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ArticleMarch 30, 2017

How Solvent Dynamics Controls the Schlenk Equilibrium of Grignard Reagents: A Computational Study of CH₃MgCl in Tetrahydrofuran
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The Journal of Physical Chemistry B

Cite this: J. Phys. Chem. B 2017, 121, 16, 4226–4237

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https://doi.org/10.1021/acs.jpcb.7b02716

Published March 30, 2017

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Abstract

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The Schlenk equilibrium is a complex reaction governing the presence of multiple chemical species in solution of Grignard reagents. The full characterization at the molecular level of the transformation of CH₃MgCl into MgCl₂ and Mg(CH₃)₂ in tetrahydrofuran (THF) by means of ab initio molecular dynamics simulations with enhanced-sampling metadynamics is presented. The reaction occurs via formation of dinuclear species bridged by chlorine atoms. At room temperature, the different chemical species involved in the reaction accept multiple solvation structures, with two to four THF molecules 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 symmetrically solvated dinuclear species, (THF)CH₃Mg(μ-Cl)₂MgCH₃(THF) and (THF)CH₃Mg(μ-Cl)(μ-CH₃)MgCl(THF), need to evolve to less stable asymmetrically 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 dissociation. In addition, 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 equilibrium. These results shed light on one of the most used organometallic reagents whose structure in solvent remains experimentally unresolved. These results may also help to develop a more efficient catalyst for reactions involving these species.

Subjects

Introduction

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In 1900, the presentation by Victor Grignard of a new compound, completely soluble in ether and formed upon reaction of magnesium with alkyl halides, (1) paved the way to establish one of the most widely used organometallic reagents in organic synthesis, worth the Noble prize in 1912. (2) The so-called Grignard reagent, with nominal formula RMgX, is used in nucleophilic addition or substitution reactions, taking advantage of the enriched electron density in the R group coordinated to the Mg atom.

Initial limitations to the direct use of this reagent were found due to its relatively modest tolerance to different functional groups compared to that of corresponding boron and zinc metals. However, the use of Ni catalysts in coupling reactions using the Grignard reagent, independently developed by Corriu and Massé and Kumada and Tamao, increased the relevance of this reagent. (3, 4) Nowadays, interest in the functionalization of phenol-based derivatives involving earth-abundant metal catalysts and the development of efficient synthetic protocols allowing work at very mild conditions and with large functional tolerance make organomagnesium reagents very attractive. (5-12)

Despite the use of Grignard reagents in organic synthesis, their molecular structure in solution has remained elusive so far, even if considerable research effort has been spent on this topic. In an illuminating essay, Seyferth described the difficulties in characterizing the structures of Grignard reagents, which can be affected by both the solvent, and the halide and organic groups bonded to Mg. (13) Solid-state structures determined by X-ray diffraction studies revealed a diversity of coordination modes for Mg, and of nuclearity for the molecular system. Tetrahedral coordination is commonly observed in crystals structures obtained from ether solutions as EtMgBr(OEt₂)₂, (14) where two molecules of solvent are bound to Mg. Instead, both trigonal-bipyramidal and square-pyramidal structures were found for CH₃MgBrTHF₃ when working in tetrahydrofuran (THF) solvent. (15) X-ray data of aggregates of two EtMg₂Cl₃ moieties showed a greater than four coordination for the Mg centers. (16, 17) Due to lattice packing restrictions, the structures of Grignard reagents observed in the crystalline solid state may not be necessarily representative of the stable species present in solution. Investigations using molecular weight, (18) calorimetric measurements, (19) and NMR and IR spectroscopy (20) support in fact the existence of structures other than those detected by X-ray crystallography.

