques. We show that the RI approxn. to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Moller-Plesset (MP2) calcns. are well suitable for RPA, as is demonstrated for the HEAT and MOLEKEL benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4logN) operations and O(N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the no. of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approxn. to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II. (c) 2010 American Institute of Physics.

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91. 91

    Furche, F.; Ahlrichs, R.; Hättig, C.; Klopper, W.; Sierka, M.; Weigend, F. Turbomole. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 91– 100,  DOI: 10.1002/wcms.1162

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    91

    Turbomole

    Furche, Filipp; Ahlrichs, Reinhart; Haettig, Christof; Klopper, Wim; Sierka, Marek; Weigend, Florian

    Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (2), 91-100CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)

    Turbomole is a highly optimized software package for large-scale quantum chem. simulations of mols., clusters, and periodic solids. Turbomole uses Gaussian basis sets and specializes on predictive electronic structure methods with excellent cost to performance characteristics, such as (time-dependent) d. functional theory (TDDFT), second-order Moller-Plesset theory, and explicitly correlated coupled cluster (CC) methods. These methods are combined with ultraefficient and numerically stable algorithms such as integral-direct and Laplace transform methods, resoln.-of-the-identity, pair natural orbitals, fast multipole, and low-order scaling techniques. Apart from energies and structures, a variety of optical, elec., and magnetic properties are accessible from anal. energy derivs. for electronic ground and excited states. Recent addns. include post-Kohn-Sham calcns. within the RPA, periodic calcns., spin-orbit couplings, explicitly correlated CC singles doubles and perturbative triples methods, CC singles doubles excitation energies, and nonadiabatic mol. dynamics simulations using TDDFT. A dedicated graphical user interface and a user support network are also available.

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92. 92

    Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865

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    92

    Generalized gradient approximation made simple

    Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias

    Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.

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93. 93

    Perdew, J. P.; Burke, K.; Ernzerhof, M. Erratum: Generalized gradient approximation made simple (Physical Review Letters (1996) 77 (3865. Phys. Rev. Lett. 1997, 78, 1396,  DOI: 10.1103/PhysRevLett.78.1396

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    93

    Generalized gradient approximation made simple. [Erratum to document cited in CA126:51093]

    Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias

    Physical Review Letters (1997), 78 (7), 1396CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

    The errors were not reflected in the abstr. or the index entries.

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94. 94

    Del Ben, M.; Hutter, J.; Vandevondele, J. Electron correlation in the condensed phase from a resolution of identity approach based on the gaussian and plane waves scheme. J. Chem. Theory Comput. 2013, 9, 2654– 2671,  DOI: 10.1021/ct4002202

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    94

    Electron Correlation in the Condensed Phase from a Resolution of Identity Approach Based on the Gaussian and Plane Waves Scheme

    Del Ben, Mauro; Hutter, Jurg; VandeVondele, Joost

    Journal of Chemical Theory and Computation (2013), 9 (6), 2654-2671CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    The second-order Moller-Plesset perturbation energy (MP2) and the RPA correlation energy are increasingly popular post-Kohn-Sham correlation methods. Here, a novel algorithm based on a hybrid Gaussian and Plane Waves (GPW) approach with the resoln.-of-identity (RI) approxn. is developed for MP2, scaled opposite-spin MP2 (SOS-MP2), and direct-RPA (dRPA) correlation energies of finite and extended system. The key feature of the method is that the three center electron repulsion integrals (μν|P) necessary for the RI approxn. are computed by direct integration between the products of Gaussian basis functions μν and the electrostatic potential arising from the RI fitting densities P. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. This scheme is highly efficient for condensed phase systems and offers a particularly easy way for parallel implementation. The RI approxn. allows to speed up the MP2 energy calcns. by a factor 10 to 15 compared to the canonical implementation but still requires O(N5) operations. On the other hand, the combination of RI with a Laplace approach in SOS-MP2 and an imaginary frequency integration in dRPA reduces the computational effort to O(N4) in both cases. In addn. to that, our implementations have low memory requirements and display excellent parallel scalability up to tens of thousands of processes. Furthermore, exploiting graphics processing units (GPU), a further speedup by a factor ∼2 is obsd. compared to the std. only CPU implementations. In this way, RI-MP2, RI-SOS-MP2, and RI-dRPA calcns. for condensed phase systems contg. hundreds of atoms and thousands of basis functions can be performed within minutes employing a few hundred hybrid nodes. In order to validate the presented methods, various mol. crystals have been employed as benchmark systems to assess the performance, while solid LiH has been used to study the convergence with respect to the basis set and system size in the case of RI-MP2 and RI-dRPA.

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95. 95

    R̆ezáč, J.; Hobza, P. Describing noncovalent interactions beyond the common approximations: How accurate is the ”gold standard,” CCSD(T) at the complete basis set limit?. J. Chem. Theory Comput. 2013, 9, 2151– 2155,  DOI: 10.1021/ct400057w

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    95

    Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the "Gold Standard," CCSD(T) at the Complete Basis Set Limit?

