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The Grignard Reaction – Unraveling a Chemical Puzzle

  • Raphael Mathias Peltzer
    Raphael Mathias Peltzer
    Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O. Box 1033 Blindern, Oslo 0315, Norway
    More by Raphael Mathias Peltzer
  • , 
  • Jürgen Gauss
    Jürgen Gauss
    Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz 55128, Germany
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  • , 
  • Odile Eisenstein*
    Odile Eisenstein
    Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O. Box 1033 Blindern, Oslo 0315, Norway
    ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier 34095 Cedex 5, France
    *[email protected]
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    Orcidhttp://orcid.org/0000-0001-5056-0311
  • , and 
  • Michele Cascella*
    Michele Cascella
    Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O. Box 1033 Blindern, Oslo 0315, Norway
    *[email protected]
    More by Michele Cascella
    Orcidhttp://orcid.org/0000-0003-2266-5399
Cite this: J. Am. Chem. Soc. 2020, 142, 6, 2984–2994
Publication Date (Web):January 17, 2020
https://doi.org/10.1021/jacs.9b11829

Copyright © 2020 American Chemical Society. This publication is licensed under CC-BY-NC-ND.

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Abstract

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More than 100 years since its discovery, the mechanism of the Grignard reaction remains unresolved. Ambiguities arise from the concomitant presence of multiple organomagnesium species and the competing mechanisms involving either nucleophilic addition or the formation of radical intermediates. To shed light on this topic, quantum-chemical calculations and ab initio molecular dynamics simulations are used to study the reaction of CH3MgCl in tetrahydrofuran with acetaldehyde and fluorenone as prototypical reagents. All organomagnesium species coexisting in solution due to the Schlenk equilibrium are found to be competent reagents for the nucleophilic pathway. The range of activation energies displayed by all of these compounds is relatively small. The most reactive species are a dinuclear Mg complex in which the substrate and the nucleophile initially bind to different Mg centers and the mononuclear dimethyl magnesium. The radical reaction, which requires the homolytic cleavage of the Mg–CH3 bond, cannot occur unless a substrate with a low-lying π*(CO) orbital coordinates the Mg center. This rationalizes why a radical mechanism is detected only in the presence of substrates with a low reduction potential. This feature, in turn, does not necessarily favor the nucleophilic addition, as shown for the reaction with fluorenone. The solvent needs to be considered as a reactant for both the nucleophilic and the radical reactions, and its dynamics is essential for representing the energy profile. The similar reactivity of several species in fast equilibrium implies that the reaction does not occur via a single process but by an ensemble of parallel reactions.

Introduction

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The Grignard reaction is a prominent textbook process to form carbon–carbon bonds. (1) In this reaction, the so-called Grignard reagent, an organomagnesium species RMgX where R is an organic residue and X is a halogen (usually Cl or Br), promotes the addition of its organic residue to an electrophilic substrate. Discovered by Victor Grignard (2) already in 1900, Grignard reagents rapidly became important compounds for organic synthesis in research laboratories and in industry. (3) Even though the reaction today is applied to a large variety of electrophiles, the prototypic substrates are carbonyl moieties R1R2(C═O) yielding a magnesium-alcoholate (eq 1). The R1 and R2 residues usually include hydrogen as well as alkyl-, vinyl-, or aryl- groups. The Grignard reaction usually takes place in ethereal solvents, the final alcohol product being obtained by hydrolysis.
(1)
Despite more than 100 years of extensive studies, the mechanism of this reaction has remained elusive, with little quantitative information and missing consensus. Difficulties in elucidating this mechanism are prominently related to the fact that the ethereal solutions of Grignard reagents contain a variety of chemical species. (4,5) In fact, the nominal reactant RMgX is just a condensed representation of numerous mono- and polymetallic molecules that coexist at equilibrium (eq 2) and whose relative abundance depends on the nature of R and X as well as the experimental conditions. (4,6)
(2)
Furthermore, while the polarity of the C(δ−)–Mg(δ+) bond suggests that the Grignard reagent acts as a nucleophile, it has been argued that an electron-transfer mechanism may occur in the presence of appropriate substrates. (5)
This multifaceted aspect of the Grignard chemistry is per se fascinating; in fact, the lack of understanding of its molecular mechanisms has slowed progress in the rational design of more efficient variants of the reaction. Indeed, while the efficiency of Grignard reagents has been heuristically improved, for example by the synergistic effect of additives like alkali ions, the reasons for these improvements remain unclear. (7) Elucidation of the mechanism of the basic Grignard reaction is the required step to better understand a wide variety of related reactions.
Although the nucleophilic mechanism (also known as the polar mechanism) is currently recognized in the literature as a route to the alcohol product, no experimental study was able to assign the relative reactivity of the various forms of the organomagnesium species. In parallel, experimental evidence consistently supported the presence of an alternative mechanism (called radical or single electron-transfer mechanism) involving the formation of radical intermediates (Figure 1). In particular, products were detected, which could not originate from a nucleophilic addition but could be only obtained through a combination of organic radicals. (8−15) Furthermore, electron spin resonance spectroscopy identified the presence of ketyl radicals in benzophenone/Grignard reagent mixtures. (16) Factors favoring the radical mechanism were searched. Thus, using the distribution of products as an indicator for the mechanism, Ashby and co-workers inferred that an electron-transfer mechanism depends on the reduction potential of the substrate, the oxidation potential of the Grignard reagent, and the polarity of the solvent. Ketones with low reduction potential favored the radical mechanism. Indeed, a radical-type reaction was established for aromatic and conjugated ketones (such as benzophenone and fluorenenone) in the case of tertiary as well as primary Grignard reagents. (14)

Figure 1

Figure 1. Schematic representation of possible mechanisms for the Grignard reaction: (a) polar mechanism, heterolytic Mg–C bond breaking, with subsequent formation of a nucleophilic carbon that adds to the electrophilic carbonyl carbon; or (b) radical mechanism, homolytic Mg–C bond breaking, with subsequent recombination of the species with unpaired electrons.

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Chiral Grignard reagents were also used to probe the reaction pathway. It was in this way shown that chiral secondary Grignard reagents react largely, but not exclusively, by a radical mechanism with benzophenone, but essentially by nucleophilic addition with benzaldehyde. (17,18) The secondary H/D kinetic isotope effect indicated that the competition between the nucleophilic and the single electron-transfer mechanisms depends on the reagent (i.e., magnesium or lithium organometallic species) and the substrate. (19) Recently, it was shown that the Grignard reaction with aliphatic aldehydes does not involve single electron transfer. (20) These last results point at a clear preference for nucleophilic addition for aliphatic aldehyde and a possible competition between the radical and nucleophilic pathways for substrates with lower reduction potential, that is, aromatic or conjugated aldehydes or ketones.
While various aspects of the chemistry of Grignard species, including their formation, (21−23) their structure, and their thermodynamics in solution, (24−27) were addressed by computational approaches, the Grignard reaction itself has been the subject of only a few studies. (28) In particular, in 2002 Yamazaki and Yamabe used density functional theory (DFT) calculations together with implicit solvation models to suggest that dinuclear Grignard moieties are more reactive in a nucleophilic addition than are monomeric species. (29) Similar results were obtained with second-order Møller–Plesset perturbation theory together with implicit solvation models. (30) Yamazaki and Yamabe suggested that a mechanism going through Mg–C homolytic cleavage could be preferred in the case of bulky organic residues, for which the nucleophilic addition is sterically hindered. (29)
Recently, some of us carried out an ab initio molecular dynamics (AIMD) study of CH3MgCl in tetrahydrofuran (THF) to get insight on the role of the solvent in the Schlenk equilibrium. (31) Among other findings, this study showed that the magnesium centers of the mononuclear and dinuclear species can accommodate a variable number of solvent molecules in their first coordination spheres and that the interchange of the methyl and chloride groups between the two magnesium centers is associated with a change in the solvation number. (31) This study thus revealed that it was essential to allow a synergy between the solvent contribution and the chemical event at the Mg centers and to represent the associated solvent reorganization, an effect that cannot be properly described by a static approach.
The purpose of the present study is to use computational approaches to determine the factors that drive the Grignard reaction toward preferred pathways (in particular nucleophilic vs single electron transfer) in the presence of prototypical carbonyl substrates, as well as to elucidate the mechanistic details for each specific transformation. The employment of ab initio molecular dynamics and enhanced-sampling methods in explicit solvent facilitates an unbiased exploration of the conformational space. In particular, it allows a thorough sampling of the solvation states of all organomagnesium species and a reliable description of solvent dynamics. Finally, state-of-the-art quantum-chemical calculations provide solid data to understand the factors that promote a single electron-transfer pathway.

Computational Methods

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Ab Initio Molecular Dynamics Simulations

Simulation Protocol

The thermodynamically equilibrated structures of the Grignard reagent in THF in different protomeric and solvated forms were determined in a previous study. (31) In this work, the initial geometry of each reactive complex was built starting from that of the respective Grignard reagent by replacing one THF coordinated to Mg with a substrate molecule. All systems were simulated in an orthorhombic periodic box of dimensions 25.2 × 15.0 × 15.0 Å3, containing 41 THF molecules. The quantum-chemical problem was solved at the DFT (32,33) level using the Perdew–Burke–Ernzerhof (PBE) exchange correlation (xc) functional. (34) The Kohn–Sham orbitals were expanded over mixed Gaussian and plane-wave basis functions. The DZVP basis set for first and second row elements and a molecular optimized basis set for chlorine were employed. (35) The auxiliary plane-wave basis set was expanded up to a 200 Ry cutoff. The core electrons were integrated out using pseudopotentials of the Goedecker–Teter–Hutter type (GTH). (36) Dispersion forces were included using the D3 Grimme approximation. (37) AIMD simulations were run over the ground-state potential energy surface, adopting a threshold for the energy gradient of 10–5 au as numerical convergence criterion for the electronic energy. The equations of motion were integrated employing the velocity Verlet algorithm (38) with a time-step of 0.25 fs. Relaxation to the target temperature was first performed using a canonical sampling/velocity rescaling (CSVR) thermostat (39) with a time constant of 10 fs until the temperature of the system oscillated around the target value. A Nosé–Hoover chain thermostat with a chain length of 3 and a time constant of 1 ps then was used for data production. (40−42) Trajectory analysis was performed using the tools available in the VMD 1.9.2 package. (43)

Polar Mechanism – Activation Energies

The activation barriers for the nucleophilic addition were estimated by constraint dynamics in the blue-moon ensemble (44) using the distance between the methyl group and the carbonyl carbon as reaction coordinate λ. The constraint force f(λ) was collected over independent AIMD runs at nine fixed values of λ spaced by 0.2–0.1 Å. The average value of f at each λ point (⟨f⟩λ) converged with steady mean values of ∼0.5 kcal mol–1 Å–1 within ∼2 ps of simulations. The activation free energy ΔA⧧ was computed by trapezoidal integration of ⟨f⟩λ between λ values corresponding to the reactant and the TS. This last point was identified as the value of λ at which ⟨f⟩λ = 0. The work reports Helmholtz free energies as AIMD are performed at constant volume conditions.

Radical Formation Energy

The dissociation energy associated with the homolytic cleavage of the Mg–methyl bond for different Grignard reagent/substrate complexes was estimated as the difference between the total energy of the reactant and that of the individual fragments. THF molecules directly bound to Mg were explicitly considered in the model, while the rest of the solvent was treated implicitly using a continuum dielectric model. (45) The electronic problem was solved at the DFT level using the M06-2X xc functional (46) and the 6-31+G(d,p) basis set. (47) Calculations were performed using the Gaussian 09 package. (48) The choice of the M06-2X functional was done after assessing the quality of different xc functionals in reproducing coupled-cluster (CC) data for the radical formation energy in a simplified model (Table S1). The reference energies were obtained using the CC singles and doubles (CCSD) approximation augmented by a perturbative treatment of triple excitations (CCSD(T)) (49) with an energy convergence threshold of 10–9 hartree, using a cc-pVTZ basis set. (50) The CCSD(T) calculations were carried out using the CFOUR package. (51)

Results and Discussion

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Polar Mechanism

Alkyl carbonyl substrates have been shown to prefer a nucleophilic pathway in their reaction with Grignard reagents. (20) For this reason, we modeled the reaction of acetaldehyde (ACA hereafter) with CH3MgCl in THF. All forms of CH3MgCl identified in our previous study as stable species coexisting at thermal equilibrium in THF (31) were considered as potential reactive systems after replacing one coordinated THF by ACA. (31)
Figure 2 shows the labels used throughout this work to identify the organometallic mononuclear and binuclear species and the associated possible pathways, which are characterized by the position of the reactive groups on the Mg centers. The pathway is called geminal if the two groups are on the same magnesium atom and is called vicinal if they are on two different magnesiums. Finally, a pathway where the methyl group bridges the two magnesium atoms was also considered.

Figure 2

Figure 2. Organomagnesium complexes considered as reactants for the polar mechanism, classified as a function of the relative positions of the substrate (ACA) and nucleophile (methyl group). The labels geminal, vicinal, and bridging describe the initial position of the reactive groups with respect to the Mg center(s). The activation free energies, ΔA⧧, defined as the difference in free energy between the TS and the related reactant species, are given in kcal mol–1.

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Reaction with Geminal and Bridging Groups

Both mononuclear and dinuclear Mg species can be associated with geminal pathways. Of the two mononuclear systems, Bgem gives the energetically lowest transition state (TS), with an ΔA⧧ of 6.5 ± 0.7 kcal mol–1 (Figure 2). The pathway starting from CH3MgCl (Agem) has a higher lying TS with ΔA⧧ = 8.7 ± 0.8 kcal mol–1. Egem is the most reactive dinuclear complex via a geminal pathway. This species is a variant of Bgem in which the coordinated THF is replaced by a Cl-coordinated MgCl2(THF)2 moiety. It is thus not surprising that the TSs associated with Bgem and Egem have similar activation energies. However, our earlier study on the Schlenk equilibrium (31) indicated that Egem is less abundant than Bgem. This suggests that Egem may contribute only marginally to the formation of the product. Species Cgem and Dgem are instead characterized by a significantly higher activation energy (both around 13 kcal mol–1, Figure 2). Finally, the bridging methyl group is unlikely to act as a nucleophile, as indicated by the high activation energy of ΔA⧧ = 22.6 kcal mol–1 for Dbrd. As could be expected, a nucleophile is less reactive at a bridging than at a terminal position.

Structural Features of the Geminal Reaction

The reaction in Bgem is used here as a representative case to describe the structural details of the geminal pathway (Figure 3). In THF, Mg(CH3)2 forms Mg(CH3)2(THF)2. This complex has a distorted tetrahedral structure with an angle of 135 ± 9° between the two Mg–CH3 bonds, larger than that formed by the two Mg–O bonds (92 ± 8°, Figure S1). Replacement of one THF molecule by ACA yields compound Bgem, which also has a distorted tetrahedral structure with obtuse CH3–Mg–CH3 and O(ACA)–Mg–O(THF) angles (153 ± 9° and 137 ± 9°, respectively) and an O(ACA)–Mg–CH3 angle of 92 ± 11° (Figure S2). This arrangement leads to a close proximity between the nucleophilic and the electrophilic groups.

Figure 3

Figure 3. Geminal reaction for compound Bgem. Representative geometries for the reactant, transition state, and product. The Mg atom and its ligands are represented as balls-and-sticks. Other solvating THF molecules are drawn as lines. The color codes are mauve for magnesium, red for oxygen, gray for carbon, and white for hydrogen.

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In the reactant, the methyl group is tightly bound to Mg with an average Mg–C bond distance of 2.15 ± 0.08 Å. In contrast, ACA is more loosely bound, with a Mg–O distance of 2.4 ± 0.2 Å, which is longer than the Mg–THF distance of 2.2 ± 0.1 Å. The Mg atom lies in the plane of ACA with a C–O–Mg angle of 118 ± 9°, indicating that the magnesium ion interacts with the two lone pairs of the carbonyl oxygen.
At the TS, the addition of one THF molecule from the bulk solvent leads to a complex with a distorted trigonal-bipyramidal structure where ACA and the approaching THF reside at the apical sites with an average O(ACA)–Mg–O(THF) angle of 164 ± 10° (Figure 4). Reaching the TS also requires a rotation of ACA around the C═O axis to establish the interaction of the nucleophile with the carbonyl π system (Figure 4). The formation of the bond between the two carbon atoms is also promoted by a slight bending of ACA toward the methyl group, indicated by a decrease in the C–O–Mg angle to a value of 97 ± 3°. On the contrary, the CH3–Mg–O(ACA) angle of (93 ± 3°) remains similar to that in Bgem.

Figure 4

Figure 4. Transition state structures of the geminal and vicinal reactions (Bgem, Fvic). Left: Evidence of the structural similarity of the two TSs. Balls-and-sticks are used to represent the reacting moiety, while the rest of the system is drawn as transparent cylinders. THF molecules not bound to Mg are not shown. The green line marks the incipient C–CH3 bond and its associated distance. Top right: Schematic definition of the angles formed by the C3 axis of the nucleophile methyl group. Bottom right: Distances and angles formed by the atoms involved in the four-center TS. Distances are reported in angstroms, and angles are in degrees. ϕX is the angle at the vertex X in the four-member ring (top right panel). The color code is as in Figure 3.