Determination of the structures of Grignard reagents in solution is particularly complex because of the presence of multiple chemical species at thermodynamic equilibrium. This complication has been evident since 1929, when Schlenk father and son (21) proposed that redistribution of ligands yielding MgR₂ and MgX₂ from RMgX could take place (original Schlenk equilibrium in Scheme 1). At present, it is commonly recognized that the halide groups in RMgX and MgX₂ tend to form bridges between magnesium atoms to yield dimers and oligomeric structures, which are in equilibrium with monomeric species (generalized Schlenk equilibrium in Scheme 1). This causes association between the various moieties, eventually favoring ligand exchange. The degree of association among the Mg centers is dependent on the solvent, as shown by Ashby and Walker, who found a degree of association of around ∼1 in THF and between 1 and 4, depending on the nature of R and X, in diethyl ether. (22) Further studies suggested that some complex equilibrium between RMgCl(THF)_n, MgR₂(μ-Cl)₂Mg(THF)_5/4 and RMg₂(μ-Cl)₃(THF)₅ better describes the traditional Schlenk equilibrium. (23, 24)

Given the complexity of the problem, computational modeling offers an excellent tool to determine in detail the chemical nature of the species involved in the Schlenk equilibrium. In the past, examination of the Cambridge Crystallographic Database and density functional theory (DFT) (25-27) calculations for isolated molecules led to establishing the overwhelming prevalence of structures with two over three bridging ligands and a preference for halide over alkyl ligands in that position. Moreover, they observed that the maximum stabilizing effect of the coordinating solvent is obtained for dimeric moieties. (28) Including the solvent as a continuum model in a systematic way and combining generalized valence bond, second-order Møller–Plesset perturbation theory (MP2), and DFT calculations indicated that radical and charged species may be present at equilibrium, although in small concentrations. (29) Explicit solvent was limited to the first coordination sphere of the Mg atom, and in many cases, the total number of ligands at Mg including the solvent was fixed to four. However, both crystallographic (30-32) and computational studies (33) showed that Mg could expand its coordination sphere over more than four ligands, up to hexacoordination. This limitation is probably even more inappropriate when trying to understand the dynamic processes involved in the Schlenk equilibrium (Scheme 1).

In consideration of the longstanding and recently renewed importance of Grignard in organic synthesis, (34-36) it is important to reach a better understanding of its structure and dynamic behavior in solvent. In this respect, dynamic modeling approaches may constitute the optimal choice for an accurate description of the Grignard reagent. In the past decades, ab initio molecular dynamics simulations (AIMD) have been shown to be especially appropriate to study processes in the liquid phase. (37, 38) For example, this technique was used to study structural properties of various metal ions in solution, including Na, (39) Mg, (40, 41) or Co and Ag. (42) In addition, AIMD with enhanced sampling methods were effectively used to provide an accurate description of solvent effects in various organic (43, 44) and organometallic reactions. (45, 46) Larger metallo-organic systems have also been been treated by coupling AIMD to molecular mechanics schemes. (47) This approach was used to describe, for example, electronic solute–solvent coupling in photoexcitation dynamics of ruthenium metallo-organic compounds, (48) the reaction mechanisms of hydrolysis in zinc β-lactamases, (49, 50) the redox properties of copper in azurin, (51) the functional role of Mg²⁺ ions in ribonuclease H, (52) and the design of organoruthenium anticancer complexes. (53)

In this work, this methodology was used to investigate the equilibria that take place when CH₃MgCl, a model of the Grignard reagent, is dissolved in THF. Our study was also complemented by DFT static calculations on selected structures identified as minima by ab initio molecular dynamics. The data presented in this work show that multiple structures with different solvation patterns are in equilibrium and evidence how the dynamic exchange of solvent molecules in the Mg coordination sphere is key to evolution from the reactant to product in the Schlenk equilibrium.

Computational Methods

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System Setup

The Schlenk equilibrium was investigated through a set of simulations describing monomeric reactants, monomeric products, and different intermediate dimeric states.