    Rezac, Jan; Hobza, Pavel

    Journal of Chemical Theory and Computation (2013), 9 (5), 2151-2155CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    We have quantified the effects of approxns. usually made even in accurate CCSD(T)/CBS calcns. of noncovalent interactions, often considered as the "gold std." of computational chem. We have investigated the effect of excitation series truncation, frozen core approxn., and relativistic effects in a set of 24 model complexes. The final CCSD(T) results at the complete basis set limit with corrections to these approxns. are the most accurate est. of the true interaction energies in noncovalent complexes available. The av. error due to these approxns. was found to be about 1.5% of the interaction energy.

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96. 96

    Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a generalpurpose quantum chemistry program package. WIREs Comp. Mol. Sci. 2012, 2, 242– 253,  DOI: 10.1002/wcms.82

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    96

    Molpro: a general-purpose quantum chemistry program package

    Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald; Manby, Frederick R.; Schuetz, Martin

    Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (2), 242-253CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)

    Molpro is a general-purpose quantum chem. program. The original focus was on high-accuracy wave function calcns. for small mols., but using local approxns. combined with explicit correlation treatments, highly accurate coupled-cluster calcns. are now possible for mols. with up to approx. 100 atoms. Recently, multireference correlation treatments were also made applicable to larger mols. Furthermore, an efficient implementation of d. functional theory is available.

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97. 97

    Gonthier, J. F.; Sherrill, C. D. Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps. J. Chem. Phys. 2016, 145, 134106,  DOI: 10.1063/1.4963385

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    97

    Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps

    Gonthier, Jerome F.; Sherrill, C. David

    Journal of Chemical Physics (2016), 145 (13), 134106/1-134106/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component anal. of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermol. interaction and zeroth-order in the intramol. correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize d.-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against ref. values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a pos. charge. (c) 2016 American Institute of Physics.

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98. 98

    Parrish, R. M.; Burns, L. A.; Smith, D. G.; Simmonett, A. C.; DePrince, A. E.; Hohenstein, E. G.; Bozkaya, U.; Sokolov, A. Y.; Di Remigio, R.; Richard, R. M.; Gonthier, J. F.; James, A. M.; McAlexander, H. R.; Kumar, A.; Saitow, M.; Wang, X.; Pritchard, B. P.; Verma, P.; Schaefer, H. F.; Patkowski, K.; King, R. A.; Valeev, E. F.; Evangelista, F. A.; Turney, J. M.; Crawford, T. D.; Sherrill, C. D. Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability. J. Chem. Theory Comput. 2017, 13, 3185– 3197,  DOI: 10.1021/acs.jctc.7b00174

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    98

    PSI4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability

    Parrish, Robert M.; Burns, Lori A.; Smith, Daniel G. A.; Simmonett, Andrew C.; DePrince, A. Eugene; Hohenstein, Edward G.; Bozkaya, Ugur; Sokolov, Alexander Yu.; Di Remigio, Roberto; Richard, Ryan M.; Gonthier, Jerome F.; James, Andrew M.; McAlexander, Harley R.; Kumar, Ashutosh; Saitow, Masaaki; Wang, Xiao; Pritchard, Benjamin P.; Verma, Prakash; Schaefer, Henry F.; Patkowski, Konrad; King, Rollin A.; Valeev, Edward F.; Evangelista, Francesco A.; Turney, Justin M.; Crawford, T. Daniel; Sherrill, C. David

    Journal of Chemical Theory and Computation (2017), 13 (7), 3185-3197CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

    Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, d. functional theory, CI, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as d. fitting, Cholesky decompn., and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chem. Finally, a wide range of new theor. methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory (F-SAPT and O-SAPT), d.-fitted coupled cluster with frozen natural orbitals [DF-FNO-CCSD(T)], orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-CCSD), d.-fitted MC-SCF (DF-MCSCF), d. cumulant functional theory (DCT), algebraic-diagrammatic construction [ADC(2)] excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

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99. 99

    Parker, T. M.; Burns, L. A.; Parrish, R. M.; Ryno, A. G.; Sherrill, C. D. Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies. J. Chem. Phys. 2014, 140, 094106,  DOI: 10.1063/1.4867135

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    99

    Levels of symmetry adapted perturbation theory (SAPT). I. Efficiency and performance for interaction energies

    Parker, Trent M.; Burns, Lori A.; Parrish, Robert M.; Ryno, Alden G.; Sherrill, C. David

    Journal of Chemical Physics (2014), 140 (9), 094106/1-094106/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

    A systematic examn. of the computational expense and accuracy of Symmetry-Adapted Perturbation Theory (SAPT) for the prediction of non-covalent interaction energies is provided with respect to both method [SAPT0, DFT-SAPT, SAPT2, SAPT2+, SAPT2+(3), and SAPT2+3; with and without CCD dispersion for the last three] and basis set [Dunning cc-pVDZ through aug-cc-pV5Z wherever computationally tractable, including truncations of diffuse basis functions]. To improve accuracy for hydrogen-bonded systems, we also include two corrections based on exchange-scaling (sSAPT0) and the supermol. MP2 interaction energy (δMP2). When considering the best error performance relative to computational effort, we recommend as the gold, silver, and bronze std. of SAPT: SAPT2+(3)δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ. Their resp. mean abs. errors in interaction energy across the S22, HBC6, NBC10, and HSG databases are 0.15 (62.9), 0.30 (4.4), and 0.49 kcal mol-1 (0.03 h for adenine·thymine complex). (c) 2014 American Institute of Physics.