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The geminal reaction occurs via a concerted mechanism, with the TS showing partial formation and cleavage of the C–C and Mg–CH3 bonds, respectively. An informative parameter is the direction of the C3 axis of the methyl group, which is significantly displaced away from the CH3–Mg direction, but not yet aligned to the new C–C direction (ϕ1, ϕ2 angles in Figure 4). The four atoms involved in the bond rearrangement are coplanar (Figure 4), with a CH3···C–O angle of attack of 107 ± 4°, consistent with expected values for a nucleophilic addition to a carbonyl group. (52,53) The four-centered TS has a reactant-like geometry, with a relatively long C···C bond distance of 2.55 Å and the ACA carbon with an out-of-plane angle (defined by the improper CH3–C–O–H dihedral angle) of 161 ± 7°, closer to the ideal value of 180° for an sp2 atom than 120° for an sp3 one. Both ACA and the methyl groups are slightly farther away from the Mg center than in the reactant geometry, as indicated by the Mg–CH3 and Mg–O distances of 2.23 ± 0.07 and 2.5 ± 0.3 Å, respectively.
In the relaxed product CH3Mg(OCH(CH3)2)(THF)2, the Mg atom is again tetracoordinated, with the CH3–Mg–O(iso-propanol) and O(THF)–Mg–O(THF) angles similar to those in the reactant geometry (134 ± 8° and 93 ± 7°, respectively, Figure S3).
The coordination of the solvent assists the heterolytic cleavage of the Mg–CH3 bond by donating electron density to the Mg atom. It appears that the reactivity of the Mg complex increases when the coordinated ligands are better electron donors and/or more ligands coordinate to the magnesium center. These electron-donating ligands screen the charge on the Mg center, making the nucleophilic CH3 a better leaving group. In particular, Mg(CH3)2 is found to be slightly more reactive than CH3MgCl, which is consistent with the known greater electron-donating ability of a methyl group relative to chloride in these magnesium complexes as it also appeared in our previous study. (31) Moreover, the slightly higher reactivity of the mononuclear over dinuclear species correlates to the fact that terminal ligands are better electron donors than are the bridging ones.

Reaction with Vicinal Groups

The vicinal reaction was studied for species Cvic and Fvic (Figure 2). The most solvated dinuclear complex Fvic, with two pentacoordinated Mg atoms, has an activation energy for the C–C bond formation of ΔA⧧ ∼ 4.8 kcal mol–1. This is the lowest activation energy that has been calculated for all mononuclear and dinuclear species considered in this study. According to our previous study, Fvic is also one of the most abundant species in the Schlenk equilibrium, with a free energy of only 1.3 kcal mol–1 higher than that of the most stable dichloro-bridged compound (Cvic). (31)Fvic is therefore a key contributor to the formation of product by way of the nucleophilic addition. The most reactive species has ACA and the nucleophilic methyl group initially coordinated to two distinct magnesium atoms (Mg1 and Mg2, respectively) and thus rather far from each other. Considerable structural reorganization is occurring on the way to the transition state. At the TS, characterized by a C···C distance of 2.6 Å, ACA enters in the coordination sphere of Mg2 while still interacting with Mg1, as shown by the similar Mg1–O and Mg2–O distances of 2.12 ± 0.07 and 2.27 ± 0.19 Å, respectively (Figure 4). Consequently, Mg1 retains a pentacoordinated structure at the TS. In parallel, Mg2 acquires an octahedral coordination (Figure 5), with an O(ACA)−Mg2−CH3 angle between the two reacting cis-ligands of ∼90°.

Figure 5

Figure 5. Vicinal reaction for Fvic. Representative geometries for the reactant, transition state, and product. The Mg atoms (left Mg1, right Mg2) and first coordination sphere ligands are represented as balls-and-sticks. Other solvating THF molecules are drawn as lines. The color code is cyan for chlorine and green for the nucleophilic methyl, while the other elements are colored as in Figure 3.

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The four-center TS shares strong similarities with that found for the geminal reaction, with an elongated Mg2–CH3 bond (∼2.3 Å), a methyl lone-pair axis twisted ∼30° away from the Mg2–CH3 direction, and a favorable CH3···C═O angle (52,53) of 114 ± 10° (Figure 4). Also, in this case, the ACA carbon essentially retains an sp2 hybridization at the transition, similar to that found earlier for Bgem.
Relaxation from the transition state yields a product where the alcoholate bridges the two magnesium atoms (Figure 5). The chlorine atom that is anti to the nucleophilic CH3 in the reactant leaves its bridging position to occupy a terminal site at Mg2. Reorganization of the bridging ligands yields the final product where Mg1 is tetracoordinated and Mg2 is pentacoordinated (Figure 5).
The significantly higher activation energy (ΔA⧧ ∼ 13.0 kcal mol–1) required for the most stable dinuclear species Cvic (Figure 2) to undergo the nucleophilic reaction highlights the role of the coordinated solvent. Both Fvic and Cvic have two bridged chloride ligands and a terminal methyl group on each magnesium atom. Thus, the difference between them resides in the number of THF solvent molecules coordinated to each magnesium, the more reactive species being more solvated. The least solvated Cvic is in fact a rigid species in which ACA cannot approach the nucleophilic methyl group coordinated to the other magnesium. Interestingly, the calculations indicate that an additional THF binds Cvic on the ACA-bonded magnesium prior to reaching the transition state. This event occurs when the carbon–carbon distance is ∼4 Å, still more than 1 Å longer than at the TS. The formation of a pentacoordinated species on the ACA-coordinated Mg facilitates the migration of ACA toward the methyl bearing Mg, enabling the reaction. The solvent thus appears to be a key factor in the reaction by increasing the flexibility of the Mg complex, thus lowering the energy needed for getting the electrophile and nucleophile close to each other (Figure 5).
A previous work proposed that the Grignard reaction would occur starting from a dinuclear structure characterized by a single bridging chloride and two methyl groups each bound to a different Mg atom. (30) Nonetheless, the calculations showed that this complex was not stable in solution and it rapidly evolved into a dichloro-bridged structure. This is consistent with what has been already observed in our previous work: the monochloride bridged structures were not associated with free-energy minima, but they corresponded to the transition states during the transmetalation step in the Schlenk equilibrium. (31) Because of their instability, and the already high reactivity of more stable compounds, it is unlikely that such moieties play a significant role in the Grignard reaction.

Role of the Schlenk Equilibrium in the Nucleophilic Grignard Reaction

Figure 6 compiles the activation energies of the reaction pathways considered in this work, together with the relative stability of the various organomagnesium species involved in the Schlenk equilibrium as previously derived. (31)

Figure 6

Figure 6. Red: Activation energies of all Grignard species derived from CH3MgCl in THF solution when reacting with acetaldehyde. Blue: Relative free energies of the species involved in the Schlenk equilibrium (data from ref (31)). The green box highlights the intrinsically most reactive species identified in this work.

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The Schlenk equilibrium is driven by the dynamics of the coordinating solvent in the Grignard reagent dimers, (31) and its mechanism shares structural similarities with the vicinal pathway. Specifically, in the Schlenk equilibrium, the increased coordination of the solvent assists the displacement of the ionic ligands from the terminal to the bridging positions by increasing the flexibility of the organomagnesium complex. In the Grignard reaction, the most reactive structure Fvic has two pentacoordinated Mg centers, Mg1 with one THF and ACA, and Mg2 with two THF molecules. This high coordination of the two Mg centers facilitates the shift of ACA from a terminal to a bridging position while minimizing the motion of the other ligands (Figure 5). At the bridging position, the electrophilicity of ACA is significantly increased. In the same time, the coordination of Mg2 augments from five to six, which in turn helps in the departure of the nucleophilic methyl group. Thus, through different coordination to the Mg centers, the solvent has contributed to make the substrate ACA more electrophilic and the methyl group more nucleophilic. The entropic factor also favors the vicinal reaction in this dinuclear complex relative to the most favorable geminal reaction. Indeed, in the latter, the coordination of an additional THF is necessary at the transition state, while in the former, there is no need for a THF from the bulk of the solvent to enter the coordination sphere of any of the two magnesium centers. The dinuclear complex needs only to modify the position of the various ligands and coordinated solvent to reach the transition state. Thus, cleaving the terminal Mg2–CH3 bond is accompanied by the displacement of a bridging chloride to a terminal position to ensure appropriate anionic coordination at Mg2. Two coordinating THF solvent molecules are sufficient to stabilize the pentacordinated Mg2 linked also to a terminal Cl and to the bridging alcoholate and chloride ligands.
In practice, the Grignard reaction can be viewed as a variant of the Schlenk equilibrium where the nonreactive solvent is replaced by an unsaturated substrate that becomes a strong electrophile when entering the coordination sphere of Mg. The energetically easy exchange between terminal and bridging ligands under the assistance of the solvent is at the heart of this chemistry.
While the vicinal pathway through the dinuclear Mg complex (Fvic) looks intrinsically the most reactive, the geminal pathway should nevertheless be considered as a competitive alternative. In particular, mononuclear species have activation energies only slightly higher than that of the most reactive dinuclear complex. Thus, the preferred pathway for the Grignard reaction would be determined by the relative abundance of the mononuclear and dinuclear compounds. Likely, several forms may be active simultaneously in the complex mixture formed by the Grignard reagent in solution. It should be kept in mind that the Grignard reagent forms clusters whose nature and relative abundance depend on the solvent and the halide ligand in a nontrivial manner. (6,54)
Our findings stress the importance of an unbiased exploration of the conformational space and, in particular, of the explicit treatment of the solvent. In fact, the solvent is a direct player in all reactive pathways identified in the present work, in particular by structurally and dynamically affecting the coordination sphere of Mg. This is particularly relevant for the determination of the free energy barrier in the geminal reaction where the C–C bond formation, associated with a cleavage of the Mg–CH3 bond, occurs with the assistance of an incoming solvent entering the coordination sphere of Mg. This ensures that the magnesium is coordinated to at least four ligands as it was found to be required. (31) The direct role of the solvent in modulating the reaction is the main reason for the discrepancies found with the preceding studies by Yamazaki and Yamabe (29) and by Mori and Kato. (30) In particular, our study contrasts with their hypothesis that mononuclear species may be significantly less able to promote the Grignard reaction. In fact, such divergences arise because of, in these previous investigations, a fixed number of ligands at the magnesium centers, in particular disregarding the dynamic role of the solvent and its capability of entering in the coordination sphere during the reaction.

Radical Mechanism

Quantum-chemical calculations indicate that the homolytic cleavage of the Mg–CH3 bond in the solvated Grignard reagent CH3MgCl(THF)n requires a high energy of 66.6 kcal mol–1 for n = 2, which is not lowered by increasing solvation (66.4 kcal mol–1 for n = 3). The calculated values compare well with those determined experimentally for CH3MgBr in diethyl ether (55) (∼61 kcal mol–1), suggesting a marginal influence of the halide and solvent on the Mg–CH3 bond dissociation energy (BDE).
The high value of the Mg–CH3 BDE indicates that alkyl radicals cannot be formed in pure solutions of the Grignard reagent. (56) Indeed, the experiment reports the presence of organic radicals only when electrophilic substrates of low reduction potential are present. (14) This suggests that the substrate may promote the homolytic cleavage.
The M–CH3 BDEs were thus calculated for complexes with coordinated substrates. Figure 7 reports the Mg–CH3 BDE for substrates of decreasing reduction potential (acetaldehyde > formaldehyde > carbonyl difluoride) with one or two coordinated THF molecules. Indeed, the nature of the coordinated substrate influences significantly the Mg–CH3 BDE, as shown by its decrease from acetaldehyde (37.9 kcal mol–1) to carbonyl difluoride (24.8 kcal mol–1) (Figure 7, values for two bound THFs). The strong influence of the substrate on the BDE can be rationalized by considering the localization of the unpaired electron on the organomagnesium radical product. As shown in Figure 7, the electron spin density mostly resides on the substrate carbonyl group and not on the Mg atom regardless of the nature of the substrate and the number of bound THFs. Consequently, the BDE correlates to the energy of the singly occupied π*(CO) Kohn–Sham orbital in the radical product, as indicated by the corresponding orbital energies of −0.18057, −0.18846, and −0.25703 au for acetaldehyde, formaldehyde, and carbonyl difluoride, respectively.

Figure 7

Figure 7. Mg–CH3 BDE and spin-density localization (in fractions of e) for MgCl(Sub)(THF)nCH3 (Sub = substrate). The green wire-frame shows the isosurface of the spin density map at a value of 0.0065 au.

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The role of a low-lying empty π* orbital at the substrate in the stabilization of the radical species rationalizes the high BDE values in the absence of any coordinated carbonyl substrate. In fact, in the case of MgCl(THF)2• radical, the unpaired electron remains located on Mg, with about 0.8 e of the spin density. The previous analysis also explains why the degree of solvation has a stronger influence for the BDE in the substrate-bound species than in the substrate-free Grignard reagent. In the presence of the substrate, the delocalization of the unpaired electron produces an effective increase of the electrostatic charge on the Mg atom, which can be stabilized by additional electron-donating ligands. Thus, increased solvation decreases the Mg–CH3 BDE. The effect of the solvent depends only slightly on the nature of the coordinated substrate because the stabilization is from 13 to 10 kcal mol–1 for acetaldehyde to carbonyl difluoride, respectively. For a similar reason, Mg(CH3)2 promotes the homolytic dissociation of the methyl radical more than does CH3MgCl, with a decrease in the BDE by roughly 10%.

Nucleophilic Attack versus Homolytic Cleavage: The Case of Fluorenone

The quantum-chemical calculations of the Mg–CH3 BDE presented here show that the formation of radical species by cleavage of the Mg–CH3 bond is unlikely in the absence of a coordinated substrate with a low-lying empty orbital. This observation accounts for previous conclusions by Otte and Woerpel (20) that the Grignard reaction does not proceed via a radical mechanism with alkyl aldehydes and ketones. The same finding is also consistent with the experimental evidence that a radical mechanism is often preferred for aromatic ketones and, in particular, for benzophenone and fluorenone. (8−15)
To evaluate the competition between the radical and nucleophilic addition pathways in aromatic substrates, we considered the case of the fluorenone. The calculations were carried out with monomeric Mg(CH3)2. This form of the Grignard reagent was selected because it is only slightly less reactive than the most reactive dinuclear complex, while it allows faster ab initio MD simulations.
The Mg–CH3 BDE in CH3MgCl(fluorenone)(THF)2 is 16.5 kcal mol–1, a value more than 20 kcal mol–1 smaller than that for ACA. Such a drastic lowering of the BDE is associated with a significant delocalization of the unpaired electron over the extended π system of fluorenone (Figure 8). In particular, the spin density surrounding the carbonyl carbon integrates to only 0.5 e, as compared to values larger than 0.8 e for the other substrates (Figure 7), with the rest of the spin density being distributed on the conjugated aromatic ring (Figure 8). Considering an entropic contribution to the free energy (−TΔS) for a bond dissociation on the order of 10 kcal mol–1, the formation of a methyl radical would reach an overall free energy cost of only ∼6 kcal mol–1, which is in the same range of the most favorable free energy barriers for the nucleophilic addition mechanism with ACA.

Figure 8

Figure 8. Energetics of the Grignard reaction mechanisms for fluorenone. Top panel: Activation free energy of the nucleophilic addition with Mg(CH3)2. Bottom panel: Bond dissociation energy. All energy values are in kcal mol–1. On the right is the distribution of the spin density in Mg(CH3)(fluorenone)THF2: 33% of the unpaired electron localizes on the carbonyl carbon, 16% on the carbonyl oxygen, and 45% on the remaining π system.

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Interestingly, ab initio MD simulations reveal that fluorenone is significantly less reactive than ACA via the nucleophilic pathway. For Mg(CH3)2(fluorenone)(THF), we estimated an activation energy of 14.5 ± 1.2 kcal mol–1 (Figure 8), a value around 8 kcal mol–1 higher than that for ACA.
The TS for the nucleophilic addition to fluorenone has structural features similar to those for ACA, as indicated by a C···C bond distance of 2.5 Å, a C out-of-plane angle of 164 ± 4°, and an approach angle of 106 ± 4°. However, the geometries of the reactant states are significantly different in the two species. For ACA, the Mg–CH3 and C═O bonds in the reactant state are essentially eclipsed, as shown by a CH3–Mg–O–C dihedral angle of 14 ± 15° (Figure 9). Therefore, a rotation of the ACA around the C═O axis by ∼90° is the main structural change required to reach the TS (Figure 9). For fluorenone, the bulky aryl group precludes an eclipsed conformation for the Mg–CH3 and C═O bonds, as indicated by an average CH3–Mg–O–C dihedral of 114 ± 30° (Figure 9). Consequently, in this case, an additional rotation around the Mg–O bond is required to reach the TS. This suggests that the higher barrier calculated in the case of fluorenone originates in good part from a larger structural reorganization going from reactant to TS.

Figure 9

Figure 9. Structural reorganization from (left) reactant to (right) transition state in the nucleophilic pathway for (top) ACA and (bottom) fluorenone. The CH3–Mg–O–C dihedral angle (corresponding to the blue arrow) is 14 ± 15° for ACA and 114 ± 30° for fluorenone.

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The present calculations help in understanding why the radical mechanism was observed with substrates characterized by a low reduction potential. Interestingly, such substrates are often bulky due to the presence of aryl groups and other conjugated substituents. These large groups may thus require larger structural rearrangement on the way to the TS for the nucleophilic addition, which can further disfavor such a mechanism against the radical one, as shown in the representative case of fluorenone.