Monomeric Species

We built three different systems, each containing 1 molecule of either CH₃MgCl, MgCl₂, or Mg(CH₃)₂ surrounded by 25 molecules of THF in a periodic box of dimensions 15.0 × 15.0 × 15.0 Å³. The initial coordinates of THF were obtained from a previous 20 ps long equilibration run in a similar box containing the pure solvent. The number of solvent molecules was set to be consistent with the experimental density of THF at room temperature. (54) All systems were first relaxed for 15 ps in the microcanonical ensemble at energies matching an average temperature of 300 K. Relaxation at the target temperature was performed using a canonical sampling/velocity rescaling (CSVR) thermostat with a time constant of 10 fs until the temperature of the system oscillated around the target value. Production runs were simulated in the NVT ensemble at 300 K. The Nosé–Hoover chain thermostat with a chain length of 3 and time constant of 1 ps was used for data production. (55-57)

Dimeric Species

The (MgCH₃Cl)₂ species were simulated in an orthorhombic periodic box of dimensions 25.2 × 15.0 × 15.0 Å³, containing 42 THF molecules (Figure 1). A larger box of dimensions 25.2 × 20.0 × 20.0 Å³ with 74 THF molecules was also simulated to verify that there is no significant bias due to finite-size effects (see the Supporting Information). The systems were thermalized following the same protocol as that described for the monomers.

Figure 1. Simulation box used in this study. The atoms of the Grignard reagent are represented by spheres and the THF solvent molecules by sticks in licorice and red. Hydrogen atoms of THF are not shown for clarity.

Ab Initio Molecular Dynamics Simulations

The electronic problem was solved by DFT (25, 26) using the Perdew–Burke–Ernzerhof approximation to the exchange–correlation functional. (58) Kohn–Sham orbitals were expanded over mixed Gaussian and plane-wave basis functions. (59) The DZVP basis set for first and second row elements and Mg and a molecularly optimized basis set for the chlorine atoms were employed. (60) The auxiliary plane-wave basis set was expanded to a 200 Ry cutoff. The core electrons were integrated using pseudopotentials of Goedecker–Teter–Hutter type. (61) Dispersion forces were accounted for using the D3 Grimme approximation. (62) AIMD simulations were run over the Born–Oppenheimer surface, with a time step of 0.25 fs, optimizing the energy gradient to a threshold of 10^–5 au.

Free-Energy Calculations

Exploration of the conformational and reactive landscape and determination of the corresponding free-energy surface (FES) were performed by coupling AIMD to metadynamics simulations. (37, 63) Solvation of different chemical species observed during the AIMD runs, as well as the transmetalation reaction, was investigated by independent metadynamics runs. All collective variables (CVs) employed in this study were defined as the coordination number of specific ligand species to individual Mg atoms. The coordination number of a species X around Mg at a given time t (CN[X](t)) was evaluated according to the formula shown in eq 1, as defined in previous works (38)

(1)where N_X is the number of species X present in the system, d_i is the distance of the i^th atom X from Mg, and d₀, p, and q are free parameters (see the Supporting Information).

The time-dependent bias potential was formed by sets of Gaussians of 0.25 kcal mol^–1 height and 0.04 width for coordination variables and added every 50 steps of AIMD for the dichloride bridged system. Additional details of the metadynamics parameters used as well as the associated errors are given in Table S1 of the Supporting Information.

The metadynamics simulations convergence was confirmed by checking that the calculations reached the diffusion limit within their wall constraints; statistical errors, computed according to refs 64 and 65, are within 1–3kT (see the Supporting Information).

AIMD runs were computed using the QUICKSTEP (66, 67) module of the CP2K 2.5.1 package. Trajectory analysis was performed using the tools available in the VMD 1.9.2 package. (68)

Static Calculations and Electronic Structure Analysis

Chemically relevant geometries sampled by AIMD were fully optimized at the DFT(PBE+GD3) level by using the Gaussian09 software package. (69) Mg, C, H, and O were described with the all-electron double-ζ 6-31+G** basis set. (70-72) Vibrational frequencies were computed analytically to verify that the stationary points found were energy minima. In addition to the solvent molecules bound to Mg, implicit solvation was modeled by using the SMD solvation model. (73) In selected cases, Gibbs energies were obtained for T = 298.15 K and p = 1 atm. In the bimolecular steps, these energies were corrected for the 1 M standard state (T = 298.15 K and p = 24.465 atm). Donor–acceptor interactions were explored by means of natural bond orbital (NBO) calculations (NBO6 version). (74) The nature of these interactions was determined by computing the associated natural localized molecular orbitals (NLMOs). (75)