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100. 100

     Becke, A. D. Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J. Chem. Phys. 1997, 107, 8554,  DOI: 10.1063/1.475007

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     100

     Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals

     Becke, Axel D.

     Journal of Chemical Physics (1997), 107 (20), 8554-8560CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     A systematic procedure for refining gradient corrections in Kohn-Sham exchange-correlation functionals is presented. The procedure is based on least-squares fitting to accurate thermochem. data. In this first application of the method, we use the G2 test set of Pople and co-workers to generate what we believe to be an optimum GGA/exact-exchange d.-functional theory (i.e., generalized gradient approxn. with mixing of exactly computed exchange).

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101. 101

     Dobson, J. F. Beyond pairwise additivity in London dispersion interactions. Int. J. Quantum Chem. 2014, 114, 1157– 1161,  DOI: 10.1002/qua.24635

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     101

     Beyond pairwise additivity in London dispersion interactions

     Dobson, John F.

     International Journal of Quantum Chemistry (2014), 114 (18), 1157-1161CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)

     The simplest way to predict London dispersion energies involving complex multiatom objects is to add sep. contributions from each pair of atoms. Semiempirical, and even certain less empirical, ways to do this can be very efficient computationally and have recently been developed to a high level of sophistication, with considerable success. There are, however, effects that are not captured in this way, including surprising dependences of the dispersion energy on the no. N of atoms and on sepn. D. Higher level quantum chem., perturbative, and RPA (RPA)-like theories can capture these beyond pairwise effects, but at a high computational cost. Very recent simplified RPA-like approaches based on localized oscillators account for the unusual N dependence in a computationally efficient way. To proceed further, the present work proposes three phys. distinct categories of nonpairwise effects (types A, B, and C) against which the performance of existing and future theories can be assessed.

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102. 102

     Axilrod, B. M.; Teller, E. Interaction of the van der Waals Type Between Three Atoms. J. Chem. Phys. 1943, 11, 299– 300,  DOI: 10.1063/1.1723844

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     102

     Interaction of the van der Waals type among three atoms

     Axilrod, B. M.; Teller, E.

     Journal of Chemical Physics (1943), 11 (), 299-300CODEN: JCPSA6; ISSN:0021-9606.

     The interaction is calcd. for (1) the equilateral triangle, (2) a right triangle, (3) 3 atoms in line, and (4) one atom remote from the other 2.

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103. 103

     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, 154104,  DOI: 10.1063/1.3382344

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     103

     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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104. 104

     Tkatchenko, A.; Distasio, R. A.; Car, R.; Scheffler, M. Accurate and efficient method for many-body van der Waals interactions. Phys. Rev. Lett. 2012, 108, 236402,  DOI: 10.1103/PhysRevLett.108.236402

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     104

     Accurate and efficient method for many-body van der Waals interactions

     Tkatchenko, Alexandre; DiStasio, Robert A., Jr.; Car, Roberto; Scheffler, Matthias

     Physical Review Letters (2012), 108 (23), 236402/1-236402/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap mols. and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of mols. and solids. The screened long-range many-body vdW energy is obtained from the soln. of the Schroedinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small mols., becoming crucial for an accurate treatment of conformational energies for biomols. and binding of mol. crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calcn.

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105. 105

     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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     105

     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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106. 106

     Ruzsinszky, A.; Perdew, J. P.; Tao, J.; Csonka, G. I.; Pitarke, J. M. Van der Waals Coefficients for Nanostructures: Fullerenes Defy Conventional Wisdom. Phys. Rev. Lett. 2012, 109, 233203,  DOI: 10.1103/PhysRevLett.109.233203

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     106

     Van der Waals coefficients for nanostructures: fullerenes defy conventional wisdom

     Ruzsinszky, Adrienn; Perdew, John P.; Tao, Jianmin; Csonka, Gabor I.; Pitarke, J. M.

     Physical Review Letters (2012), 109 (23), 233203/1-233203/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     The van der Waals coeffs. between quasispherical nanostructures can be modeled accurately and anal. by those of classical solid spheres (for nanoclusters) or spherical shells (for fullerenes) of uniform valence electron d., with the true static dipole polarizability. Here, we derive anal. and confirm numerically from this model the size dependencies of the van der Waals coeffs. of all orders, showing, for example, that the asymptotic dependence for C6 is the expected n2 for pairs of nanoclusters An-An, each contg. n atoms, but n2.75 for pairs of single-walled fullerenes Cn-Cn. Large fullerenes are argued to have much larger polarizabilities and dispersion coeffs. than those predicted by either the std. atom pair-potential model or widely used nonlocal van der Waals correlation energy functionals.

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107. 107

     Otero-de-la Roza, A.; Johnson, E. R. Many-body dispersion interactions from the exchange-hole dipole moment model. J. Chem. Phys. 2013, 138, 054103,  DOI: 10.1063/1.4789421

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     107

     Many-body dispersion interactions from the exchange-hole dipole moment model

     Otero-de-la-Roza, A.; Johnson, Erin R.