Conclusions

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The activation of both the nucleophilic and the radical mechanisms depends in a complex way on the nature of the substrate, on its binding to the Mg center, and on solvent dynamics. The combination of these subtle effects is the cause of the difficulties in determining and predicting the preferred pathways for the Grignard reaction.
The nucleophilic reaction occurs between the substrate and the nucleophile, which are both in the coordination sphere of Mg centers. Several organomagnesium species that coexist at thermal equilibrium in solution can promote the nucleophilic reaction with similar activation energies. This implies that several pathways involving different forms of the Grignard reagent may occur in parallel. The number of Mg atoms in the Mg species does not appear to influence significantly its reactivity because the two most reactive species with very similar activation energies are a dinuclear and a mononuclear compound. Likewise, similar activation energies are found when the substrate and the nucleophile are initially coordinated on the same or on nearby Mg atoms.
The solvent plays an essential role in the reaction. More solvated Mg species are more reactive. This seems to be due to the higher flexibility of the entire Mg species, which favors the structural reorganization from the reactant to the transition state. In less solvated species, additional coordination of solvent molecules coming from the bulk is still needed to promote the reaction, but the associated entropic cost makes these species less reactive. Thus, in all pathways, the solvent should be considered as one of the reactants. Similar effects probably apply in numerous organometallic reactions notably involving alkali, alkali-earth metals, and related lanthanide complexes, which are all known to be highly sensitive to solvent effects.
Like for the nucleophilic addition, the radical mechanism is strongly dependent on the coordination of the Mg center. The pure Grignard reagent is unlikely to release an organic radical even if heavily solvated. However, when one of the coordinated ligands is a substrate with a low-lying empty π orbital and when the solvation is high, the Mg–carbon bond breaks much more easily. Interestingly, the substituents able to lower the reduction potential of the substrate are often rather bulky, which in turn disfavors the nucleophilic pathway. The combination of electronic effects stabilizing the radical species and steric hindrance hampering the nucleophilic addition explains why a radical pathway has been observed with substrates like fluorenone or benzophenone but not with benzaldehyde.
The coexistence of multiple species in rapid exchange due to the Schlenk equilibrium and the evidence that the activation energy range of all possible reactions is relatively modest indicate that the Grignard reaction should not be described by an individual process. Instead, it should rather be thought of as an ensemble of transformations that can occur simultaneously in solution. It is likely that improvements of the Grignard reaction, for example, by alkali (7,57) or copper salt additives, (58,59) occur by interference with one or more of the possible pathways. In fact, the determination of all possible reaction pathways for the Grignard reaction and the key factors regulating them establishes the foundation for rational improvements of this process.
In this respect, it is noticeable that most reactive dinuclear species found in this study share strong similarities with the two-metal ion mechanism universally found in nature in the general class of catalytic RNA or metalloendonuclease enzymes. (60) In these cases, hydrolysis of a phosphate ester by a nucleophilic water involves binding to two Mg’s with nonequal 5-, 6-fold coordination, and a vicinal mechanism where the substrate moves into a bridging position with a trigonal geometry, to form a four-center TS with the nucleophile hydroxyl group attacking from its Mg-coordinating position. (61−65) The structural analogy between the two reactions suggests that the evolutionary pressure has selected among the many chemically possible pathways the most advantageous organization of the Mg ions and their coordinating groups to catalyze a nucleophilic attack having both the substrate and the nucleophile as initial coordinating ligands to the metal centers. The Grignard reaction puzzle is finally assembling together with potential impacts on related chemistry.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.9b11829.

  • Reference coupled-cluster calculations and benchmark BDE calculations, and structures of Mg(CH3)2, Mg(CH3)2(CH3CHO), and CH3Mg(OCH(CH3)2) in THF (PDF)

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Author Information

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  • Corresponding Authors
  • Authors
    • Raphael Mathias Peltzer - Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, P.O. Box 1033 Blindern, Oslo 0315, Norway
    • Jürgen Gauss - Department Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, Mainz 55128, Germany
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the Research Council of Norway (RCN) through the CoE Hylleraas Center for Quantum Molecular Sciences (Grant number 262695) and by the Norwegian Supercomputing Program (NOTUR) (Grant number NN4654K). M.C. and J.G. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) within the project B5 of the TRR 146 (project number 233630050). We thank Mats Tilset for being at the right place at the right time to ask the right question. We also thank Filippo Lipparini for useful discussions.