Results

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We restricted our investigation to monomers and dinuclear species, excluding higher aggregation states, because experimental studies showed that in THF the aggregation is very low, mainly consisting of monomeric species. (22)

Monomeric Structures

The solvation of CH₃MgCl, Mg(CH₃)₂, and MgCl₂ species was investigated over 40 ps of AIMD simulations at 300 K. CH₃MgCl and Mg(CH₃)₂ were found with only two THF molecules in the solvation sphere of Mg and tetrahedral coordination at this atom (Figure 2). On the contrary, both tetrameric and pentameric coordination were found for MgCl₂. The nature of the solvation of MgCl₂ was then further investigated by metadynamics simulations, using the coordination number of oxygen atoms of THF to Mg as the CV. These simulations showed that the most likely solvation state is MgCl₂(THF)₃ arranged in trigonal-bipyramidal coordination at Mg. MgCl₂(THF)₃ is ∼1.6 and ∼2.8 kcal mol^–1 more stable than the tetrahedral or octahedral complexes with two and four coordinating THF molecules, respectively. Thus, at room temperature, the different solvation states are in equilibrium in solution in a 0.07:1.0:0.01 ratio for the di-, tri-, and tetra-solvated complexes, yielding an average MgCl₂(THF)_x solvation with value x = 2.9.

Figure 2. Most likely solvation structures for MgCl₂ (left), Mg(CH₃)₂ (middle), and (CH₃)MgCl (right). The dotted black lines represent coordination of the ligands to the Mg center.

DFT optimization of the structures located as minima on the FES showed that they are also minima on the potential energy surface (PES) with similar structural features (these structures are shown in Figure 2). NBO analysis on these optimized structures showed higher electron donation of CH₃ to Mg compared to Cl. This is shown by the Mg contribution on the lone pairs’ NLMOs of CH₃ and Cl (χ^Mg), which are 10.2 and 5.3%, respectively, in CH₃MgCl (see Figure S1 and Table S1 for further details). This may explain the need for additional coordination of THF in MgCl₂ to improve the screening of the Mg charge.

Dinuclear Structures

The formation of dinuclear species was first studied by performing an AIMD simulation at 300 K starting from two molecules of CH₃MgCl placed with their respective Mg atoms at a distance of 9.5 Å. In order to accelerate the dimerization, a bias restraining potential to induce the approach of the two molecules was used (see the Computational Methods section). A dimeric structure with two bridging chlorides was formed as soon as the two Mg atoms were at a distance of 5.5 Å.

Cl/CH₃ Exchange Process

Chloride/methyl exchange between the two Mg centers was investigated combining AIMD and metadynamics simulations, using as CVs the THF solvation number on one arbitrary Mg atom (CV1) and the difference in methyl coordination between the two Mg atoms (CV2). The CVs where chosen to monitor the free energy change upon methyl transfer between the Mg atoms as a function of the local solvation of Mg.

The resulting FES (Figure 3) shows five separated wells (A, B, C, D, and E) that can be classified according to the nature of the Mg bridging groups. The most representative structures captured in each well are shown in Figure 3. Wells A and B correspond to dichloride bridged dinuclear species, C and D correspond to the mixed Me and Cl bridged species, and E encloses monochloride bridged structures of formula ClMg(μ-Cl)MgMe₂. While wells A and B represent the structures of the reactants, well E represents the preproduct state prior to final dissociation into MgCl₂ and Mg(CH₃)₂.

Figure 3. FES of the Schlenk equilibrium. The CVs for this representation are the difference in Mg–CH₃ coordination number between Mg² and Mg¹ (CV1) and the THF coordination number to Mg¹ (CV2). The chemical structures drawn in the figure depict the most representative species obtained for wells A–E.