     Journal of Chemical Physics (2013), 138 (5), 054103/1-054103/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     We present the extension of the exchange-hole dipole moment model (XDM) of dispersion interactions to the calcn. of two-body and three-body dispersion energy terms to any order, 2l-pole oscillator strengths, and polarizabilities. By using the newly-formulated coeffs., we study the relative importance of the higher-order two-body and the leading non-additive three-body (triple-dipole) interactions in gas-phase as well as in condensed systems. We show that the two-body terms up to R-10, but not the terms of higher-order, are essential in the correct description of the dispersion energy, while there are a no. of difficulties related to the choice of the damping function, which precludes the use three-body triple-dipole contributions in XDM. We conclude that further study is required before the three-body term can be used in prodn. XDM d.-functional calcns. and point out the salient problems regarding its use. (c) 2013 American Institute of Physics.

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108. 108

     Ambrosetti, A.; Alfè, D.; DiStasio, R. A.; Tkatchenko, A. Hard Numbers for Large Molecules: Toward Exact Energetics for Supramolecular Systems. J. Phys. Chem. Lett. 2014, 5, 849– 855,  DOI: 10.1021/jz402663k

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     108

     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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109. 109

     Otero-de-la Roza, A.; Johnson, E. R. Predicting Energetics of Supramolecular Systems Using the XDM Dispersion Model. J. Chem. Theory Comput. 2015, 11, 4033– 4040,  DOI: 10.1021/acs.jctc.5b00044

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     109

     Predicting Energetics of Supramolecular Systems Using the XDM Dispersion Model

     Otero-de-la-Roza, A.; Johnson, Erin R.

     Journal of Chemical Theory and Computation (2015), 11 (9), 4033-4040CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

     We examine the ability of the exchange-hole dipole moment (XDM) model of dispersion to treat large supramol. systems. We benchmark several XDM-cor. functionals on the S12L set proposed by Grimme, which comprises large dispersion-bound host-guest systems, for which back-cor. exptl. and Quantum Monte Carlo (QMC) ref. data are available. PBE-XDM coupled with the relatively economical and efficient pc-2-spd basis set gives excellent statistics (mean abs. error (MAE) = 1.5 kcal/mol), below the deviation between exptl. and QMC data. When compared only to the (more accurate) QMC results, PBE-XDM/pc-2-spd (MAE = 1.2 kcal/mol) outperforms all other dispersion-cor. DFT results in the literature, including PBE-dDsC/QZ4P (6.2 kcal/mol), PBE-NL/def2-QZVP (4.7 kcal/mol), PBE-D2/def2-QZVP' (3.5 kcal/mol), PBE-D3/def2-QZVP'(2.3 kcal/mol), M06-L/def2-QZVP (1.9 kcal/mol), and PBE-MBD (1.8 kcal/mol), with no significant bias (mean error (ME) = 0.04 kcal/mol). PBE-XDM/pc-2-spd gives binding energies relatively close to the complete basis-set limit and does not necessitate the use of counterpoise corrections, which facilitates its use. The dipole-quadrupole and quadrupole-quadrupole pairwise dispersion terms (C8 and C10) are crit. for the correct description of the dimers. XDM-cor. functionals different from PBE that work well for small dimers do not yield good accuracy for the large supramol. systems in the S12L, presenting errors that scale linearly with the dispersion contribution to the binding energy.

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110. 110

     Johnson, E. R.; Becke, A. D. A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections. J. Chem. Phys. 2006, 124, 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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111. 111

     Vydrov, O. A.; Van Voorhis, T. Nonlocal van der Waals density functional: The simpler the better. J. Chem. Phys. 2010, 133, 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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112. 112

     Najibi, A.; Goerigk, L. The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches. J. Chem. Theory Comput. 2018, 14, 5725– 5738,  DOI: 10.1021/acs.jctc.8b00842

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     112

     The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches

     Najibi, Asim; Goerigk, Lars

     Journal of Chemical Theory and Computation (2018), 14 (11), 5725-5738CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

     The development of van der Waals d. functional approxns. (vdW-DFAs) has gained considerable interest over the past decade. While in a strictest sense, energy calcns. with vdW-DFAs should be carried out fully self-consistently, we demonstrate conclusively for a total of 11 methods that such a strategy only increases the computational time effort without having any significant effect on energetic properties, electron densities, or orbital-energy differences. The strategy to apply a nonlocal vdW-DFA kernel as an additive correction to a fully converged conventional DFA result is therefore justified and more efficient. As part of our study, we utilize the extensive GMTKN55 database for general main-group thermochem., kinetics, and noncovalent interactions [Phys. Chem. Chem. Phys.2017, 19, 32184], which allows us to analyze the very promising B97M-V [J. Chem. Phys. 2015, 142, 074111] and ωB97M-V [J. Chem. Phys. 2016, 144, 214110] DFAs. We also present new DFT-D3(BJ) based counterparts of these two methods and of ωB97X-V [J. Chem. Theory Comput 2013, 9, 263], which are faster variants with similar accuracy. Our study concludes with updated recommendations for the general method user, based on our current overview of 325 dispersion-cor. and -uncorrected DFA variants analyzed for GMTKN55. VdW-DFAs are the best representatives of the three highest rungs of Jacob's Ladder, namely, B97M-V, ωB97M-V, and DSD-PBEP86-NL.