References

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    The rate of change in the N.M.R. spectrum of a mixt. of the Grignard reagent from neopentyl chloride and benzophenone in tetrahydrofuran was studied. The expected addn. reaction was complicated by the simultaneous occurrence of a radical reaction to produce neopentane and benzopinacol. These spectra are interpretable in terms of a reaction to give an initial product which in turn undergoes further reaction with the Grignard reagent to give a new reactive species. This reactive intermediate presumably is either the alkylmagnesium alkoxide (RMgOR') or a complex of the initial product with the Grignard reagent (RMgCl.R'OMgCl). This constitutes a direct observation of a process often postulated in the reaction of a Grignard compd. Qual. generalizations could be made but because of these complications it was not possible to make a quant. kinetic anal. of the data.
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  17. 17
    Hoffmann, R. W.; Hölzer, B. Concerted and stepwise Grignard additions, probed with a chiral Grignard reagent. Chem. Commun. 2001, 491– 492,  DOI: 10.1039/b009678o
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    17
    Concerted and stepwise Grignard additions, probed with a chiral Grignard reagent
    Hoffmann, Reinhard W.; Holzer, Bettina
    Chemical Communications (Cambridge, United Kingdom) (2001), (5), 491-492CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
    The Grignard reagent (S)-PhCH2CH(MgCl)CH2CH3 6, in which the magnesium-bearing carbon atom is the sole stereogenic center has been added to CO2, PhNCO, PhNCS and certain aldehydes with full retention of configuration. Reaction with benzophenone, electron-deficient aldehydes and several allyl halides proceeded with partial or complete racemization. The findings are discussed with respect to a dichotomy between concerted polar and stepwise SET reaction pathways.
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  18. 18
    Hoffmann, R. W. The quest for chiral Grignard reagents. Chem. Soc. Rev. 2003, 32, 225– 230,  DOI: 10.1039/b300840c
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    The quest for chiral Grignard reagents
    Hoffmann, Reinhard W.
    Chemical Society Reviews (2003), 32 (4), 225-230CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
    A review on the prepn. of chiral Grignard reagents. The involvement of single electron transfer, i.e. of free radicals in the reactions of organomagnesium reagents could be detected with the aid of a chiral secondary Grignard reagent, in which the magnesium-bearing carbon atom is the sole stereogenic center. So far, however, such reagents have not been accessible, because the std. prepn. of Grignard reagents proceeds via free radicals. The authors review and summarize here their efforts to generate (S)-1-Benzylpropylmagnesium chloride 36 by asym. synthesis starting from an enantiomerically pure compd. ArSOCH(Cl)CH2Ph (Ar = p-cl-C6H5) 30b using a sulfoxide/magnesium exchange reaction to give trans-β-chloro-α-phenylbenzenepropanol 33 followed by a carbenoid homologation reaction. Grignard reagent 36 turned out to be an ideal probe to learn about the extent to which SET is involved in reactions of organomagnesium reagents.
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  19. 19
    Gajewski, J. J.; Bocian, W.; Harris, N. J.; Olson, L. P.; Gajewski, J. P. Secondary deuterium kinetic isotope effects in irreversible additions of hydride and carbon nucleophiles to aldehydes: a spectrum of transition states from complete bond formation to single electron transfer. J. Am. Chem. Soc. 1999, 121, 326– 334,  DOI: 10.1021/ja982504r
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    Secondary deuterium kinetic isotope effects in irreversible additions of hydride and carbon nucleophiles to aldehydes: a spectrum of transition states from complete bond formation to single electron transfer
    Gajewski, Joseph J.; Bocian, Wojciech; Harris, Nathan J.; Olson, Leif P.; Gajewski, John P.
    Journal of the American Chemical Society (1999), 121 (2), 326-334CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The competitive kinetics of hydride and organometallic addns. to PhCHO and PhCDO were detd. at -78° using LiAlH4, LiBHEt3, NaBH4, LiBH4, LiAlH(OCMe3)3, NaBH(OMe)3, NaBH(OAc)3 (at 20°), RMgBr (R = Me, Ph, allyl), and RLi (R = Me, Ph, Bu, Me3C, allyl). The hydride addns. had an inverse secondary D kinetic isotope effects in all cases, but the magnitude of the effect varied inversely with the apparent reactivity of the hydride. In the addns. of MeMgBr and of MeLi and PhLi, inverse secondary D isotope effects were obsd.; little if any isotope effect was obsd. with PhMgBr, BuLi or Me3CLi. With CH2:CHCH2M (M = MgBr, Li), a normal secondary D kinetic isotope effect was obsd. Rate-detg. single-electron transfer occurs with allyl reagents, but direct nucleophilic reaction occurs with all of the other reagents, with the extent of bond formation depending on the reactivity of the reagent. In the addn. of MeLi to cyclohexanecarboxaldehyde (I), a less inverse secondary D kinetic isotope effect was obsd. than that obsd. in the addn. of MeLi to PhCHO, and allyllithium addn. to I had a kinetic isotope effect near unity. The data with organometallic addns., which are not incompatible with observations of carbonyl C isotope effects, suggest that electrochem. detd. redox potentials which indicate endoergonic electron transfer with energies .ltorsim.13 kcal/mol allow electron-transfer mechanisms to compete well with direct polar addns. to aldehydes, provided that the reagent is highly stabilized, like allyl species. MeLi, PhLi, MeMgBr and PhMgBr are estd. to undergo electron transfer with endoergonicities >30 kcal/mol with PhCHO, so these react by direct polar addns. A working hypothesis is that BuLi reagents undergo polar addns., despite redox potentials which indicate ≤13 kcal/mol endoergonic electron transfer, because of the great exoergonicity assocd. with the 2-electron addn., which is responsible for a low barrier for polar reactions.
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  20. 20
    Otte, D. A. L.; Woerpel, K. A. Evidence that Additions of Grignard Reagents to Aliphatic Aldehydes do Not Involve Single-Electron-Transfer Processes. Org. Lett. 2015, 17, 3906– 3909,  DOI: 10.1021/acs.orglett.5b01893
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    Evidence that Additions of Grignard Reagents to Aliphatic Aldehydes Do Not Involve Single-Electron-Transfer Processes
    Otte, Douglas A. L.; Woerpel, K. A.
    Organic Letters (2015), 17 (15), 3906-3909CODEN: ORLEF7; ISSN:1523-7052. (American Chemical Society)
    Addn. of allylmagnesium reagents to an aliph. aldehyde bearing a radical clock gave only addn. products and no evidence of ring-opened products that would suggest single-electron-transfer reactions. The analogous Barbier reaction also did not provide evidence for a single-electron-transfer mechanism in the addn. step. Other Grignard reagents (methyl-, vinyl-, t-Bu-, and triphenylmethylmagnesium halides) also do not appear to add to an alkyl aldehyde by a single-electron-transfer mechanism.
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  21. 21
    Garst, J. F.; Soriaga, M. P. Grignard reagent formation. Coord. Chem. Rev. 2004, 248, 623– 652,  DOI: 10.1016/j.ccr.2004.02.018
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    Grignard reagent formation
    Garst, John F.; Soriaga, Manuel P.
    Coordination Chemistry Reviews (2004), 248 (7-8), 623-652CODEN: CCHRAM; ISSN:0010-8545. (Elsevier Science B.V.)
    A review with 74 refs. Probably reactions of Mg metal with org. halides RX in ether solvents are typical metallic corrosions in which the stabilization of Mg2+, substantially through its coordination by the solvent, drives its loss from the metal and consequently the redns. of RX and reaction intermediates such as R· at the metal surface. Although alkyl halides form Grignard reagents through nonchain mechanisms in which intermediate radicals diffuse in soln., very small amts. of radical isomerization occur in Grignard reactions of certain vinyl and aryl halides, even when intermediate radicals R· would isomerize very rapidly. This suggests a dominant nonradical mechanism for these vinyl and aryl halides or a mechanism in which intermediate radicals R· have extremely short lifetimes. Since the former seems more likely, a dianion mechanism, through a transition state [RX2-]‡, is proposed. Surface studies of polycryst. Mg show that the oxide layer is mostly Mg(OH)2 and that it is mech. passivating. In the absence of promoters, Grignard reactions occur very slowly until enough RX has seeped to the Mg surface and reacted there to undercut and cause the Mg(OH)2 layer to flake off.
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  22. 22
    Chen, Z.-N.; Fu, G.; Xu, X. Theoretical studies on Grignard reagent formation: radical mechanism versus non-radical mechanism. Org. Biomol. Chem. 2012, 10, 9491– 9500,  DOI: 10.1039/c2ob26658j
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    Theoretical studies on Grignard reagent formation: radical mechanism versus non-radical mechanism
    Chen, Zhe-Ning; Fu, Gang; Xu, Xin
    Organic & Biomolecular Chemistry (2012), 10 (47), 9491-9500CODEN: OBCRAK; ISSN:1477-0520. (Royal Society of Chemistry)
    Here the systematic theor. study on the mechanisms of Grignard reagent formation is presented (GRF) for CH3Cl reacting with Mg atom, Mg2 and Mg clusters (Mg4-Mg20). The calcns. reveal that the ground state Mg atom is inactive under matrix condition, whereas it is active under metal vapor synthesis (MVS) conditions. However, the excited state Mg (3P) atom, as produced by laser-ablation, can react with CH3Cl without barriers, and hence is active under matrix condition. The prediction is that the bimagnesium Grignard reagent, though often proposed, can barely be obsd. exptl., due to its high reactivity towards addnl. CH3Cl to produce more stable Grignard reagent dimer, and that the cluster Grignard reagent RMg4X possesses a flat Mg4 unit rather than a tetrahedral geometry. The calcns. further reveal that the radical pathway (T4) is prevalent on Mg, Mg2 and Mgn clusters of small size, while the no-radical pathway (T2), which starts at Mg4, becomes competitive with T4 as the cluster size increases. A structure-reactivity relation between barrier heights and ionization potentials of Mgn is established. These findings not only resolve controversy in expt. and theory, but also provide insights which can be used in the design of effective synthesis approaches for the prepn. of chiral Grignard reagents.
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  23. 23
    Shao, Y.; Liu, Z.; Huang, P.; Liu, B. A unified model of Grignard reagent formation. Phys. Chem. Chem. Phys. 2018, 20, 11100– 11108,  DOI: 10.1039/C8CP01031E
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    A unified model of Grignard reagent formation
    Shao, Yunqi; Liu, Zhen; Huang, Pan; Liu, Boping
    Physical Chemistry Chemical Physics (2018), 20 (16), 11100-11108CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Grignard reagents are among the most fundamental reagents in org. synthesis, yet studies have hitherto failed to fully explain the selectivity and kinetics of Grignard reagent formation (GRF). The present study provides new insights into the intermediates and pathways of GRF using d. functional theory (DFT) calcns. Potential energy surfaces of RX dissocn. along different directions reveal the origin of configuration retention of alkenyl and arom. halides. Radical intermediates participate solely in the dissocn. stage, and depend on the geometry of the reactant halide. Dissocn. of org. halides yields stabilized surface anions, and the rest of the reaction is ionic in nature. MgX+/RMg+ are proposed as the key intermediates of Mg leaving from the surface in the self-activation of GRF, which explains the accelerated kinetics upon addn. of RMgX or MgX2. The intermediacy of the cations was supported by a simple electrochem. expt. To the best of the authors' knowledge, this is the 1st unified ionic model (I-model) developed for resolving the controversial issues of GRF.
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    Axten, J.; Troy, J.; Jiang, P.; Trachtman, M.; Bock, C. W. An ab initio molecular orbital study of the Grignard reagents CH3MgCl and [CH3MgCl]2: the Schlenk equilibrium. Struct. Chem. 1994, 5, 99– 108,  DOI: 10.1007/BF02265351
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    An ab initio molecular orbital study of the Grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium
    Axten, Jeffrey; Troy, Jennifer; Jiang, Peter; Trachtman, Mendel; Bock, Charles W.
    Structural Chemistry (1994), 5 (2), 99-108CODEN: STCHES; ISSN:1040-0400.
    Ab initio MO calcns. are used to study the modified Schlenk equil.: 2RMgCl .dblharw. MgR2 + MgCl2 .dblharw. Mg(Cl2)MgR2 with R = H and CH3. In the absence of any solvents, calcns. indicate that the formation of the various possible bridged dimers (RMgCl)2 is substantially exothermic. However, using di-Me ether as a model solvent, we show that the formation of the dimer (Me2O)(CH3)Mg(μ-Cl2)Mg(CH3)(OMe2) is exothermic only when entropic effects are included.
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    Ehlers, A. W.; van Klink, G. P. M.; van Eis, M. J.; Bickelhaupt, F.; Nederkoorn, P. H. J.; Lammertsma, K. Density-Functional study of (solvated) Grignard complexes. J. Mol. Model. 2000, 6, 186– 194,  DOI: 10.1007/s0089400060186
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    Density-functional study of (solvated) Grignard complexes
    Ehlers, Andreas W.; Van Klink, Gerard P. M.; Van Eis, Maurice J.; Bickelhaupt, Friedrich; Nederkoorn, Paul H. J.; Lammertsma, Koop
    Journal of Molecular Modeling (2000), 6 (2), 186-194CODEN: JMMOFK; ISSN:0948-5023. (Springer-Verlag)
    D. functional calcns. have been used to study the solvent effect of di-Et ether on the Schlenk equil. and the aggregation of Grignard reagents RMgX with R = Me, Et, Ph. Solvent stabilization of the Mg complexes of the first solvent is larger than that of the second one. The solvation energy decreases on going from the dihalides MgX2 to the monohalides RMgX to the diorgano compds. MgR2. The calcns. indicate that the energetic preference of the unsym. species reduces upon solvation. The strong tendency to dimerization of the un- and partly solvated compd. vanishes for the higher solvated cases.
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    Tammiku, J.; Burk, P.; Tuulmets, A. 1,10-phenanthroline and its complexes with magnesium compounds. Disproportionation equilibria. J. Phys. Chem. A 2001, 105, 8554– 8561,  DOI: 10.1021/jp011476n
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    1,10-Phenanthroline and Its Complexes with Magnesium Compounds. Disproportionation Equilibria
    Tammiku, Jaana; Burk, Peeter; Tuulmets, Ants
    Journal of Physical Chemistry A (2001), 105 (37), 8554-8561CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The solvation, complexation, and disproportionation equil., which might be important during titrn. of a Grignard reagent RMgX with an alc. in the presence of 1,10-phenanthroline (phen), have been studied both in the gas phase and soln. using the d. functional theory (DFT) B3LYP/6-31+G* method. Solvation was modeled using the supermol. approach. NBO at. charge analyses were performed at the B3LYP/6-31G* level. The absorption spectra of the complexes were calcd. by the DFT TD/MPW1PW91/6-311+G** method. According to our calcns. the complexation of magnesium halide MgX2 with 1,10-phenanthroline is the reason for the disappearance of the red color of the complex RMgX(phen) near the titrn. end point.
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    Tammiku-Taul, J.; Burk, P.; Tuulmets, A. Theoretical study of magnesium compounds: The Schlenk equilibrium in the gas phase and in the presence of Et2O and THF molecules. J. Phys. Chem. A 2004, 108, 133– 139,  DOI: 10.1021/jp035653r
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    Theoretical Study of Magnesium Compounds: The Schlenk Equilibrium in the Gas Phase and in the Presence of Et2O and THF Molecules
    Tammiku-Taul, Jaana; Burk, Peeter; Tuulmets, Ants
    Journal of Physical Chemistry A (2004), 108 (1), 133-139CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The Schlenk equil. involving RMgX, R2Mg, and MgX2 (R = Me, Et, Ph and X = Cl, Br) has been studied both in the gas phase and in Et2O and THF solns. by the d. functional theory (DFT) B3LYP/6-31+G* method. Solvation was modeled using the supermol. approach. The stabilization due to interaction with solvent mols. decreases in the order MgX2 > RMgX > R2Mg and among the groups (R and X) Ph > Me > Et and Cl > Br. Studied magnesium compds. are more strongly solvated by THF compared to Et2O. The magnesium halide is solvated with up to four solvent mols. in THF soln., assuming that trans-dihalotetrakis(tetrahydrofurano)magnesium(II) complex forms. The formation of cis-dihalotetrakis(tetrahydrofurano)magnesium(II) is energetically less favorable than the formation of corresponding disolvated complexes. The predominant species in the Schlenk equil. are RMgX in Et2O and R2Mg + MgX2 in THF, which is consistent with exptl. data.
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    Yamabe, S.; Yamazaki, S. In The Chemistry of Organomagnesium Compounds; Rappoport, Z., Marek, I., Eds.; Wiley-VCH: Weinheim, Germany, 2008; pp 369– 402.
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    Yamazaki, S.; Yamabe, S. A computational study on addition of grignard reagents to carbonyl compounds. J. Org. Chem. 2002, 67, 9346– 9353,  DOI: 10.1021/jo026017c
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    A Computational Study on Addition of Grignard Reagents to Carbonyl Compounds
    Yamazaki, Shoko; Yamabe, Shinichi
    Journal of Organic Chemistry (2002), 67 (26), 9346-9353CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
    The mechanism of stereoselective addn. of Grignard reagents to carbonyl compds. was studied using B3LYP d. functional theory calcns. The study of the reaction of methylmagnesium chloride and formaldehyde in di-Me ether revealed a new reaction path involving carbonyl compd. coordination to Mg atoms in a dimeric Grignard reagent. The structure of the transition state for the addn. step shows that an interaction between a vicinal-Mg bonding alkyl group and C:O causes the C-C bond formation. The simplified mechanism shown by this model is in accord with the aggregation nature of Grignard reagents and their high reactivities toward carbonyl compds. Concerted and four-centered formation of strong O-Mg and C-C bonds was suggested as a polar mechanism. When the alkyl group is bulky, C-C bond formation is blocked and the Mg-O bond formation takes precedence. A diradical is formed with the odd spins localized on the alkyl group and carbonyl moiety. Diradical formation and its recombination probably are a single electron transfer (SET) process. The criteria for the concerted polar and stepwise SET processes were discussed in terms of precursor geometries and relative energies.
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    Mori, T.; Kato, S. Grignard reagents in solution: Theoretical study of the equilibria and the reaction with a carbonyl compound in diethyl ether solvent. J. Phys. Chem. A 2009, 113, 6158– 6165,  DOI: 10.1021/jp9009788
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    Grignard Reagents in Solution: Theoretical Study of the Equilibria and the Reaction with a Carbonyl Compound in Diethyl Ether Solvent
    Mori, Toshifumi; Kato, Shigeki
    Journal of Physical Chemistry A (2009), 113 (21), 6158-6165CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    The equil. of Grignard reagents, CH3MgCl and CH3MgBr, in di-Et ether (Et2O) solvent as well as the reaction of the reagents with acetone are studied theor. To describe the equil. and reactions in Et2O solvent, the authors employ the ref. interaction site model SCF method with the second-order Moller-Plesset perturbation (RISM-MP2) free energy gradient method. Since the solvent mols. strongly coordinate to the Grignard reagents, the authors construct a cluster model by including several Et2O mols. into the quantum mech. region and embed it into the bulk solvent. Probably instead of the traditionally accepted cyclic dimer, the linear form of dimer is as stable as the monomer pair and participates in the equil. For the reaction with acetone, two important reaction paths (i.e., monomeric and linear dimeric paths) are studied. The barrier height for the monomeric path is much higher than that for the linear dimeric path, indicating that the reaction of the Grignard reagent with acetone proceeds through the linear dimeric reaction path. The change of solvation structure during the reaction is examd. From the calcd. free energy profiles, the entire reaction mechanisms of the Grignard reagents with aliph. ketones in Et2O solvent are discussed.
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    Peltzer, R. M.; Eisenstein, O.; Nova, A.; Cascella, M. How solvent dynamics controls the Schlenk equilibrium of Grignard reagents: A computational study of CH3MgCl in tetrahydrofuran. J. Phys. Chem. B 2017, 121, 4226– 4237,  DOI: 10.1021/acs.jpcb.7b02716
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    How Solvent Dynamics Controls the Schlenk Equilibrium of Grignard Reagents: A Computational Study of CH3MgCl in Tetrahydrofuran
    Peltzer, Raphael M.; Eisenstein, Odile; Nova, Ainara; Cascella, Michele
    Journal of Physical Chemistry B (2017), 121 (16), 4226-4237CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
    The Schlenk equil. is a complex reaction governing the presence of multiple chem. species in soln. of Grignard reagents. The full characterization at the mol. level of the transformation of CH3MgCl into MgCl2 and Mg(CH3)2 in THF by means of ab initio mol. dynamics simulations with enhanced-sampling metadynamics is presented. The reaction occurs via formation of dinuclear species bridged by chlorine atoms. At room temp., the different chem. species involved in the reaction accept multiple solvation structures, with two to four THF mols. that can coordinate the Mg atoms. The energy difference between all dinuclear solvated structures is lower than 5 kcal mol-1. The solvent is shown to be a direct key player driving the Schlenk mechanism. In particular, this study illustrates how the most stable sym. solvated dinuclear species, (THF)CH3Mg(μ-Cl)2MgCH3(THF) and (THF)CH3Mg(μ-Cl)(μ-CH3)MgCl(THF), need to evolve to less stable asym. solvated species, (THF)CH3Mg(μ-Cl)2MgCH3(THF)2 and (THF)CH3Mg(μ-Cl)(μ-CH3)MgCl(THF)2, in order to yield ligand exchange or product dissocn. In addn., the transferred ligands are always departing from an axial position of a pentacoordinated Mg atom. Thus, solvent dynamics is key to successive Mg-Cl and Mg-CH3 bond cleavages because bond breaking occurs at the most solvated Mg atom and the formation of bonds takes place at the least solvated one. The dynamics of the solvent also contributes to keep relatively flat the free energy profile of the Schlenk equil. These results shed light on one of the most used organometallic reagents whose structure in solvent remains exptl. unresolved. These results may also help to develop a more efficient catalyst for reactions involving these species.
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    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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    VandeVondele, J.; Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 2007, 127, 114105,  DOI: 10.1063/1.2770708
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    Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
    VandeVondele, Joost; Hutter, Jurg
    Journal of Chemical Physics (2007), 127 (11), 114105/1-114105/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    We present a library of Gaussian basis sets that has been specifically optimized to perform accurate mol. calcns. based on d. functional theory. It targets a wide range of chem. environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition no. of the overlap matrix for a set of mols. with respect to the exponents and contraction coeffs. of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles mol. dynamics simulations and is well suited for linear scaling calcns.