We introduce a notation for describing the nature of the dimer D. The notation D_ij^XY stands for dimer (D) where i and j are the numbers of THF molecules on Mg¹ and Mg², respectively, and X and Y describe the nature of the bridging ligands. D^XY describes the entire family of X and Y bridging species regardless of the number of THF molecules on either Mg. The FES plot in Figure 3 shows that the ensemble of D^ClCl structures is more stable by ∼3.5 kcal mol^–1 than the one for D^ClMe. In addition, the FES shows a clear path connecting the A–E wells, thus giving information on the ligand exchange reaction. The transformation from wells A and B to D goes preferentially via well C, while exchange directly connecting B to D does not constitute a similarly viable path. The energy barriers for the A–C and C–D transition are ∼8 and ∼6 kcal mol^–1, respectively, while the free energy barrier between B and D is 13 kcal mol^–1 higher than that of well A. The preference for this path was analyzed by studying more closely the solvation structures of D^ClCl and D^ClMe.

Solvation of Dichloride Bridged Structures

The accessible solvation states of D^ClCl in the A and B wells (Figure 3) were investigated by metadynamics simulations using the coordination number of the oxygen atoms of THF to each of the Mg atoms as CVs. The simulations revealed the existence of three solvation states, corresponding to distinct free-energy minima reported in Figure 4a–c. The solvation state with the lowest free energy corresponds to a symmetric dimeric structure in which each Mg atom is solvated by a single THF (D₁₁^ClCl). The second most stable solvation state, only 1.3 kcal mol^–1 higher in energy, corresponds to another symmetric adduct with two THF molecules coordinating each Mg (D₂₂^ClCl). In the later, each Mg is five-coordinated. The interconversion between these two structures occurs through a metastable asymmetric solvation state D₁₂^ClCl with one THF solvent on one Mg and two on the other. This asymmetric solvation state D₁₂^ClCl, which is 2.7 kcal mol^–1 higher in energy than D₁₁^ClCl, is expected to be statistically present in 1% of room-temperature samples, also taking into account degenerate states. Higher solvation states with three THF molecules in the first solvation shell of a single Mg center are more than 5 kcal mol^–1 higher in energy than D₁₁^ClCl and therefore are expected to be present only in minor amounts in room-temperature samples. Both the relative stability and activation energies for the interchange between D₁₁^ClCl, D₁₂^ClCl, and D₂₂^ClCl are low (less than 5 kcal mol^–1), implying fast interconversion between the different structures at room temperature.

Figure 4. Solvated D^ClCl structures found by metadynamics simulations (left) and the corresponding FES (right). CV1 and CV2 are defined as the coordination numbers of THF at Mg¹ and Mg², respectively, following eq 1. The two minima b correspond to the chemically equivalent D₁₂^ClCl and D₂₁^ClCl structures. Only D₁₂^ClCl is shown for simplicity.

Analysis of the structural changes from D₁₁^ClCl to D₁₂^ClCl showed that the addition of THF to Mg² (Figure 4) occurs always anti to one of the chlorides, producing local trigonal-bipyramidal coordination with the bridging Cl’s in axial and equatorial positions. AIMD simulations indicated significant lengthening of the Mg–Cl_ax bond relative to the Mg–Cl_eq one. Reversible cleavage of the axial Cl–Mg bond and the consequential formation of transient single chloride bridged structures were observed during the analysis of AIMD trajectories. In order to analyze the influence of the solvent on Mg–Cl cleavage, the statistical distribution of the Mg–Cl bond lengths in D₁₁^ClCl, D₁₂^ClCl, and D₂₂^ClCl was computed (Figure 5). As expected, an increase in solvation is associated with statistical elongation of the Mg–Cl bonds.

Figure 5. (Top) Mg–Cl distance distributions in D^ClCl dimeric structures. (Bottom) Mg¹–Cl (blue) and Mg²–Cl (red) distance distributions in D₁₂^ClCl. Mg–Cl bond cleavage is observed when the Mg–Cl distance is larger than 3.7 Å.