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113. 113

     Caldeweyher, E.; Bannwarth, C.; Grimme, S. Extension of the D3 dispersion coefficient model. J. Chem. Phys. 2017, 147, 034112,  DOI: 10.1063/1.4993215

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     113

     Extension of the D3 dispersion coefficient model

     Caldeweyher, Eike; Bannwarth, Christoph; Grimme, Stefan

     Journal of Chemical Physics (2017), 147 (3), 034112/1-034112/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     A new model, termed D4, for the efficient computation of mol. dipole-dipole dispersion coeffs. is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-mol. dispersion coeffs. over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent d. functional theory calcns. for atoms in different chem. environments employing fractional at. coordination nos. for interpolation. Different from the D3 model, the coeffs. are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, at. polarizabilities α(iω). Most importantly, electronic d. information is now incorporated via at. partial charges computed at a semiempirical quantum mech. tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coeffs. with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-mol. static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three std. d. functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets. (c) 2017 American Institute of Physics.

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114. 114

     Caldeweyher, E.; Ehlert, S.; Hansen, A.; Neugebauer, H.; Spicher, S.; Bannwarth, C.; Grimme, S. A generally applicable atomic-charge dependent London dispersion correction. J. Chem. Phys. 2019, 150, 154122,  DOI: 10.1063/1.5090222

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     114

     A generally applicable atomic-charge dependent London dispersion correction

     Caldeweyher, Eike; Ehlert, Sebastian; Hansen, Andreas; Neugebauer, Hagen; Spicher, Sebastian; Bannwarth, Christoph; Grimme, Stefan

     Journal of Chemical Physics (2019), 150 (15), 154122/1-154122/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     The so-called D4 model is presented for the accurate computation of London dispersion interactions in d. functional theory approxns. (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the at. coordination-dependent dipole polarizabilities are scaled based on at. partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an at. electronegativity equilibration procedure for which efficient anal. derivs. with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-mol. dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coeffs. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 mol. dipole-dipole dispersion coeffs., the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addn. to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are detd. for more than 60 common d. functionals. For various std. energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Esp. for metal contg. systems, the introduced charge dependence of the dispersion coeffs. improves thermochem. properties. We suggest (DFT-)D4 as a phys. improved and more sophisticated dispersion model in place of DFT-D3 for DFT calcns. as well as other low-cost approaches like semi-empirical models. (c) 2019 American Institute of Physics.

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115. 115

     Gill, P. M.; Johnson, B. G.; Pople, J. A. A standard grid for density functional calculations. Chem. Phys. Lett. 1993, 209, 506– 512,  DOI: 10.1016/0009-2614(93)80125-9

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     A standard grid for density functional calculations

     Gill, Peter M. W.; Johnson, Benny G.; Pople, John A.

     Chemical Physics Letters (1993), 209 (5-6), 506-12CODEN: CHPLBC; ISSN:0009-2614.

     An efficient and reasonably accurate grid, designated SG-1, is proposed for use in d. functional calcns. Defined for all atoms from H to Ar, SG-1 is recommended as a std. grid, analogous to the various std. basis sets which are used in contemporary quantum chem. In calcns. on systems of moderate size, the differences between SG-1 and very large grids are of the order of 0.2 kcal/mol, yet SG-1 is sufficiently small to be applied to large systems.

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116. 116

     Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 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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117. 117

     Furche, F.; Van Voorhis, T. Fluctuation-dissipation theorem density-functional theory. J. Chem. Phys. 2005, 122, 164106,  DOI: 10.1063/1.1884112

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     Fluctuation-dissipation theorem density-functional theory

     Furche, Filipp; Van Voorhis, Troy

     Journal of Chemical Physics (2005), 122 (16), 164106/1-164106/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     Using the fluctuation-dissipation theorem (FDT) in the context of d.-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent d. response function. When combined with time-dependent d.-functional theory, a new class of d. functionals results that use approxns. to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of mols. using FDT-DFT beyond the RPA (RPA)-i.e., the first such results with fxc ≠ 0. We show that kernels derived from the adiabatic local-d. approxn. and other semilocal functionals suffer from an "UV catastrophe," producing a pair d. that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approxns. to fxc should satisfy and discuss the prospects of FDT-DFT.

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118. 118

     Janesko, B. G.; Henderson, T. M.; Scuseria, G. E. Long-range-corrected hybrids including random phase approximation correlation. J. Chem. Phys. 2009, 130, 081105,  DOI: 10.1063/1.3090814

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     Long-range-corrected hybrids including random phase approximation correlation

     Janesko, Benjamin G.; Henderson, Thomas M.; Scuseria, Gustavo E.

     Journal of Chemical Physics (2009), 130 (8), 081105/1-081105/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     We recently demonstrated a connection between the RPA and coupled cluster theory. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into d. functional theory. Our method provides good thermochem. results and models van der Waals interactions accurately. (c) 2009 American Institute of Physics.