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    Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 1996, 54, 1703– 1710,  DOI: 10.1103/PhysRevB.54.1703
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    Separable dual-space Gaussian pseudopotentials
    Goedecker, S.; Teter, M.; Hutter, J.
    Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
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    Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
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    A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
    Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
    Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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    Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 1982, 76, 648,  DOI: 10.1063/1.442716
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    Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101,  DOI: 10.1063/1.2408420
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    Canonical sampling through velocity rescaling
    Bussi, Giovanni; Donadio, Davide; Parrinello, Michele
    Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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    A unified formulation of the constant-temperature molecular-dynamics methods
    Nose, Shuichi
    Journal of Chemical Physics (1984), 81 (1), 511-19CODEN: JCPSA6; ISSN:0021-9606.
    Three recently proposed const. temp. mol. dynamics methods [N., (1984) (1); W. G. Hoover et al., (1982) (2); D. J. Evans and G. P. Morris, (1983) (2); and J. M. Haile and S. Gupta, 1983) (3)] are examd. anal. via calcg. the equil. distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N-1/2 from the canonical distribution (N the no. of particles). The results for the const. temp.-const. pressure ensemble are similar to the canonical ensemble case.
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    Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A 1985, 31, 1695– 1697,  DOI: 10.1103/PhysRevA.31.1695
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    Canonical dynamics: Equilibrium phase-space distributions
    Hoover
    Physical review. A, General physics (1985), 31 (3), 1695-1697 ISSN:0556-2791.
    There is no expanded citation for this reference.
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    Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé—Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 1992, 97, 2635– 2643,  DOI: 10.1063/1.463940
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    Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33– 38,  DOI: 10.1016/0263-7855(96)00018-5
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    VDM: visual molecular dynamics
    Humphrey, William; Dalke, Andrew; Schulten, Klaus
    Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
    VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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    Carter, E. A.; Ciccotti, G.; Heynes, J. T.; Kapral, R. Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 1989, 156, 472– 477,  DOI: 10.1016/S0009-2614(89)87314-2
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    Constrained reaction coordinate dynamics for the simulation of rare events
    Carter, E. A.; Ciccotti, Giovanni; Hynes, James T.; Kapral, Raymond
    Chemical Physics Letters (1989), 156 (5), 472-7CODEN: CHPLBC; ISSN:0009-2614.
    A computationally efficient mol. dynamics method for estg. the rates of rare events that occur by activated processes is described. The system is constrained at "bottleneck" regions on a general many-body reaction coordinate in order to generate a biased configurational distribution. Suitable reweighting of this biased distribution, along with correct momentum distribution sampling, provides a new ensemble, the constrained-reaction-coordinate-dynamics ensemble, with which to study rare events of this type. Applications to chem. reaction rates are made.
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    Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B 2009, 113, 6378– 6396,  DOI: 10.1021/jp810292n
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    Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions
    Marenich, Aleksandr V.; Cramer, Christopher J.; Truhlar, Donald G.
    Journal of Physical Chemistry B (2009), 113 (18), 6378-6396CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We present a new continuum solvation model based on the quantum mech. charge d. of a solute mol. interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "d." to denote that the full solute electron d. is used without defining partial at. charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielec. medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liq. medium for which a few key descriptors are known (in particular, dielec. const., refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the soln. of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calcn. are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent mols. in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality consts. called at. surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aq. ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and DMSO, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaq. org. solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 org. solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic at. Coulomb radii and at. surface tension coeffs.) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calcns. in which the solute is represented by its electron d. in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on av. for ions with either Gaussian03 or GAMESS.
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    Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215– 241,  DOI: 10.1007/s00214-007-0310-x
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    The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals
    Zhao, Yan; Truhlar, Donald G.
    Theoretical Chemistry Accounts (2008), 120 (1-3), 215-241CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)
    We present two new hybrid meta exchange-correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amt. of nonlocal exchange (2X), and it is parametrized only for nonmetals. The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree-Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree-Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochem., four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for mol. excitation energies. We also illustrate the performance of these 17 methods for three databases contg. 40 bond lengths and for databases contg. 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochem., kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chem. and for noncovalent interactions.
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    Ditchfield, R.; Hehre, W. J.; Pople, J. A. Self-consistent molecular-orbital methods. IX. An extended Gaussian-type basis for molecular-orbital studies of organic molecules. J. Chem. Phys. 1971, 54, 724– 728,  DOI: 10.1063/1.1674902
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    Self-consistent molecular-orbital methods. IX. Extended Gaussian-type basis for molecular-orbital studies of organic molecules
    Ditchfield, R.; Hehre, Warren J.; Pople, John A.
    Journal of Chemical Physics (1971), 54 (2), 724-8CODEN: JCPSA6; ISSN:0021-9606.
    An extended basis set of at. functions expressed as fixed linear combinations of Gaussian functions is presented for H and the first-row atoms C to F. In this set. described as 4-31 G, each inner shell is represented by a single basis function taken as a sum of 4 Gaussians, and each valence orbital is split into inner and outer parts described by 3 and 1 Gaussian function, resp. The expansion coeffs. and Gaussian exponents are detd. by minimizing the total calcd. energy of the at. ground state. This basis set is then used in single-determinant MO studies of a group of small polyat. mols. Optimization of valence-shell scaling factors shows that considerable rescaling of at. functions occurs in mols., the largest effects being obsd. for H and C. However, the range of optimum scale factors for each atom is small enough to allow the selection of a std. mol. set. The use of this std. basis gives theoretical equil. geometries in reasonable 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. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2016.
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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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    CFOUR, a quantum-chemical program package written by Stanton, J. F.; Gauss, J.; Cheng, L.; Harding, M. E.; Matthews, D. A.; Szalay, P. G. with contributions from Auer, A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J.; Christiansen, O.; Engel, F.; Faber, R.; Heckert, M.; Heun, O.; Hilgenberg, M.; Huber, C.; Jagau, T.-C.; Jonsson, D.; Jusélius, J.; Kirsch, T.; Klein, K.; Lauderdale, W. J.; Lipparini, F.; Metzroth, T.; Mück, L.A.; O’Neill, D. P.; Price, D. R.; Prochnow, E.; Puzzarini, C.; Ruud, K.; Schiffmann, F.; Schwalbach, W.; Simmons, C.; Stopkowicz, S.; Tajti, A.; Vázquez, J.; Wang, F.; Watts, J. D. and the integral packages MOLECULE (Almlöf, J.; Taylor, P. R.), PROPS (Taylor, P. R.), ABACUS (Helgaker, T.; Jensen, H. J. Aa.; Jørgensen, P.; Olsen, J.), and ECP routines by Mitin, A. V. and van Wüllen, C.; website: http://www.cfour.de.
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    Buergi, H. B.; Lehn, J. M.; Wipff, G. Ab initio study of nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1974, 96, 1956– 1957,  DOI: 10.1021/ja00813a062
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    Ab initio study of nucleophilic addition to a carbonyl group
    Buergi, H. B.; Lehn, J. M.; Wipff, G.
    Journal of the American Chemical Society (1974), 96 (6), 1956-7CODEN: JACSAT; ISSN:0002-7863.
    Ab initio SCF-LCGO (linear combination of Gaussian orbitals)-MO computations were performed on the reaction of hydride ion with HCHO, considered as model for nucleophilic addns. to the carbonyl group. Geometrical changes and electronic rearrangements were obtained as a function of the reaction coordinate. Orientational constraints in the course of the reaction bear relation to orbital steering, togetherness, and proximity effects considered in the literature. The calcd. geometrical changes correlate with the changes obsd. in crystal structures for the approach of an amino site toward a carbonyl group. A computation of the NH3-HCHO system at one fixed sepn. was also performed for comparison purposes.
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    Walker, F. W.; Ashby, E. C. Composition of Grignard compounds. VI. Nature of association in tetrahydrofuran and diethyl ether solutions. J. Am. Chem. Soc. 1969, 91, 3845– 3850,  DOI: 10.1021/ja01042a027
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    Composition of Grignard compounds. VI. Nature of association in tetrahydrofuran and diethyl ether solutions
    Walker, Frank W.; Ashby, E. C.
    Journal of the American Chemical Society (1969), 91 (14), 3845-50CODEN: JACSAT; ISSN:0002-7863.
    Ebullioscopic data are presented for tetrahydrofuran (I) and Et2O solns. of several Grignard and related Mg compounds over a wide concn. range. Anal. of the data is accomplished by observing the change in assocn. with concn. and by consideration of the constancy of the equil. consts. calcd. for several possible descriptions of the assocd. system. The expected nonideality of the solns. studied was considered in the interpretation of the data. While all the compds. studied were monomeric in I, the alkyl- and arylmagnesium bromides and iodides were monomeric in Et2O only at low concn. (<0.1 m), exhibiting in general an increase in assocn. with concn. These compds. are assocd. in a polymeric fashion. In contrast, the alkylmagnesium chlorides assoc. in Et2O to form stable dimers with the assocn. insensitive to concn. changes. Comparison of the data for Mg halides and dialkylmagnesium compds. in Et2O indicates that, except for the Me compd., assocn. is considerably stronger for the Mg halides than for the dialkylmagnesium compds. Thus, except for methylmagnesium halides, Grignard compds. assoc. with bridging mainly through the halogen atom. The methylmagnesium halides are exceptional since Me bridging is strong enough in Et2O to permit assocn. by bridging through either the Me group or the halogen atom. Although the steric and electronic nature of the alkyl group has some effect on the assocn. of Grignard compds., the effect is generally small compared to to the effect of halogen or solvent.
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    We consider here thermodynamically equilibrated solutions of the Grignard reagent. In fact, the formation of the Grignard reagent may occur via a radical mechanism; see, for instance, the recent study:Henriques, A. M.; Barbosa, A. G. H. Chemical bonding and the equilibrium composition of Grignard reagents in ethereal solution. J. Phys. Chem. A 2011, 115, 12259– 12270,  DOI: 10.1021/jp202762p
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    Chemical bonding and the equilibrium composition of Grignard reagents in ethereal solutions
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    A thorough anal. of the electronic structure and thermodn. aspects of Grignard reagents and its assocd. equil. compn. in ethereal solns. is performed. Considering methylmagnesium halides contg. fluorine, chlorine, and bromine, we studied the neutral, charged, and radical species assocd. with their chem. equil. in soln. The ethereal solvents considered, THF and di-Et ether, were modeled using the polarizable continuum model (PCM) and also by explicit coordination to the Mg atoms in a cluster. The chem. bonding of the species that constitute the Grignard reagent is analyzed in detail with generalized valence bond (GVB) wave functions. Equil. consts. were calcd. with the DFT/M06 functional and GVB wave functions, yielding similar results. According to our calcns. and existing kinetic and electrochem. evidence, the species R·, R-, ·MgX, and RMgX2- must be present in low concn. in the equil. We conclude that depending on the halogen, a different route must be followed to produce the relevant equil. species in each case. Chloride and bromide must preferably follow a "radical-based" pathway, and fluoride must follow a "carbanionic-based" pathway. These different mechanisms are contrasted against the available exptl. results and are proven to be consistent with the existing thermodn. data on the Grignard reagent equil.
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    A review. This Minireview describes the scope of the halogen-magnesium exchange. It shows that the use of the turbo-Grignard reagent (iPrMgCl·LiCl) greatly enhances the rate of the Br- and I-Mg exchange. Furthermore, this magnesium reagent allows the performance of a fast sulfoxide-magnesium exchange. Also, the use of s-BuMgOR·LiOR (R=2-ethylhexyl) enables a Br-Mg exchange in toluene leading to various Grignard reagents in toluene. Addnl., the new exchange reagent s-Bu2Mg·2LiOR (R = 2-ethylhexyl) further increases the rate of the halogen-magnesium exchange allowing one to perform a chlorine-magnesium exchange for arom. chlorides bearing an ortho-methoxy substituent in toluene.
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    On the Mechanism of the Copper-Catalyzed Enantioselective 1,4-Addition of Grignard Reagents to α,β-Unsaturated Carbonyl Compounds
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    The mechanism of the enantioselective 1,4-addn. of Grignard reagents to α,β-unsatd. carbonyl compds. promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochem. anal. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examd. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodn. activation parameters were detd. from the temp. dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.
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    A review on recent advances in Cu-catalyzed asym. conjugate addn. of Grignard reagents, asym. SN2' substitution reactions of allylic bromides with Grignard reagents, and application to synthesis of natural products.
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    De Vivo, Marco; Dal Peraro, Matteo; Klein, Michael L.
    Journal of the American Chemical Society (2008), 130 (33), 10955-10962CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    RNase H belongs to the nucleotidyl-transferase (NT) superfamily and hydrolyzes the phosphodiester linkages that form the backbone of the RNA strand in RNA•DNA hybrids. This enzyme is implicated in replication initiation and DNA topol. restoration and represents a very promising target for anti-HIV drug design. Structural information has been provided by high-resoln. crystal structures of the complex RNase H/RNA•DNA from Bacillus halodurans (Bh), which reveals that two metal ions are required for formation of a catalytic active complex. Here, we use classical force field-based and quantum mechanics/mol. mechanics calcns. for modeling the nucleotidyl transfer reaction in RNase H, clarifying the role of the metal ions and the nature of the nucleophile (water vs. hydroxide ion). During the catalysis, the two metal ions act cooperatively, facilitating nucleophile formation and stabilizing both transition state and leaving group. Importantly, the two Mg2+ metals also support the formation of a meta-stable phosphorane intermediate along the reaction, which resembles the phosphorane intermediate structure obtained only in the debated β-phosphoglucomutase crystal (Lahiri, S. D.; et al. Science 2003, 299 (5615), 2067-2071). The nucleophile formation (i.e., water deprotonation) can be achieved in situ, after migration of one proton from the water to the scissile phosphate in the transition state. This proton transfer is actually mediated by solvation water mols. Due to the highly conserved nature of the enzymic bimetal motif, these results might also be relevant for structurally similar enzymes belonging to the NT superfamily.
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    Rosta, E.; Nowotny, M.; Yang, W.; Hummer, G. Catalytic mechanism of RNA backbone cleavage by ribonuclease H from quantum mechanics/molecular mechanics simulations. J. Am. Chem. Soc. 2011, 133, 8934– 8941,  DOI: 10.1021/ja200173a
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    Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations
    Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard
    Journal of the American Chemical Society (2011), 133 (23), 8934-8941CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    We use quantum mechanics/mol. mechanics simulations to study the cleavage of the RNA (RNA) backbone catalyzed by RNase H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temp. string method, we calc. the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water mol. attacks the scissile phosphate. Consistent with thiol-substitution expts., a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissocd. but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ∼15 kcal mol-1, encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ∼1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction.
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    Casalino, L.; Palermo, G.; Rothlisberger, U.; Magistrato, A. Who activates the nucleophile in ribozyme catalysis? An answer from the splicing mechanism of group II introns. J. Am. Chem. Soc. 2016, 138, 10374– 10377,  DOI: 10.1021/jacs.6b01363
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    Who Activates the Nucleophile in Ribozyme Catalysis? An Answer from the Splicing Mechanism of Group II Introns
    Casalino, Lorenzo; Palermo, Giulia; Rothlisberger, Ursula; Magistrato, Alessandra
    Journal of the American Chemical Society (2016), 138 (33), 10374-10377CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Group II introns are Mg2+-dependent ribozymes that are considered to be the evolutionary ancestors of the eukaryotic spliceosome, thus representing an ideal model system to understand the mechanism of conversion of premature mRNA (mRNA) into mature mRNA. Neither in splicing nor for self-cleaving ribozymes has the role of the two Mg2+ ions been established, and even the way the nucleophile is activated is still controversial. Here we employed hybrid quantum-classical QM(Car-Parrinello)/MM mol. dynamics simulations in combination with thermodn. integration to characterize the mol. mechanism of the first and rate-detg. step of the splicing process (i.e., the cleavage of the 5'-exon) catalyzed by group II intron ribozymes. Remarkably, our results show a new RNA-specific dissociative mechanism in which the bulk water accepts the nucleophile's proton during its attack on the scissile phosphate. The process occurs in a single step with no Mg2+ ion activating the nucleophile, at odds with nucleases enzymes. We suggest that the novel reaction path elucidated here might be an evolutionary ancestor of the more efficient two-metal-ion mechanism found in enzymes.
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  64. 64
    Genna, V.; Vidossich, P.; Ippoliti, E.; Carloni, P.; De Vivo, M. A self-activated mechanism for nucleic acid polymerization catalyzed by DNA/RNA polymerases. J. Am. Chem. Soc. 2016, 138, 14592– 14598,  DOI: 10.1021/jacs.6b05475
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    A Self-Activated Mechanism for Nucleic Acid Polymerization Catalyzed by DNA/RNA Polymerases
    Genna, Vito; Vidossich, Pietro; Ippoliti, Emiliano; Carloni, Paolo; Vivo, Marco De
    Journal of the American Chemical Society (2016), 138 (44), 14592-14598CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The enzymic polymn. of DNA and RNA is at the basis of genetic inheritance for all living organisms. It is catalyzed by the DNA/RNA polymerase (Pol) superfamily. Here, bioinformatics anal. revealed that the incoming nucleotide substrate always forms an H-bond between its 3'-OH and β-phosphate moieties upon formation of the Michaelis complex. This previously unrecognized H-bond implies a novel self-activated mechanism (SAM), which synergistically connects the in situ nucleophile formation with subsequent nucleotide addn. and, importantly, nucleic acid translocation. Thus, SAM allows an elegant and efficient closed-loop sequence of chem. and phys. steps for Pol catalysis. This is markedly different from previous mechanistic hypotheses. This proposed mechanism was corroborated via ab initio QM/MM simulations on a specific Pol, human DNA polymerase-η, an enzyme involved in repairing damaged DNA. The structural conservation of DNA and RNA Pols supports the possible extension of SAM to Pol enzymes from the 3 domains of life.
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    Genna, V.; Donati, E.; De Vivo, M. The catalytic mechanism of DNA and RNA polymerases. ACS Catal. 2018, 8, 11103– 11118,  DOI: 10.1021/acscatal.8b03363
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    The Catalytic Mechanism of DNA and RNA Polymerases
    Genna, Vito; Donati, Elisa; De Vivo, Marco
    ACS Catalysis (2018), 8 (12), 11103-11118CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
    A review. DNA and RNA polymerases (Pols) catalyze nucleic acid biosynthesis in all domains of life, with implications for human diseases and health. Pols carry out nucleic acid extension through the addn. of one incoming nucleotide trisphosphate at the 3'-OH terminus of the growing primer strand, at every catalytic cycle. Thus, Pol catalysis involves chem. reactions for nucleophile 3'-OH deprotonation and nucleotide addn., as well as major protein conformational motions and structural rearrangements for nucleotide selection, binding, and nucleic acid translocation to complete the overall catalytic cycle. In this respect, quantum and mol. mechanics simulations, integrated with exptl. data, have advanced our mechanistic understanding of how Pols operate at the at. level. This Perspective outlines how modern mol. simulations can further deepen our understanding of Pol catalytic reactions and fidelity, which may help in devising strategies for designing drugs and artificial Pols for biotechnol. and clin. purposes.
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  • Abstract

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    Figure 1

    Figure 1. Schematic representation of possible mechanisms for the Grignard reaction: (a) polar mechanism, heterolytic Mg–C bond breaking, with subsequent formation of a nucleophilic carbon that adds to the electrophilic carbonyl carbon; or (b) radical mechanism, homolytic Mg–C bond breaking, with subsequent recombination of the species with unpaired electrons.

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    Figure 2

    Figure 2. Organomagnesium complexes considered as reactants for the polar mechanism, classified as a function of the relative positions of the substrate (ACA) and nucleophile (methyl group). The labels geminal, vicinal, and bridging describe the initial position of the reactive groups with respect to the Mg center(s). The activation free energies, ΔA⧧, defined as the difference in free energy between the TS and the related reactant species, are given in kcal mol–1.

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    Figure 3

    Figure 3. Geminal reaction for compound Bgem. Representative geometries for the reactant, transition state, and product. The Mg atom and its ligands are represented as balls-and-sticks. Other solvating THF molecules are drawn as lines. The color codes are mauve for magnesium, red for oxygen, gray for carbon, and white for hydrogen.

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    Figure 4

    Figure 4. Transition state structures of the geminal and vicinal reactions (Bgem, Fvic). Left: Evidence of the structural similarity of the two TSs. Balls-and-sticks are used to represent the reacting moiety, while the rest of the system is drawn as transparent cylinders. THF molecules not bound to Mg are not shown. The green line marks the incipient C–CH3 bond and its associated distance. Top right: Schematic definition of the angles formed by the C3 axis of the nucleophile methyl group. Bottom right: Distances and angles formed by the atoms involved in the four-center TS. Distances are reported in angstroms, and angles are in degrees. ϕX is the angle at the vertex X in the four-member ring (top right panel). The color code is as in Figure 3.

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    Figure 5

    Figure 5. Vicinal reaction for Fvic. Representative geometries for the reactant, transition state, and product. The Mg atoms (left Mg1, right Mg2) and first coordination sphere ligands are represented as balls-and-sticks. Other solvating THF molecules are drawn as lines. The color code is cyan for chlorine and green for the nucleophilic methyl, while the other elements are colored as in Figure 3.

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    Figure 6

    Figure 6. Red: Activation energies of all Grignard species derived from CH3MgCl in THF solution when reacting with acetaldehyde. Blue: Relative free energies of the species involved in the Schlenk equilibrium (data from ref (31)). The green box highlights the intrinsically most reactive species identified in this work.

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    Figure 7

    Figure 7. Mg–CH3 BDE and spin-density localization (in fractions of e) for MgCl(Sub)(THF)nCH3 (Sub = substrate). The green wire-frame shows the isosurface of the spin density map at a value of 0.0065 au.

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    Figure 8

    Figure 8. Energetics of the Grignard reaction mechanisms for fluorenone. Top panel: Activation free energy of the nucleophilic addition with Mg(CH3)2. Bottom panel: Bond dissociation energy. All energy values are in kcal mol–1. On the right is the distribution of the spin density in Mg(CH3)(fluorenone)THF2: 33% of the unpaired electron localizes on the carbonyl carbon, 16% on the carbonyl oxygen, and 45% on the remaining π system.

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    Figure 9

    Figure 9. Structural reorganization from (left) reactant to (right) transition state in the nucleophilic pathway for (top) ACA and (bottom) fluorenone. The CH3–Mg–O–C dihedral angle (corresponding to the blue arrow) is 14 ± 15° for ACA and 114 ± 30° for fluorenone.

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  • References

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    This article references 65 other publications.