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119. 119

     Toulouse, J.; Gerber, I. C.; Jansen, G.; Savin, A.; Ángyán, J. G. Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation. Phys. Rev. Lett. 2009, 102, 096404,  DOI: 10.1103/PhysRevLett.102.096404

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     Adiabatic-Connection Fluctuation-Dissipation Density-Functional Theory Based on Range Separation

     Toulouse, Julien; Gerber, Iann C.; Jansen, Georg; Savin, Andreas; Angyan, Janos G.

     Physical Review Letters (2009), 102 (9), 096404/1-096404/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     An adiabatic-connection fluctuation-dissipation theorem approach based on a range sepn. of electron-electron interactions is proposed. It involves a rigorous combination of short-range d.-functional and long-range random phase approxns. This method corrects several shortcomings of the std. RPA and it is particularly well suited for describing weakly bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be2 and Ne2.

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120. 120

     Zhu, W.; Toulouse, J.; Savin, A.; Ángyán, J. G. Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions. J. Chem. Phys. 2010, 132, 244108,  DOI: 10.1063/1.3431616

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     Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions

     Zhu, Wuming; Toulouse, Julien; Savin, Andreas; Angyan, Janos G.

     Journal of Chemical Physics (2010), 132 (24), 244108/1-244108/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     Range-sepd. methods combining a short-range d. functional with long-range random phase approxns. (RPAs) with or without exchange response kernel are tested on rare-gas dimers and the S22 benchmark set of weakly interacting complexes of Jurecka et al. (Phys. Chem. Chem. Phys., 8, 1985 (2006)). The methods are also compared to full-range RPA approaches. Both range sepn. and inclusion of the Hartree-Fock exchange kernel largely improve the accuracy of intermol. interaction energies. The best results are obtained with the method called RSH + RPAx, which yields interaction energies for the S22 set with an estd. mean abs. error of about 0.5-0.6 kcal/mol, corresponding to a mean abs. percentage error of about 7%-9% depending on the ref. interaction energies used. In particular, the RSH + RPAx method is found to be overall more accurate than the range-sepd. method based on long-range second-order Moller-Plesset (MP2) perturbation theory (RSH + MP2). (c) 2010 American Institute of Physics.

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121. 121

     Toulouse, J.; Zhu, W.; Savin, A.; Jansen, G.; Ángyán, J. G. Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions. J. Chem. Phys. 2011, 135, 084119,  DOI: 10.1063/1.3626551

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     Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions

     Toulouse, Julien; Zhu, Wuming; Savin, Andreas; Jansen, Georg; Angyan, Janos G.

     Journal of Chemical Physics (2011), 135 (8), 084119/1-084119/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     We explore different variants of the RPA to the correlation energy derived from closed-shell ring-diagram approxns. to coupled cluster doubles theory. We implement these variants in range-sepd. d.-functional theory, i.e., by combining the long-range random phase approxns. with short-range d.-functional approxns. We perform tests on the rare-gas dimers He2, Ne2, and Ar2, and on the weakly interacting mol. complexes of the S22 set of Jurecka. The two best variants correspond to the ones originally proposed by Szabo and Ostlund. With range sepn., they reach mean abs. errors on the equil. interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean abs. percentage errors of about 4%, with the aug-cc-pVDZ basis set. (c) 2011 American Institute of Physics.

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122. 122

     Harl, J.; Kresse, G. Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 045136,  DOI: 10.1103/PhysRevB.77.045136

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     Cohesive energy curves for noble gas solids calculated by adiabatic connection fluctuation-dissipation theory

     Harl, Judith; Kresse, Georg

     Physical Review B: Condensed Matter and Materials Physics (2008), 77 (4), 045136/1-045136/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)

     We present first-principles calcns. for the fcc noble gas solids Ne, Ar, and Kr applying the adiabatic connection fluctuation-dissipation theorem (ACFDT) to evaluate the correlation energy. The ACFDT allows us to describe long-range correlation effects including London dispersion or van der Waals interaction on top of conventional d. functional theory calcns. Even within the RPA, the typical 1/V2 vol. dependence for the cohesive energy of the noble gas solids is reproduced, and equil. cohesive energies and lattice consts. are improved compared to d. functional theory calcns. Furthermore, we present atomization energies for H2, N2, and O2 within the same post-d.-functional-theory framework, finding an excellent agreement with previously published data.

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123. 123

     Lu, D.; Li, Y.; Rocca, D.; Galli, G. Ab initio calculation of van der Waals bonded molecular crystals. Phys. Rev. Lett. 2009, 102, 206411,  DOI: 10.1103/PhysRevLett.102.206411

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     Ab initio Calculation of van der Waals Bonded Molecular Crystals

     Lu, Deyu; Li, Yan; Rocca, Dario; Galli, Giulia

     Physical Review Letters (2009), 102 (20), 206411/1-206411/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     Intermol. interactions in the van der Waals bonded benzene crystal are studied from first principles, by combining exact exchange energies with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the RPA. Correlation energies are evaluated using an iterative procedure to compute the eigenvalues of dielec. matrixes, which eliminates the computation of unoccupied electronic states. Our results for the structural and binding properties of solid benzene are in very good agreement with exptl. results and show that the framework adopted here is a very promising one to investigate mol. crystals and other condensed systems bound by dispersion forces.