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      [Machine Translation of Descriptors]. During effect of CH3J on magnesium powders in presence of anhydrous ether, an organo-metallic compound forms under a very lively reaction. The Mg dissolves gradually, and finally receives a clear liquid, which leaves a gray, crystalline, hygroscopic mass with the evaporation of the ether. One sets to that more ether solution which on 1 atom Mg of 1 mole CH3J contains 1 mole an aldehyde or a ketone, then takes place under a very lively reaction for formation of an organo-metallic compound, which supplies the appropriate secondary or tertiary alcohol with decomposing with acidified water with an yield of about 70%. The reaction takes place after the subsequent equations. 1. CH3I + Mg = CH3MgI. 2. CH3MgI + RCHO = R. CH (CH3) OMgI. 3. R. CH (CH3) OMgI + H2O = R. CH (OH) . CH3 + MgIOH. The bromine and iodine compounds of the saturated and unsaturated alkyls in the same way benzyl bromide give appropriate alcohol in same way. Author represented the subsequent alcohols in this way: Phenylisobutylcarbinol, C6H5. CH (OH): C4H9, from benzaldehyde, Isobutylbromide and Mg are colorless and weakly smelling liquid, Kp9, 122°. Dimethylphenylcarbinol, C6H5. C (OH) (CH3) 2, from acetophenone, Mg and CH3I, are pleasantly smelling and colorless liquid, Kp10, 93-95°. Dimethylbenzylcarbinol, C6H5. CH2. C (OH) (CH3) 2, from acetone, benzyl bromide and Mg are weakly smelling and colorless liquid, Kp10, 103-105°. With application of unsaturated aldehydes and ketones, yields with the double bond of the cobalt group and the developing alcohol is sometimes changeable. It splits off, then with the distillation H2O, and an unsaturated hydrocarbon develops. Thus the Dimethyl-2.4-pentadien-2.4 becomes, CH3. during effect of Mesityloxide on magnesium methyl iodide; C (CH3): CH. C (CH3): CH3, Kp750, 92-93°.
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      Journal of Organometallic Chemistry (1968), 13 (2), 519-22CODEN: JORCAI; ISSN:0022-328X.
      Chem. and E.S.R. evidence is reported for the occurrence of radicals during the reaction of the Grignard reagent from neopentyl chloride with benzophenone in tetrahydrofuran; 1,1-diphenyl-3,3-dimethylbutanol and benzopinacol were isolated and the formation of neopentane was observed. The steric bulk of the neopentyl group (R') so retards the normal addn. reaction [Ph2CO:Mg(R') X → Rh2R'COMgX] that the radicals, formed in the process [Ph2CO:Mg(R')X → Ph2C·OMgX + R·'], are able to escape from the solvent cage. The neopentyl radical can then react with the solvent to give R' and the ketyl can dimerize to give the Mg halide salt of benzopinacol.
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    10. 10
      Blomberg, C.; Grootveld, H.; Gerner, T.; Bickelhaupt, F. Radical formation during reactions of Grignard reagents with quinones. J. Organomet. Chem. 1970, 24, 549– 553,  DOI: 10.1016/S0022-328X(00)84483-6
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      Radical formation during reactions of Grignard reagents with quinones
      Blomberg, Cornelis; Grootveld, H. H.; Gerner, T. H.; Bickelhaupt, F.
      Journal of Organometallic Chemistry (1970), 24 (3), 549-53CODEN: JORCAI; ISSN:0022-328X.
      In dil. soln. the addn. of PhMgBr to acenaphthenequinone and phenanthrenequinone (I) leads by single electron transfer to the formation of the corresponding semiquinones, which can be identified by ESR. I yields ∼20% 9-hydroxy-10-phenoxyphenanthrene, the formation of which is explained by combination of the initially formed semiquinone and Ph radicals. The analogy with photochem. reactions and the possible occurrence of similar reactions in organomagnesium and organozinc chemistry are briefly discussed.
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    11. 11
      Ashby, E. C.; Nackashi, J.; Parris, G. E. Composition of Grignard compounds. X. NMR, IR, and molecular association studies of some methylmagnesium alkoxides in diethyl ether, tetrahydrofuran, and benzene. J. Am. Chem. Soc. 1975, 97, 3162– 3171,  DOI: 10.1021/ja00844a040
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      11
      Composition of Grignard compounds. X. NMR, ir, and molecular association studies of some methylmagnesium alkoxides in diethyl ether, tetrahydrofuran, and benzene
      Ashby, E. C.; Nackashi, J.; Parris, G. E.
      Journal of the American Chemical Society (1975), 97 (11), 3162-71CODEN: JACSAT; ISSN:0002-7863.
      Mol. assocn. of MeMgOR (R = OCPh2Me, OCMe3, OCHMe2, OPr) in Et2O, THF, and C6H6 was examd. using ir and NMR spectral data. The steric bulk of the alkoxy group and the coordinating ability of the solvent determine the thermodynamically preferred soln. compn. In THF, solvated dimers are preferred. In Et2O, linear oligomers and cubane tetramers are preferred provided the alkoxy group is not bulkier than the tert-butoxy group. In C6H6, cubane tetramers are obsd. for alkoxy groups of intermediate bulk such as tert-butoxy and isopropoxy, but the less bulky n-propoxy group permits the formation of an oligomer contg. seven to nine monomer units. For the reagents with alkoxy groups less bulky than tert-butoxy, the equilibria involving various structures are established very rapidly. However, the dimer-linear oligomer ↹ cubane tetramer equilibrium is established very slowly for methylmagnesium tert-butoxide compds. The cubane form is very inert and does not exchange or otherwise interact with Me2Mg in Et2O. The dimer-linear oligomer form is quite labile and readily exchanges with Me2Mg forming mixed-bridged compds. However, in Et2O, the mixed bridge is not sufficiently strong to prevent slow conversion of methylmagnesium tert-butoxide to the cubane form thus releasing Me2Mg.
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    12. 12
      Ashby, E. C.; Lopp, I. G.; Buhler, J. D. Mechanisms of Grignard reactions with ketones. Polar vs. single electron transfer pathways. J. Am. Chem. Soc. 1975, 97, 1964– 1966,  DOI: 10.1021/ja00840a066
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      Mechanisms of Grignard reactions with ketones. Polar vs. single electron transfer pathways
      Ashby, E. C.; Lopp, Irene G.; Buhler, Jerry D.
      Journal of the American Chemical Society (1975), 97 (7), 1964-6CODEN: JACSAT; ISSN:0002-7863.
      The addn. of MeMgBr to 2-methylbenzophenone in Et2O proceeds via a normal polar mechanism, whereas in the presence of small amts. of transition metal catalysts (e.g. 0.05 mole % FeCl3) the reaction proceeds via a single electron transfer pathway. The role of an intermediate (I) in by-product formation is examd.
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      Ashby, E. C. A detailed description of the mechanism of reaction of Grignard reagents with ketones. Pure Appl. Chem. 1980, 52, 545– 569,  DOI: 10.1351/pac198052030545
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      13
      A detailed description of the mechanism of reaction of Grignard reagents with ketones
      Ashby, E. C.
      Pure and Applied Chemistry (1980), 52 (3), 545-69CODEN: PACHAS; ISSN:0033-4545.
      A review, chiefly of the work of the author, with 29 refs.
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    14. 14
      Ashby, E. C.; Bowers, J. R. Organometallic reaction mechanisms. 17. Nature of alkyl transfer in reactions of Grignard reagents with ketones. Evidence for radical intermediates in the formation of 1,2-addition product involving tertiary and primary Grignard reagents. J. Am. Chem. Soc. 1981, 103, 2242– 2250,  DOI: 10.1021/ja00399a018
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      Organometallic reaction mechanisms. 17. Nature of alkyl transfer in reactions of Grignard reagents with ketones. Evidence for radical intermediates in the formation of 1,2-addition product involving tertiary and primary Grignard reagents
      Ashby, E. C.; Bowers, Joseph R., Jr.
      Journal of the American Chemical Society (1981), 103 (9), 2242-50CODEN: JACSAT; ISSN:0002-7863.
      The title 1,2-addn. products (formed after dissocn. of the radical anion-radical cation pair) show free-radical character, as indicated by the cyclized 1,2-addn. products formed from the reaction of a tertiary Grignard reagent probe with Ph2CO in THF and from the reaction of a primary Grignard reagent probe (neooctenyl Grignard reagent) with Ph2CO in Et2O. The 1,6-addn. products show free-radical character, as evidenced by the cyclized 1,6-addn. products formed in all of the reactions which involve the tertiary Grignard reagent probe (in all solvents studied) with Ph2CO and 2-MeC6H4COPh (I) and also in the reaction of the neooctenyl Grignard reagent probe with I.
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    15. 15
      Lund, T.; Pedersen, M. L.; Frandsen, L. A. Does the reaction between fluorenone and grignard reagents involve free fluorenone anion radicals?. Tetrahedron Lett. 1994, 35, 9225– 9226,  DOI: 10.1016/0040-4039(94)88472-2
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      Does the reaction between fluorenone and Grignard reagents involve free fluorenone anion radicals?
      Lund, Torben; Pedersen, Morten L.; Frandsen, Lars A.
      Tetrahedron Letters (1994), 35 (49), 9225-6CODEN: TELEAY; ISSN:0040-4039. (Elsevier)
      The ratio between 1,6- and 1,2-addn. in the reactions of electrogenerated fluorenone anion radicals with RX in THF were similar to the ratio obtained in the Grignard reaction of fluorenone with RMgX in THF. This indicates that the addn. products in the Grignard reaction may be obtained via the coupling of freely diffusing fluorenone anion radicals with R radicals.
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    16. 16
      Blomberg, C.; Salinger, R. M.; Mosher, H. S. Reaction of Grignard reagent from neopentyl chloride with benzophenone. A nuclear magnetic resonance study. J. Org. Chem. 1969, 34, 2385– 2388,  DOI: 10.1021/jo01260a028
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      Reaction of the Grignard reagent from neopentyl chloride with benzophenone. Nuclear magnetic resonance study.
      Blomberg, Cornelis; Salinger, Rudolf M.; Mosher, Harry S.
      Journal of Organic Chemistry (1969), 34 (8), 2385-8CODEN: JOCEAH; ISSN:0022-3263.
      The rate of change in the N.M.R. spectrum of a mixt. of the Grignard reagent from neopentyl chloride and benzophenone in tetrahydrofuran was studied. The expected addn. reaction was complicated by the simultaneous occurrence of a radical reaction to produce neopentane and benzopinacol. These spectra are interpretable in terms of a reaction to give an initial product which in turn undergoes further reaction with the Grignard reagent to give a new reactive species. This reactive intermediate presumably is either the alkylmagnesium alkoxide (RMgOR') or a complex of the initial product with the Grignard reagent (RMgCl.R'OMgCl). This constitutes a direct observation of a process often postulated in the reaction of a Grignard compd. Qual. generalizations could be made but because of these complications it was not possible to make a quant. kinetic anal. of the data.
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    17. 17
      Hoffmann, R. W.; Hölzer, B. Concerted and stepwise Grignard additions, probed with a chiral Grignard reagent. Chem. Commun. 2001, 491– 492,  DOI: 10.1039/b009678o
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      Concerted and stepwise Grignard additions, probed with a chiral Grignard reagent
      Hoffmann, Reinhard W.; Holzer, Bettina
      Chemical Communications (Cambridge, United Kingdom) (2001), (5), 491-492CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
      The Grignard reagent (S)-PhCH2CH(MgCl)CH2CH3 6, in which the magnesium-bearing carbon atom is the sole stereogenic center has been added to CO2, PhNCO, PhNCS and certain aldehydes with full retention of configuration. Reaction with benzophenone, electron-deficient aldehydes and several allyl halides proceeded with partial or complete racemization. The findings are discussed with respect to a dichotomy between concerted polar and stepwise SET reaction pathways.
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      Hoffmann, R. W. The quest for chiral Grignard reagents. Chem. Soc. Rev. 2003, 32, 225– 230,  DOI: 10.1039/b300840c
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      The quest for chiral Grignard reagents
      Hoffmann, Reinhard W.
      Chemical Society Reviews (2003), 32 (4), 225-230CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)
      A review on the prepn. of chiral Grignard reagents. The involvement of single electron transfer, i.e. of free radicals in the reactions of organomagnesium reagents could be detected with the aid of a chiral secondary Grignard reagent, in which the magnesium-bearing carbon atom is the sole stereogenic center. So far, however, such reagents have not been accessible, because the std. prepn. of Grignard reagents proceeds via free radicals. The authors review and summarize here their efforts to generate (S)-1-Benzylpropylmagnesium chloride 36 by asym. synthesis starting from an enantiomerically pure compd. ArSOCH(Cl)CH2Ph (Ar = p-cl-C6H5) 30b using a sulfoxide/magnesium exchange reaction to give trans-β-chloro-α-phenylbenzenepropanol 33 followed by a carbenoid homologation reaction. Grignard reagent 36 turned out to be an ideal probe to learn about the extent to which SET is involved in reactions of organomagnesium reagents.
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    19. 19
      Gajewski, J. J.; Bocian, W.; Harris, N. J.; Olson, L. P.; Gajewski, J. P. Secondary deuterium kinetic isotope effects in irreversible additions of hydride and carbon nucleophiles to aldehydes: a spectrum of transition states from complete bond formation to single electron transfer. J. Am. Chem. Soc. 1999, 121, 326– 334,  DOI: 10.1021/ja982504r
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      19
      Secondary deuterium kinetic isotope effects in irreversible additions of hydride and carbon nucleophiles to aldehydes: a spectrum of transition states from complete bond formation to single electron transfer
      Gajewski, Joseph J.; Bocian, Wojciech; Harris, Nathan J.; Olson, Leif P.; Gajewski, John P.
      Journal of the American Chemical Society (1999), 121 (2), 326-334CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The competitive kinetics of hydride and organometallic addns. to PhCHO and PhCDO were detd. at -78° using LiAlH4, LiBHEt3, NaBH4, LiBH4, LiAlH(OCMe3)3, NaBH(OMe)3, NaBH(OAc)3 (at 20°), RMgBr (R = Me, Ph, allyl), and RLi (R = Me, Ph, Bu, Me3C, allyl). The hydride addns. had an inverse secondary D kinetic isotope effects in all cases, but the magnitude of the effect varied inversely with the apparent reactivity of the hydride. In the addns. of MeMgBr and of MeLi and PhLi, inverse secondary D isotope effects were obsd.; little if any isotope effect was obsd. with PhMgBr, BuLi or Me3CLi. With CH2:CHCH2M (M = MgBr, Li), a normal secondary D kinetic isotope effect was obsd. Rate-detg. single-electron transfer occurs with allyl reagents, but direct nucleophilic reaction occurs with all of the other reagents, with the extent of bond formation depending on the reactivity of the reagent. In the addn. of MeLi to cyclohexanecarboxaldehyde (I), a less inverse secondary D kinetic isotope effect was obsd. than that obsd. in the addn. of MeLi to PhCHO, and allyllithium addn. to I had a kinetic isotope effect near unity. The data with organometallic addns., which are not incompatible with observations of carbonyl C isotope effects, suggest that electrochem. detd. redox potentials which indicate endoergonic electron transfer with energies .ltorsim.13 kcal/mol allow electron-transfer mechanisms to compete well with direct polar addns. to aldehydes, provided that the reagent is highly stabilized, like allyl species. MeLi, PhLi, MeMgBr and PhMgBr are estd. to undergo electron transfer with endoergonicities >30 kcal/mol with PhCHO, so these react by direct polar addns. A working hypothesis is that BuLi reagents undergo polar addns., despite redox potentials which indicate ≤13 kcal/mol endoergonic electron transfer, because of the great exoergonicity assocd. with the 2-electron addn., which is responsible for a low barrier for polar reactions.
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      Otte, D. A. L.; Woerpel, K. A. Evidence that Additions of Grignard Reagents to Aliphatic Aldehydes do Not Involve Single-Electron-Transfer Processes. Org. Lett. 2015, 17, 3906– 3909,  DOI: 10.1021/acs.orglett.5b01893
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      20
      Evidence that Additions of Grignard Reagents to Aliphatic Aldehydes Do Not Involve Single-Electron-Transfer Processes
      Otte, Douglas A. L.; Woerpel, K. A.
      Organic Letters (2015), 17 (15), 3906-3909CODEN: ORLEF7; ISSN:1523-7052. (American Chemical Society)
      Addn. of allylmagnesium reagents to an aliph. aldehyde bearing a radical clock gave only addn. products and no evidence of ring-opened products that would suggest single-electron-transfer reactions. The analogous Barbier reaction also did not provide evidence for a single-electron-transfer mechanism in the addn. step. Other Grignard reagents (methyl-, vinyl-, t-Bu-, and triphenylmethylmagnesium halides) also do not appear to add to an alkyl aldehyde by a single-electron-transfer mechanism.
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      Garst, J. F.; Soriaga, M. P. Grignard reagent formation. Coord. Chem. Rev. 2004, 248, 623– 652,  DOI: 10.1016/j.ccr.2004.02.018
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      Grignard reagent formation
      Garst, John F.; Soriaga, Manuel P.
      Coordination Chemistry Reviews (2004), 248 (7-8), 623-652CODEN: CCHRAM; ISSN:0010-8545. (Elsevier Science B.V.)
      A review with 74 refs. Probably reactions of Mg metal with org. halides RX in ether solvents are typical metallic corrosions in which the stabilization of Mg2+, substantially through its coordination by the solvent, drives its loss from the metal and consequently the redns. of RX and reaction intermediates such as R· at the metal surface. Although alkyl halides form Grignard reagents through nonchain mechanisms in which intermediate radicals diffuse in soln., very small amts. of radical isomerization occur in Grignard reactions of certain vinyl and aryl halides, even when intermediate radicals R· would isomerize very rapidly. This suggests a dominant nonradical mechanism for these vinyl and aryl halides or a mechanism in which intermediate radicals R· have extremely short lifetimes. Since the former seems more likely, a dianion mechanism, through a transition state [RX2-]‡, is proposed. Surface studies of polycryst. Mg show that the oxide layer is mostly Mg(OH)2 and that it is mech. passivating. In the absence of promoters, Grignard reactions occur very slowly until enough RX has seeped to the Mg surface and reacted there to undercut and cause the Mg(OH)2 layer to flake off.
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    22. 22
      Chen, Z.-N.; Fu, G.; Xu, X. Theoretical studies on Grignard reagent formation: radical mechanism versus non-radical mechanism. Org. Biomol. Chem. 2012, 10, 9491– 9500,  DOI: 10.1039/c2ob26658j
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      Theoretical studies on Grignard reagent formation: radical mechanism versus non-radical mechanism
      Chen, Zhe-Ning; Fu, Gang; Xu, Xin
      Organic & Biomolecular Chemistry (2012), 10 (47), 9491-9500CODEN: OBCRAK; ISSN:1477-0520. (Royal Society of Chemistry)
      Here the systematic theor. study on the mechanisms of Grignard reagent formation is presented (GRF) for CH3Cl reacting with Mg atom, Mg2 and Mg clusters (Mg4-Mg20). The calcns. reveal that the ground state Mg atom is inactive under matrix condition, whereas it is active under metal vapor synthesis (MVS) conditions. However, the excited state Mg (3P) atom, as produced by laser-ablation, can react with CH3Cl without barriers, and hence is active under matrix condition. The prediction is that the bimagnesium Grignard reagent, though often proposed, can barely be obsd. exptl., due to its high reactivity towards addnl. CH3Cl to produce more stable Grignard reagent dimer, and that the cluster Grignard reagent RMg4X possesses a flat Mg4 unit rather than a tetrahedral geometry. The calcns. further reveal that the radical pathway (T4) is prevalent on Mg, Mg2 and Mgn clusters of small size, while the no-radical pathway (T2), which starts at Mg4, becomes competitive with T4 as the cluster size increases. A structure-reactivity relation between barrier heights and ionization potentials of Mgn is established. These findings not only resolve controversy in expt. and theory, but also provide insights which can be used in the design of effective synthesis approaches for the prepn. of chiral Grignard reagents.
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      Shao, Y.; Liu, Z.; Huang, P.; Liu, B. A unified model of Grignard reagent formation. Phys. Chem. Chem. Phys. 2018, 20, 11100– 11108,  DOI: 10.1039/C8CP01031E
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      A unified model of Grignard reagent formation
      Shao, Yunqi; Liu, Zhen; Huang, Pan; Liu, Boping
      Physical Chemistry Chemical Physics (2018), 20 (16), 11100-11108CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Grignard reagents are among the most fundamental reagents in org. synthesis, yet studies have hitherto failed to fully explain the selectivity and kinetics of Grignard reagent formation (GRF). The present study provides new insights into the intermediates and pathways of GRF using d. functional theory (DFT) calcns. Potential energy surfaces of RX dissocn. along different directions reveal the origin of configuration retention of alkenyl and arom. halides. Radical intermediates participate solely in the dissocn. stage, and depend on the geometry of the reactant halide. Dissocn. of org. halides yields stabilized surface anions, and the rest of the reaction is ionic in nature. MgX+/RMg+ are proposed as the key intermediates of Mg leaving from the surface in the self-activation of GRF, which explains the accelerated kinetics upon addn. of RMgX or MgX2. The intermediacy of the cations was supported by a simple electrochem. expt. To the best of the authors' knowledge, this is the 1st unified ionic model (I-model) developed for resolving the controversial issues of GRF.
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      Axten, J.; Troy, J.; Jiang, P.; Trachtman, M.; Bock, C. W. An ab initio molecular orbital study of the Grignard reagents CH3MgCl and [CH3MgCl]2: the Schlenk equilibrium. Struct. Chem. 1994, 5, 99– 108,  DOI: 10.1007/BF02265351
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      An ab initio molecular orbital study of the Grignard reagents CH3MgCl and [CH3MgCl]2: The Schlenk equilibrium
      Axten, Jeffrey; Troy, Jennifer; Jiang, Peter; Trachtman, Mendel; Bock, Charles W.
      Structural Chemistry (1994), 5 (2), 99-108CODEN: STCHES; ISSN:1040-0400.
      Ab initio MO calcns. are used to study the modified Schlenk equil.: 2RMgCl .dblharw. MgR2 + MgCl2 .dblharw. Mg(Cl2)MgR2 with R = H and CH3. In the absence of any solvents, calcns. indicate that the formation of the various possible bridged dimers (RMgCl)2 is substantially exothermic. However, using di-Me ether as a model solvent, we show that the formation of the dimer (Me2O)(CH3)Mg(μ-Cl2)Mg(CH3)(OMe2) is exothermic only when entropic effects are included.
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      Ehlers, A. W.; van Klink, G. P. M.; van Eis, M. J.; Bickelhaupt, F.; Nederkoorn, P. H. J.; Lammertsma, K. Density-Functional study of (solvated) Grignard complexes. J. Mol. Model. 2000, 6, 186– 194,  DOI: 10.1007/s0089400060186
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      Density-functional study of (solvated) Grignard complexes
      Ehlers, Andreas W.; Van Klink, Gerard P. M.; Van Eis, Maurice J.; Bickelhaupt, Friedrich; Nederkoorn, Paul H. J.; Lammertsma, Koop
      Journal of Molecular Modeling (2000), 6 (2), 186-194CODEN: JMMOFK; ISSN:0948-5023. (Springer-Verlag)
      D. functional calcns. have been used to study the solvent effect of di-Et ether on the Schlenk equil. and the aggregation of Grignard reagents RMgX with R = Me, Et, Ph. Solvent stabilization of the Mg complexes of the first solvent is larger than that of the second one. The solvation energy decreases on going from the dihalides MgX2 to the monohalides RMgX to the diorgano compds. MgR2. The calcns. indicate that the energetic preference of the unsym. species reduces upon solvation. The strong tendency to dimerization of the un- and partly solvated compd. vanishes for the higher solvated cases.
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      Tammiku, J.; Burk, P.; Tuulmets, A. 1,10-phenanthroline and its complexes with magnesium compounds. Disproportionation equilibria. J. Phys. Chem. A 2001, 105, 8554– 8561,  DOI: 10.1021/jp011476n
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      1,10-Phenanthroline and Its Complexes with Magnesium Compounds. Disproportionation Equilibria
      Tammiku, Jaana; Burk, Peeter; Tuulmets, Ants
      Journal of Physical Chemistry A (2001), 105 (37), 8554-8561CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      The solvation, complexation, and disproportionation equil., which might be important during titrn. of a Grignard reagent RMgX with an alc. in the presence of 1,10-phenanthroline (phen), have been studied both in the gas phase and soln. using the d. functional theory (DFT) B3LYP/6-31+G* method. Solvation was modeled using the supermol. approach. NBO at. charge analyses were performed at the B3LYP/6-31G* level. The absorption spectra of the complexes were calcd. by the DFT TD/MPW1PW91/6-311+G** method. According to our calcns. the complexation of magnesium halide MgX2 with 1,10-phenanthroline is the reason for the disappearance of the red color of the complex RMgX(phen) near the titrn. end point.
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    27. 27
      Tammiku-Taul, J.; Burk, P.; Tuulmets, A. Theoretical study of magnesium compounds: The Schlenk equilibrium in the gas phase and in the presence of Et2O and THF molecules. J. Phys. Chem. A 2004, 108, 133– 139,  DOI: 10.1021/jp035653r
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      Theoretical Study of Magnesium Compounds: The Schlenk Equilibrium in the Gas Phase and in the Presence of Et2O and THF Molecules
      Tammiku-Taul, Jaana; Burk, Peeter; Tuulmets, Ants
      Journal of Physical Chemistry A (2004), 108 (1), 133-139CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      The Schlenk equil. involving RMgX, R2Mg, and MgX2 (R = Me, Et, Ph and X = Cl, Br) has been studied both in the gas phase and in Et2O and THF solns. by the d. functional theory (DFT) B3LYP/6-31+G* method. Solvation was modeled using the supermol. approach. The stabilization due to interaction with solvent mols. decreases in the order MgX2 > RMgX > R2Mg and among the groups (R and X) Ph > Me > Et and Cl > Br. Studied magnesium compds. are more strongly solvated by THF compared to Et2O. The magnesium halide is solvated with up to four solvent mols. in THF soln., assuming that trans-dihalotetrakis(tetrahydrofurano)magnesium(II) complex forms. The formation of cis-dihalotetrakis(tetrahydrofurano)magnesium(II) is energetically less favorable than the formation of corresponding disolvated complexes. The predominant species in the Schlenk equil. are RMgX in Et2O and R2Mg + MgX2 in THF, which is consistent with exptl. data.
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      Yamabe, S.; Yamazaki, S. In The Chemistry of Organomagnesium Compounds; Rappoport, Z., Marek, I., Eds.; Wiley-VCH: Weinheim, Germany, 2008; pp 369– 402.
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      Yamazaki, S.; Yamabe, S. A computational study on addition of grignard reagents to carbonyl compounds. J. Org. Chem. 2002, 67, 9346– 9353,  DOI: 10.1021/jo026017c
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      A Computational Study on Addition of Grignard Reagents to Carbonyl Compounds
      Yamazaki, Shoko; Yamabe, Shinichi
      Journal of Organic Chemistry (2002), 67 (26), 9346-9353CODEN: JOCEAH; ISSN:0022-3263. (American Chemical Society)
      The mechanism of stereoselective addn. of Grignard reagents to carbonyl compds. was studied using B3LYP d. functional theory calcns. The study of the reaction of methylmagnesium chloride and formaldehyde in di-Me ether revealed a new reaction path involving carbonyl compd. coordination to Mg atoms in a dimeric Grignard reagent. The structure of the transition state for the addn. step shows that an interaction between a vicinal-Mg bonding alkyl group and C:O causes the C-C bond formation. The simplified mechanism shown by this model is in accord with the aggregation nature of Grignard reagents and their high reactivities toward carbonyl compds. Concerted and four-centered formation of strong O-Mg and C-C bonds was suggested as a polar mechanism. When the alkyl group is bulky, C-C bond formation is blocked and the Mg-O bond formation takes precedence. A diradical is formed with the odd spins localized on the alkyl group and carbonyl moiety. Diradical formation and its recombination probably are a single electron transfer (SET) process. The criteria for the concerted polar and stepwise SET processes were discussed in terms of precursor geometries and relative energies.
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      Mori, T.; Kato, S. Grignard reagents in solution: Theoretical study of the equilibria and the reaction with a carbonyl compound in diethyl ether solvent. J. Phys. Chem. A 2009, 113, 6158– 6165,  DOI: 10.1021/jp9009788
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      Grignard Reagents in Solution: Theoretical Study of the Equilibria and the Reaction with a Carbonyl Compound in Diethyl Ether Solvent
      Mori, Toshifumi; Kato, Shigeki
      Journal of Physical Chemistry A (2009), 113 (21), 6158-6165CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      The equil. of Grignard reagents, CH3MgCl and CH3MgBr, in di-Et ether (Et2O) solvent as well as the reaction of the reagents with acetone are studied theor. To describe the equil. and reactions in Et2O solvent, the authors employ the ref. interaction site model SCF method with the second-order Moller-Plesset perturbation (RISM-MP2) free energy gradient method. Since the solvent mols. strongly coordinate to the Grignard reagents, the authors construct a cluster model by including several Et2O mols. into the quantum mech. region and embed it into the bulk solvent. Probably instead of the traditionally accepted cyclic dimer, the linear form of dimer is as stable as the monomer pair and participates in the equil. For the reaction with acetone, two important reaction paths (i.e., monomeric and linear dimeric paths) are studied. The barrier height for the monomeric path is much higher than that for the linear dimeric path, indicating that the reaction of the Grignard reagent with acetone proceeds through the linear dimeric reaction path. The change of solvation structure during the reaction is examd. From the calcd. free energy profiles, the entire reaction mechanisms of the Grignard reagents with aliph. ketones in Et2O solvent are discussed.
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      Peltzer, R. M.; Eisenstein, O.; Nova, A.; Cascella, M. How solvent dynamics controls the Schlenk equilibrium of Grignard reagents: A computational study of CH3MgCl in tetrahydrofuran. J. Phys. Chem. B 2017, 121, 4226– 4237,  DOI: 10.1021/acs.jpcb.7b02716
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      How Solvent Dynamics Controls the Schlenk Equilibrium of Grignard Reagents: A Computational Study of CH3MgCl in Tetrahydrofuran
      Peltzer, Raphael M.; Eisenstein, Odile; Nova, Ainara; Cascella, Michele
      Journal of Physical Chemistry B (2017), 121 (16), 4226-4237CODEN: JPCBFK; ISSN:1520-5207. (American Chemical Society)