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124. 124

     Li, Y.; Lu, D.; Nguyen, H. V.; Galii, G. Van der waals interactions in molecular assemblies from first-principles calculations. J. Phys. Chem. A 2010, 114, 1944– 1952,  DOI: 10.1021/jp9095425

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     van der Waals Interactions in Molecular Assemblies from First-Principles Calculations

     Li, Yan; Lu, Deyu; Nguyen, Huy-Viet; Galli, Giulia

     Journal of Physical Chemistry A (2010), 114 (4), 1944-1952CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)

     We investigated intermol. interactions in weakly bonded mol. assemblies from first principles, by combining exact exchange energies (EXX) with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the RPA. We considered three different types of mol. systems: the benzene crystal, the methane crystal, and self-assembled monolayers of phenylenediisocyanide, which involve arom. rings, sp3-hybridized C-H bonds, and isocyanide triple bonds, resp. We describe in detail how computed equil. lattice consts. and cohesive energies may be affected by the input ground state wave functions and orbital energies, by the geometries of mol. monomers in the assemblies, and by the inclusion of zero-point energy contribution to the total energy. We find that the EXX/RPA perturbative approach provides an overall satisfactory, first-principles description of dispersion forces. However, binding energies tend to be underestimated, and possible reasons for this discrepancy are discussed.

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125. 125

     Scuseria, G. E.; Henderson, T. M.; Sorensen, D. C. The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach. J. Chem. Phys. 2008, 129, 231101,  DOI: 10.1063/1.3043729

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     The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach

     Scuseria, Gustavo E.; Henderson, Thomas M.; Sorensen, Danny C.

     Journal of Chemical Physics (2008), 129 (23), 231101/1-231101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)

     We present an analytic proof demonstrating the equivalence between the RPA to the ground state correlation energy and a ring-diagram simplification of the coupled cluster doubles (CCD) equations. In the CCD framework, the RPA equations can be solved in O(N4) computational effort, where N is proportional to the no. of basis functions. (c) 2008 American Institute of Physics.

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126. 126

     Kroon-Batenburg, L.; van Duijneveldt, F. The use of a moment-optimized DZP basis set for describing the interaction in the water dimer. J. Mol. Struct.: THEOCHEM 1985, 121, 185– 199,  DOI: 10.1016/0166-1280(85)80058-0

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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, 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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128. 128

     Sherrill, C. D. Energy component analysis of π interactions. Acc. Chem. Res. 2013, 46, 1020– 1028,  DOI: 10.1021/ar3001124

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     Energy Component Analysis of π Interactions

     Sherrill, C. David

     Accounts of Chemical Research (2013), 46 (4), 1020-1028CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)

     A review. Fundamental features of biomols., such as their structure, solvation, and crystal packing and even the docking of drugs, rely on noncovalent interactions. Theory can help elucidate the nature of these interactions, and energy component anal. reveals the contributions from the various intermol. forces: electrostatics, London dispersion terms, induction (polarization), and short-range exchange-repulsion. Symmetry-adapted perturbation theory (SAPT) provides one method for this type of anal. In this Account, we show several examples of how SAPT pro-vides insight into the nature of noncovalent π-interactions. In cation-π interactions, the cation strongly polarizes electrons in π-orbitals, leading to substantially attractive induction terms. This polarization is so important that a cation and a benzene attract each other when placed in the same plane, even though a consideration of the electrostatic interactions alone would suggest otherwise. SAPT anal. can also support an understanding of substituent effects in π-π interactions. Trends in face-to-face sandwich benzene dimers cannot be understood solely in terms of electrostatic effects, esp. for multiply substituted dimers, but SAPT anal. demonstrates the importance of London dispersion forces. Moreover, detailed SAPT studies also reveal the crit. importance of charge penetration effects in π-stacking interactions. These effects arise in cases with substantial orbital overlap, such as in π-stacking in DNA or in crystal structures of π-conjugated materials. These charge penetration effects lead to attractive electrostatic terms where a simpler anal. based on atom-centered charges, electrostatic potential plots, or even distributed multipole anal. would incorrectly predict repulsive electrostatics. SAPT anal. of sandwich benzene, benzene-pyridine, and pyridine dimers indicates that dipole/induced-dipole terms present in benzene-pyridine but not in benzene dimer are relatively unimportant. In general, a nitrogen heteroatom contracts the electron d., reducing the magnitude of both the London dispersion and the exchange-repulsion terms, but with an overall net increase in attraction. Finally, using recent advances in SAPT algorithms, researchers can now perform SAPT computations on systems with 200 atoms or more. We discuss a recent study of the intercalation complex of proflavine with a trinucleotide duplex of DNA. Here, London dispersion forces are the strongest contributors to binding, as is typical for π-π interactions. However, the electrostatic terms are larger than usual on a fractional basis, which likely results from the pos. charge on the intercalators and their location between two electron-rich base pairs. These cation-π interactions also increase the induction term beyond those of typical noncovalent π-interactions.

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129. 129

     Tang, K. T.; 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, 3726,  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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130. 130

     Tang, K. T.; Toennies, J. P.; Yiu, C. L. Accurate Analytical He-He van der Waals Potential Based on Perturbation Theory. Phys. Rev. Lett. 1995, 74, 1546– 1549,  DOI: 10.1103/PhysRevLett.74.1546

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     Accurate analytical He-He van der Waals Potential based on perturbation theory

     Tang, K. T.; Toennies, J. P.; Yiu, C. L.

     Physical Review Letters (1995), 74 (9), 1546-9CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)

     A simple anal. expression for the entire van der Waals potential curve of the helium dimer is derived from perturbation theory. The repulsive part is essentially from Duman and Simirnov [Opt. Spectrosc. 29, 229, (1970)] who assume the exchange of only one pair of electrons at any one time. The potential depends only on the known dispersion coeffs. and the amplitude of the asymptotic wave function and the ionization energy of the atoms. Without any adjustable parameters the potential is in excellent agreement with the latest exptl. and theor. results and predicts the existence of the He dimer. The same method can be applied to heavier rare gases.

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131. 131

     Steinmann, S. N.; Csonka, G.; Corminboeuf, C. Unified Inter- and Intramolecular Dispersion Correction Formula for Generalized Gradient Approximation Density Functional Theory. J. Chem. Theory Comput. 2009, 5, 2950– 2958,  DOI: 10.1021/ct9002509

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     Unified Inter- and Intramolecular Dispersion Correction Formula for Generalized Gradient Approximation Density Functional Theory

     Steinmann, Stephan N.; Csonka, Gabor; Corminboeuf, Clemence

     Journal of Chemical Theory and Computation (2009), 5 (11), 2950-2958CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)

     D. functionals fail to provide a consistent description of weak intra- (i.e., short-range) and inter- (i.e., long-range) mol. interactions arising from nonoverlapping electron densities. An efficient way to correct the long-range errors is to add an empirical atom pair wise interaction-correction, inspired by the Lennard-Jones potential (R-6 dependence). We show that the universal damping function of Tang and Toennies (TT) that includes higher-order correction terms (R-8 and R-10 dependent) reduces the intramol. errors more efficiently, without altering the long-range correction. For general applicability, the TT damping function is augmented by a Fermi damping to prevent corrections at covalent distances. The performance of the new dD10 correction was tested in combination with three nonempirical GGAs (PBE, PBEsol, RGE2) on 64 illustrative reaction energies featuring both intra- and intermol. interactions. With only two empirical parameters, PBE-dD10 outperforms the computationally more demanding and most recent functionals such as M06-2X or B2PLYP-D (MAD = 3.78 and 1.95 kcal mol-1, resp.). At the cc-pVTZ level, PBE-dD10 (MAD = 1.24 kcal mol-1) considerably reduces common DFT errors successfully balancing intra- (short-range) and inter- (long-range) mol. interactions. While REG2-dD10 performs closely to PBE-dD10 (MAD = 1.48 kcal mol-1), the overall MAD of PBEsol-dD10 is again slightly higher (MAD = 1.76 kcal mol-1).

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132. 132

     Schmidt, J.; Benavides-Riveros, C. L.; Marques, M. A. L. Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory. J. Phys. Chem. Lett. 2019, 10, 6425– 6431,  DOI: 10.1021/acs.jpclett.9b02422

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     Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory

     Schmidt, Jonathan; Benavides-Riveros, Carlos L.; Marques, Miguel A. L.

     Journal of Physical Chemistry Letters (2019), 10 (20), 6425-6431CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)

     We train a neural network as the universal exchange-correlation functional of d.-functional theory that simultaneously reproduces both the exact exchange-correlation energy and the potential. This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approxns. It therefore holds the promise of solving some of the delocalization problems that plague d.-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact math. relation between the exchange-correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where d.-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.

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133. 133

     Fabrizio, A.; Grisafi, A.; Meyer, B.; Ceriotti, M.; Corminboeuf, C. Electron density learning of non-covalent systems. Chem. Sci. 2019, 10, 9424– 9432,  DOI: 10.1039/C9SC02696G

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     Electron density learning of non-covalent systems

     Fabrizio, Alberto; Grisafi, Andrea; Meyer, Benjamin; Ceriotti, Michele; Corminboeuf, Clemence

     Chemical Science (2019), 10 (41), 9424-9432CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)

     Chemists continuously harvest the power of non-covalent interactions to control phenomena in both the micro- and macroscopic worlds. From the quantum chem. perspective, the strategies essentially rely upon an in-depth understanding of the phys. origin of these interactions, the quantification of their magnitude and their visualization in real-space. The total electron d. ρ(r) represents the simplest yet most comprehensive piece of information available for fully characterizing bonding patterns and non-covalent interactions. The charge d. of a mol. can be computed by solving the Schr.ovrddot.odinger equation, but this approach becomes rapidly demanding if the electron d. has to be evaluated for thousands of different mols. or very large chem. systems, such as peptides and proteins. Here we present a transferable and scalable machine-learning model capable of predicting the total electron d. directly from the at. coordinates. The regression model is used to access qual. and quant. insights beyond the underlying ρ(r) in a diverse ensemble of sidechain-sidechain dimers extd. from the BioFragment database (BFDb). The transferability of the model to more complex chem. systems is demonstrated by predicting and analyzing the electron d. of a collection of 8 polypeptides.

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