      The Schlenk equil. is a complex reaction governing the presence of multiple chem. species in soln. of Grignard reagents. The full characterization at the mol. level of the transformation of CH3MgCl into MgCl2 and Mg(CH3)2 in THF by means of ab initio mol. dynamics simulations with enhanced-sampling metadynamics is presented. The reaction occurs via formation of dinuclear species bridged by chlorine atoms. At room temp., the different chem. species involved in the reaction accept multiple solvation structures, with two to four THF mols. that can coordinate the Mg atoms. The energy difference between all dinuclear solvated structures is lower than 5 kcal mol-1. The solvent is shown to be a direct key player driving the Schlenk mechanism. In particular, this study illustrates how the most stable sym. solvated dinuclear species, (THF)CH3Mg(μ-Cl)2MgCH3(THF) and (THF)CH3Mg(μ-Cl)(μ-CH3)MgCl(THF), need to evolve to less stable asym. solvated species, (THF)CH3Mg(μ-Cl)2MgCH3(THF)2 and (THF)CH3Mg(μ-Cl)(μ-CH3)MgCl(THF)2, in order to yield ligand exchange or product dissocn. In addn., the transferred ligands are always departing from an axial position of a pentacoordinated Mg atom. Thus, solvent dynamics is key to successive Mg-Cl and Mg-CH3 bond cleavages because bond breaking occurs at the most solvated Mg atom and the formation of bonds takes place at the least solvated one. The dynamics of the solvent also contributes to keep relatively flat the free energy profile of the Schlenk equil. These results shed light on one of the most used organometallic reagents whose structure in solvent remains exptl. unresolved. These results may also help to develop a more efficient catalyst for reactions involving these species.
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      Generalized gradient approximation made simple
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      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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      Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
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      We present a library of Gaussian basis sets that has been specifically optimized to perform accurate mol. calcns. based on d. functional theory. It targets a wide range of chem. environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition no. of the overlap matrix for a set of mols. with respect to the exponents and contraction coeffs. of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles mol. dynamics simulations and is well suited for linear scaling calcns.
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      Separable dual-space Gaussian pseudopotentials
      Goedecker, S.; Teter, M.; Hutter, J.
      Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
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      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
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      A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
      Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
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      Swope, W. C.; Andersen, H. C.; Berens, P. H.; Wilson, K. R. A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters. J. Chem. Phys. 1982, 76, 648,  DOI: 10.1063/1.442716
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      Journal of Chemical Physics (2007), 126 (1), 014101/1-014101/7CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The authors present a new mol. dynamics algorithm for sampling the canonical distribution. In this approach the velocities of all the particles are rescaled by a properly chosen random factor. The algorithm is formally justified and it is shown that, in spite of its stochastic nature, a quantity can still be defined that remains const. during the evolution. In numerical applications this quantity can be used to measure the accuracy of the sampling. The authors illustrate the properties of this new method on Lennard-Jones and TIP4P water models in the solid and liq. phases. Its performance is excellent and largely independent of the thermostat parameter also with regard to the dynamic properties.
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      Journal of Chemical Physics (1984), 81 (1), 511-19CODEN: JCPSA6; ISSN:0021-9606.
      Three recently proposed const. temp. mol. dynamics methods [N., (1984) (1); W. G. Hoover et al., (1982) (2); D. J. Evans and G. P. Morris, (1983) (2); and J. M. Haile and S. Gupta, 1983) (3)] are examd. anal. via calcg. the equil. distribution functions and comparing them with that of the canonical ensemble. Except for effects due to momentum and angular momentum conservation, method (1) yields the rigorous canonical distribution in both momentum and coordinate space. Method (2) can be made rigorous in coordinate space, and can be derived from method (1) by imposing a specific constraint. Method (3) is not rigorous and gives a deviation of order N-1/2 from the canonical distribution (N the no. of particles). The results for the const. temp.-const. pressure ensemble are similar to the canonical ensemble case.
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      Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nosé—Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 1992, 97, 2635– 2643,  DOI: 10.1063/1.463940
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      Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14, 33– 38,  DOI: 10.1016/0263-7855(96)00018-5
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      Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
      VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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      Carter, E. A.; Ciccotti, G.; Heynes, J. T.; Kapral, R. Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 1989, 156, 472– 477,  DOI: 10.1016/S0009-2614(89)87314-2
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      Carter, E. A.; Ciccotti, Giovanni; Hynes, James T.; Kapral, Raymond
      Chemical Physics Letters (1989), 156 (5), 472-7CODEN: CHPLBC; ISSN:0009-2614.
      A computationally efficient mol. dynamics method for estg. the rates of rare events that occur by activated processes is described. The system is constrained at "bottleneck" regions on a general many-body reaction coordinate in order to generate a biased configurational distribution. Suitable reweighting of this biased distribution, along with correct momentum distribution sampling, provides a new ensemble, the constrained-reaction-coordinate-dynamics ensemble, with which to study rare events of this type. Applications to chem. reaction rates are made.
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      Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J. Phys. Chem. B 2009, 113, 6378– 6396,  DOI: 10.1021/jp810292n
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      Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions
      Marenich, Aleksandr V.; Cramer, Christopher J.; Truhlar, Donald G.
      Journal of Physical Chemistry B (2009), 113 (18), 6378-6396CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We present a new continuum solvation model based on the quantum mech. charge d. of a solute mol. interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "d." to denote that the full solute electron d. is used without defining partial at. charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielec. medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liq. medium for which a few key descriptors are known (in particular, dielec. const., refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the soln. of the nonhomogeneous Poisson equation for electrostatics in terms of the integral-equation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calcn. are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersion-solvent-structure term and is the contribution arising from short-range interactions between the solute and solvent mols. in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality consts. called at. surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aq. ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and DMSO, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaq. org. solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 org. solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic at. Coulomb radii and at. surface tension coeffs.) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calcns. in which the solute is represented by its electron d. in real space. This includes, for example, the conductor-like screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on av. for ions with either Gaussian03 or GAMESS.
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      Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215– 241,  DOI: 10.1007/s00214-007-0310-x
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      The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals
      Zhao, Yan; Truhlar, Donald G.
      Theoretical Chemistry Accounts (2008), 120 (1-3), 215-241CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)
      We present two new hybrid meta exchange-correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amt. of nonlocal exchange (2X), and it is parametrized only for nonmetals. The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree-Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree-Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochem., four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for mol. excitation energies. We also illustrate the performance of these 17 methods for three databases contg. 40 bond lengths and for databases contg. 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochem., kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chem. and for noncovalent interactions.
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    47. 47
      Ditchfield, R.; Hehre, W. J.; Pople, J. A. Self-consistent molecular-orbital methods. IX. An extended Gaussian-type basis for molecular-orbital studies of organic molecules. J. Chem. Phys. 1971, 54, 724– 728,  DOI: 10.1063/1.1674902
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      47
      Self-consistent molecular-orbital methods. IX. Extended Gaussian-type basis for molecular-orbital studies of organic molecules
      Ditchfield, R.; Hehre, Warren J.; Pople, John A.
      Journal of Chemical Physics (1971), 54 (2), 724-8CODEN: JCPSA6; ISSN:0021-9606.
      An extended basis set of at. functions expressed as fixed linear combinations of Gaussian functions is presented for H and the first-row atoms C to F. In this set. described as 4-31 G, each inner shell is represented by a single basis function taken as a sum of 4 Gaussians, and each valence orbital is split into inner and outer parts described by 3 and 1 Gaussian function, resp. The expansion coeffs. and Gaussian exponents are detd. by minimizing the total calcd. energy of the at. ground state. This basis set is then used in single-determinant MO studies of a group of small polyat. mols. Optimization of valence-shell scaling factors shows that considerable rescaling of at. functions occurs in mols., the largest effects being obsd. for H and C. However, the range of optimum scale factors for each atom is small enough to allow the selection of a std. mol. set. The use of this std. basis gives theoretical equil. geometries in reasonable agreement with expt.
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    48. 48
      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. Gaussian 09, revision B.01; Gaussian, Inc.: Wallingford, CT, 2016.
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      Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. A fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 1969, 157, 479– 483,  DOI: 10.1016/S0009-2614(89)87395-6
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      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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    51. 51
      CFOUR, a quantum-chemical program package written by Stanton, J. F.; Gauss, J.; Cheng, L.; Harding, M. E.; Matthews, D. A.; Szalay, P. G. with contributions from Auer, A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J.; Christiansen, O.; Engel, F.; Faber, R.; Heckert, M.; Heun, O.; Hilgenberg, M.; Huber, C.; Jagau, T.-C.; Jonsson, D.; Jusélius, J.; Kirsch, T.; Klein, K.; Lauderdale, W. J.; Lipparini, F.; Metzroth, T.; Mück, L.A.; O’Neill, D. P.; Price, D. R.; Prochnow, E.; Puzzarini, C.; Ruud, K.; Schiffmann, F.; Schwalbach, W.; Simmons, C.; Stopkowicz, S.; Tajti, A.; Vázquez, J.; Wang, F.; Watts, J. D. and the integral packages MOLECULE (Almlöf, J.; Taylor, P. R.), PROPS (Taylor, P. R.), ABACUS (Helgaker, T.; Jensen, H. J. Aa.; Jørgensen, P.; Olsen, J.), and ECP routines by Mitin, A. V. and van Wüllen, C.; website: http://www.cfour.de.
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      Buergi, H. B.; Dunitz, J. D.; Shefter, E. Geometrical reaction coordinates. II. Nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1973, 95, 5065– 5067,  DOI: 10.1021/ja00796a058
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      Buergi, H. B.; Lehn, J. M.; Wipff, G. Ab initio study of nucleophilic addition to a carbonyl group. J. Am. Chem. Soc. 1974, 96, 1956– 1957,  DOI: 10.1021/ja00813a062
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      Ab initio study of nucleophilic addition to a carbonyl group
      Buergi, H. B.; Lehn, J. M.; Wipff, G.
      Journal of the American Chemical Society (1974), 96 (6), 1956-7CODEN: JACSAT; ISSN:0002-7863.
      Ab initio SCF-LCGO (linear combination of Gaussian orbitals)-MO computations were performed on the reaction of hydride ion with HCHO, considered as model for nucleophilic addns. to the carbonyl group. Geometrical changes and electronic rearrangements were obtained as a function of the reaction coordinate. Orientational constraints in the course of the reaction bear relation to orbital steering, togetherness, and proximity effects considered in the literature. The calcd. geometrical changes correlate with the changes obsd. in crystal structures for the approach of an amino site toward a carbonyl group. A computation of the NH3-HCHO system at one fixed sepn. was also performed for comparison purposes.
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    54. 54
      Walker, F. W.; Ashby, E. C. Composition of Grignard compounds. VI. Nature of association in tetrahydrofuran and diethyl ether solutions. J. Am. Chem. Soc. 1969, 91, 3845– 3850,  DOI: 10.1021/ja01042a027
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      Composition of Grignard compounds. VI. Nature of association in tetrahydrofuran and diethyl ether solutions
      Walker, Frank W.; Ashby, E. C.
      Journal of the American Chemical Society (1969), 91 (14), 3845-50CODEN: JACSAT; ISSN:0002-7863.
      Ebullioscopic data are presented for tetrahydrofuran (I) and Et2O solns. of several Grignard and related Mg compounds over a wide concn. range. Anal. of the data is accomplished by observing the change in assocn. with concn. and by consideration of the constancy of the equil. consts. calcd. for several possible descriptions of the assocd. system. The expected nonideality of the solns. studied was considered in the interpretation of the data. While all the compds. studied were monomeric in I, the alkyl- and arylmagnesium bromides and iodides were monomeric in Et2O only at low concn. (<0.1 m), exhibiting in general an increase in assocn. with concn. These compds. are assocd. in a polymeric fashion. In contrast, the alkylmagnesium chlorides assoc. in Et2O to form stable dimers with the assocn. insensitive to concn. changes. Comparison of the data for Mg halides and dialkylmagnesium compds. in Et2O indicates that, except for the Me compd., assocn. is considerably stronger for the Mg halides than for the dialkylmagnesium compds. Thus, except for methylmagnesium halides, Grignard compds. assoc. with bridging mainly through the halogen atom. The methylmagnesium halides are exceptional since Me bridging is strong enough in Et2O to permit assocn. by bridging through either the Me group or the halogen atom. Although the steric and electronic nature of the alkyl group has some effect on the assocn. of Grignard compds., the effect is generally small compared to to the effect of halogen or solvent.
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    55. 55
      Holm, T. Thermochemical bond dissociation energies of carbon-magnesium bonds. J. Chem. Soc., Perkin Trans. 2 1981, 2, 464– 467,  DOI: 10.1039/P29810000464
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    56. 56
      We consider here thermodynamically equilibrated solutions of the Grignard reagent. In fact, the formation of the Grignard reagent may occur via a radical mechanism; see, for instance, the recent study:Henriques, A. M.; Barbosa, A. G. H. Chemical bonding and the equilibrium composition of Grignard reagents in ethereal solution. J. Phys. Chem. A 2011, 115, 12259– 12270,  DOI: 10.1021/jp202762p
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      56
      Chemical bonding and the equilibrium composition of Grignard reagents in ethereal solutions
      Henriques, Andre M.; Barbosa, Andre G. H.
      Journal of Physical Chemistry A (2011), 115 (44), 12259-12270CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      A thorough anal. of the electronic structure and thermodn. aspects of Grignard reagents and its assocd. equil. compn. in ethereal solns. is performed. Considering methylmagnesium halides contg. fluorine, chlorine, and bromine, we studied the neutral, charged, and radical species assocd. with their chem. equil. in soln. The ethereal solvents considered, THF and di-Et ether, were modeled using the polarizable continuum model (PCM) and also by explicit coordination to the Mg atoms in a cluster. The chem. bonding of the species that constitute the Grignard reagent is analyzed in detail with generalized valence bond (GVB) wave functions. Equil. consts. were calcd. with the DFT/M06 functional and GVB wave functions, yielding similar results. According to our calcns. and existing kinetic and electrochem. evidence, the species R·, R-, ·MgX, and RMgX2- must be present in low concn. in the equil. We conclude that depending on the halogen, a different route must be followed to produce the relevant equil. species in each case. Chloride and bromide must preferably follow a "radical-based" pathway, and fluoride must follow a "carbanionic-based" pathway. These different mechanisms are contrasted against the available exptl. results and are proven to be consistent with the existing thermodn. data on the Grignard reagent equil.
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    57. 57
      Ziegler, D. S.; Wei, B.; Knochel, P. Improving the halogen–magnesium exchange by using new turbo-Grignard reagents. Chem. - Eur. J. 2019, 25, 2695– 2703,  DOI: 10.1002/chem.201803904
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      57
      Improving the Halogen-Magnesium Exchange by using New Turbo-Grignard Reagents
      Ziegler, Dorothee S.; Wei, Baosheng; Knochel, Paul
      Chemistry - A European Journal (2019), 25 (11), 2695-2703CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review. This Minireview describes the scope of the halogen-magnesium exchange. It shows that the use of the turbo-Grignard reagent (iPrMgCl·LiCl) greatly enhances the rate of the Br- and I-Mg exchange. Furthermore, this magnesium reagent allows the performance of a fast sulfoxide-magnesium exchange. Also, the use of s-BuMgOR·LiOR (R=2-ethylhexyl) enables a Br-Mg exchange in toluene leading to various Grignard reagents in toluene. Addnl., the new exchange reagent s-Bu2Mg·2LiOR (R = 2-ethylhexyl) further increases the rate of the halogen-magnesium exchange allowing one to perform a chlorine-magnesium exchange for arom. chlorides bearing an ortho-methoxy substituent in toluene.
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    58. 58
      Harutyunyan, S. R.; Lopez, F.; Browne, W. R.; Correa, A.; Pena, D.; Badorrey, R.; Meetsma, A.; Minaard, A. J.; Feringa, B. L. On the mechanism of the copper-catalyzed enantioselective 1,4-addition of Grignard reagents to α, β-unsaturated carbonyl compounds. J. Am. Chem. Soc. 2006, 128, 9103– 9118,  DOI: 10.1021/ja0585634
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      58
      On the Mechanism of the Copper-Catalyzed Enantioselective 1,4-Addition of Grignard Reagents to α,β-Unsaturated Carbonyl Compounds
      Harutyunyan, Syuzanna R.; Lopez, Fernando; Browne, Wesley R.; Correa, Arkaitz; Pena, Diego; Badorrey, Ramon; Meetsma, Auke; Minnaard, Adriaan J.; Feringa, Ben L.
      Journal of the American Chemical Society (2006), 128 (28), 9103-9118CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The mechanism of the enantioselective 1,4-addn. of Grignard reagents to α,β-unsatd. carbonyl compds. promoted by copper complexes of chiral ferrocenyl diphosphines is explored through kinetic, spectroscopic, and electrochem. anal. On the basis of these studies, a structure of the active catalyst is proposed. The roles of the solvent, copper halide, and the Grignard reagent have been examd. Kinetic studies support a reductive elimination as the rate-limiting step in which the chiral catalyst, the substrate, and the Grignard reagent are involved. The thermodn. activation parameters were detd. from the temp. dependence of the reaction rate. The putative active species and the catalytic cycle of the reaction are discussed.
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    59. 59
      Lopez, F.; Minaard, A. J.; Feringa, B. L. Catalytic enantioselective conjugate addition with Grignard reagents. Acc. Chem. Res. 2007, 40, 179– 188,  DOI: 10.1021/ar0501976
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      Catalytic enantioselective conjugate addition with Grignard reagents
      Lopez, Fernando; Minnaard, Adriaan J.; Feringa, Ben L.
      Accounts of Chemical Research (2007), 40 (3), 179-188CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
      A review on recent advances in Cu-catalyzed asym. conjugate addn. of Grignard reagents, asym. SN2' substitution reactions of allylic bromides with Grignard reagents, and application to synthesis of natural products.
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    60. 60
      Seitz, T. A.; Seitz, J. A. A general two-metal-ion mechanism for catalytic RNA. Proc. Natl. Acad. Sci. U. S. A. 1993, 90, 6498– 6502,  DOI: 10.1073/pnas.90.14.6498
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      De Vivo, M.; Dal Peraro, M.; Klein, M. L. Phosphodiester cleavage in ribonuclease H occurs via an associative two-metal-aided catalytic mechanism. J. Am. Chem. Soc. 2008, 130, 10955– 10962,  DOI: 10.1021/ja8005786
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      Phosphodiester Cleavage in Ribonuclease H Occurs via an Associative Two-Metal-Aided Catalytic Mechanism
      De Vivo, Marco; Dal Peraro, Matteo; Klein, Michael L.
      Journal of the American Chemical Society (2008), 130 (33), 10955-10962CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      RNase H belongs to the nucleotidyl-transferase (NT) superfamily and hydrolyzes the phosphodiester linkages that form the backbone of the RNA strand in RNA•DNA hybrids. This enzyme is implicated in replication initiation and DNA topol. restoration and represents a very promising target for anti-HIV drug design. Structural information has been provided by high-resoln. crystal structures of the complex RNase H/RNA•DNA from Bacillus halodurans (Bh), which reveals that two metal ions are required for formation of a catalytic active complex. Here, we use classical force field-based and quantum mechanics/mol. mechanics calcns. for modeling the nucleotidyl transfer reaction in RNase H, clarifying the role of the metal ions and the nature of the nucleophile (water vs. hydroxide ion). During the catalysis, the two metal ions act cooperatively, facilitating nucleophile formation and stabilizing both transition state and leaving group. Importantly, the two Mg2+ metals also support the formation of a meta-stable phosphorane intermediate along the reaction, which resembles the phosphorane intermediate structure obtained only in the debated β-phosphoglucomutase crystal (Lahiri, S. D.; et al. Science 2003, 299 (5615), 2067-2071). The nucleophile formation (i.e., water deprotonation) can be achieved in situ, after migration of one proton from the water to the scissile phosphate in the transition state. This proton transfer is actually mediated by solvation water mols. Due to the highly conserved nature of the enzymic bimetal motif, these results might also be relevant for structurally similar enzymes belonging to the NT superfamily.
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    62. 62
      Rosta, E.; Nowotny, M.; Yang, W.; Hummer, G. Catalytic mechanism of RNA backbone cleavage by ribonuclease H from quantum mechanics/molecular mechanics simulations. J. Am. Chem. Soc. 2011, 133, 8934– 8941,  DOI: 10.1021/ja200173a
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      Catalytic Mechanism of RNA Backbone Cleavage by Ribonuclease H from Quantum Mechanics/Molecular Mechanics Simulations
      Rosta, Edina; Nowotny, Marcin; Yang, Wei; Hummer, Gerhard
      Journal of the American Chemical Society (2011), 133 (23), 8934-8941CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      We use quantum mechanics/mol. mechanics simulations to study the cleavage of the RNA (RNA) backbone catalyzed by RNase H. This protein is a prototypical member of a large family of enzymes that use two-metal catalysis to process nucleic acids. By combining Hamiltonian replica exchange with a finite-temp. string method, we calc. the free energy surface underlying the RNA-cleavage reaction and characterize its mechanism. We find that the reaction proceeds in two steps. In a first step, catalyzed primarily by magnesium ion A and its ligands, a water mol. attacks the scissile phosphate. Consistent with thiol-substitution expts., a water proton is transferred to the downstream phosphate group. The transient phosphorane formed as a result of this nucleophilic attack decays by breaking the bond between the phosphate and the ribose oxygen. In the resulting intermediate, the dissocd. but unprotonated leaving group forms an alkoxide coordinated to magnesium ion B. In a second step, the reaction is completed by protonation of the leaving group, with a neutral Asp132 as a likely proton donor. The overall reaction barrier of ∼15 kcal mol-1, encountered in the first step, together with the cost of protonating Asp132, is consistent with the slow measured rate of ∼1-100/min. The two-step mechanism is also consistent with the bell-shaped pH dependence of the reaction rate. The nonmonotonic relative motion of the magnesium ions along the reaction pathway agrees with X-ray crystal structures. Proton-transfer reactions and changes in the metal ion coordination emerge as central factors in the RNA-cleavage reaction.
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    63. 63
      Casalino, L.; Palermo, G.; Rothlisberger, U.; Magistrato, A. Who activates the nucleophile in ribozyme catalysis? An answer from the splicing mechanism of group II introns. J. Am. Chem. Soc. 2016, 138, 10374– 10377,  DOI: 10.1021/jacs.6b01363
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      63
      Who Activates the Nucleophile in Ribozyme Catalysis? An Answer from the Splicing Mechanism of Group II Introns
      Casalino, Lorenzo; Palermo, Giulia; Rothlisberger, Ursula; Magistrato, Alessandra
      Journal of the American Chemical Society (2016), 138 (33), 10374-10377CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Group II introns are Mg2+-dependent ribozymes that are considered to be the evolutionary ancestors of the eukaryotic spliceosome, thus representing an ideal model system to understand the mechanism of conversion of premature mRNA (mRNA) into mature mRNA. Neither in splicing nor for self-cleaving ribozymes has the role of the two Mg2+ ions been established, and even the way the nucleophile is activated is still controversial. Here we employed hybrid quantum-classical QM(Car-Parrinello)/MM mol. dynamics simulations in combination with thermodn. integration to characterize the mol. mechanism of the first and rate-detg. step of the splicing process (i.e., the cleavage of the 5'-exon) catalyzed by group II intron ribozymes. Remarkably, our results show a new RNA-specific dissociative mechanism in which the bulk water accepts the nucleophile's proton during its attack on the scissile phosphate. The process occurs in a single step with no Mg2+ ion activating the nucleophile, at odds with nucleases enzymes. We suggest that the novel reaction path elucidated here might be an evolutionary ancestor of the more efficient two-metal-ion mechanism found in enzymes.
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    64. 64
      Genna, V.; Vidossich, P.; Ippoliti, E.; Carloni, P.; De Vivo, M. A self-activated mechanism for nucleic acid polymerization catalyzed by DNA/RNA polymerases. J. Am. Chem. Soc. 2016, 138, 14592– 14598,  DOI: 10.1021/jacs.6b05475
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      A Self-Activated Mechanism for Nucleic Acid Polymerization Catalyzed by DNA/RNA Polymerases
      Genna, Vito; Vidossich, Pietro; Ippoliti, Emiliano; Carloni, Paolo; Vivo, Marco De
      Journal of the American Chemical Society (2016), 138 (44), 14592-14598CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The enzymic polymn. of DNA and RNA is at the basis of genetic inheritance for all living organisms. It is catalyzed by the DNA/RNA polymerase (Pol) superfamily. Here, bioinformatics anal. revealed that the incoming nucleotide substrate always forms an H-bond between its 3'-OH and β-phosphate moieties upon formation of the Michaelis complex. This previously unrecognized H-bond implies a novel self-activated mechanism (SAM), which synergistically connects the in situ nucleophile formation with subsequent nucleotide addn. and, importantly, nucleic acid translocation. Thus, SAM allows an elegant and efficient closed-loop sequence of chem. and phys. steps for Pol catalysis. This is markedly different from previous mechanistic hypotheses. This proposed mechanism was corroborated via ab initio QM/MM simulations on a specific Pol, human DNA polymerase-η, an enzyme involved in repairing damaged DNA. The structural conservation of DNA and RNA Pols supports the possible extension of SAM to Pol enzymes from the 3 domains of life.
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    65. 65
      Genna, V.; Donati, E.; De Vivo, M. The catalytic mechanism of DNA and RNA polymerases. ACS Catal. 2018, 8, 11103– 11118,  DOI: 10.1021/acscatal.8b03363
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      The Catalytic Mechanism of DNA and RNA Polymerases
      Genna, Vito; Donati, Elisa; De Vivo, Marco
      ACS Catalysis (2018), 8 (12), 11103-11118CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)
      A review. DNA and RNA polymerases (Pols) catalyze nucleic acid biosynthesis in all domains of life, with implications for human diseases and health. Pols carry out nucleic acid extension through the addn. of one incoming nucleotide trisphosphate at the 3'-OH terminus of the growing primer strand, at every catalytic cycle. Thus, Pol catalysis involves chem. reactions for nucleophile 3'-OH deprotonation and nucleotide addn., as well as major protein conformational motions and structural rearrangements for nucleotide selection, binding, and nucleic acid translocation to complete the overall catalytic cycle. In this respect, quantum and mol. mechanics simulations, integrated with exptl. data, have advanced our mechanistic understanding of how Pols operate at the at. level. This Perspective outlines how modern mol. simulations can further deepen our understanding of Pol catalytic reactions and fidelity, which may help in devising strategies for designing drugs and artificial Pols for biotechnol. and clin. purposes.
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    • Reference coupled-cluster calculations and benchmark BDE calculations, and structures of Mg(CH3)2, Mg(CH3)2(CH3CHO), and CH3Mg(OCH(CH3)2) in THF (PDF)


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