Strikingly, Mg–Cl bond cleavage was observed only in the asymmetric D₁₂^ClCl structure with statistically significant probability of finding Mg–Cl distances with longer values than 3.7 Å, as shown in the inset of Figure 5 top. On the contrary, both the Mg–Cl bond length distributions of the least and the most solvated D₁₁^ClCl and D₂₂^ClCl species vanish above 3.7 Å, indicating statistical irrelevance of Mg–Cl bond-cleaved structures. Analysis of the AIMD trajectory evidenced that in all cases the cleavage of the Mg–Cl bond occurs between the pentacoordinated Mg² and the Cl_ax bridged atom in axial position in the trigonal bipypramid, as shown in Figure 5 bottom. The presence in thermal samples of the monochloride bridged, unsymmetrically solvated structures appears to be an essential ingredient in ligand exchange at each Mg.

Activation of the Mg–Cl bond in the axial position is also consistent with NBO analysis of D^ClCl, which shows that the pentacoordinated Mg atoms in both D₁₂^ClCl and D₂₂^ClCl receive the smallest electron donation from Cl (χ^Mg ≈ 6%). In particular, the bridging chloride, axially coordinated to Mg², Cl_ax, has the lowest contribution to this magnesium (χ^Mg ≈ 2%). Such a small donation implies an overpolarization of the Cl_ax–Mg² bond, which in turn facilitates opening of the dichloride bridged moiety of D₁₂^ClCl, as observed during AIMD. The asymmetry in the donation between the axial and the equatorial Cl explains also the selective opening of the ring at the Cl_ax–Mg² bond.

The trigonal-bipyramidal geometry on Mg² in D₁₂^ClCl was not found in D₂₂^ClCl. Instead, the coordination geometry of Mg atoms took a distorted square-pyramidal geometry, with an apical THF, and equatorial Cl atoms, a methyl group, and the remaining THF. In all D₁₁^ClCl, D₁₂^ClCl, and D₂₂^ClCl, the equilibrium values for the Cl–Mg–Cl bond angle are close to 90° (Table 1), even though the coordination geometries of the Mg atoms in the structures are different from each other. As an additional structural feature, it is observed that during AIMD simulations the four atoms of the Mg(μ-Cl)₂Mg moiety do not lie in the same plane. The average angles between the two MgCl₂ planes are reported in Table 1.

Table 1. Average Angles (α^dyn, β₁^dyn, and β₂^dyn, in degrees) with Associated Standard Deviation (in parentheses) Obtained from Cluster Analysis of the Metadynamics Trajectory and Angles from DFT Optimization with Implicit Solvent (α^st, β₁^st, and β₂^st, in degrees)

	α^dyn	α^st	β₁^dyn	β₁^st	β₂^dyn	β₂^st
D₁₁^ClCl	167(8)	169.7	89(5)	91.3	89(5)	91.6
D₁₂^ClCl	166(9)	165.4	91(7)	92.1	82(6)	83.9
D₂₂^ClCl	165(11)	160.6	94(6)	84.1	94(6)	84.2

DFT optimization of D₁₁^ClCl, D₁₂^ClCl, and D₂₂^ClCl confirmed that the minima on the FES correspond to minima on the PES. However, structural discrepancies are obtained for the species with the largest number of THF molecules in the coordination sphere of the Mg centers. Thus, the Mg centers in D₂₂^ClCl are trigonal-bipyramidal on the PES, while they are distorted square-pyramidal on the FES. This indicates that the solvent cage has an increasing influence on the structure and dynamics of the more flexible, solvated species. AIMD simulations also revealed the existence of interchange of THF molecules in the Mg solvation shell of D₂₂^ClCl taking place through an associative mechanism. In this case, a short-lived octahedral structure was formed. The statistical abundance of these structures is however marginal.

Solvation of Methyl Chloride Bridged Structures

The accessible solvation states of the D^ClMe species in C and D wells (Figure 3) were analyzed by metadynamics simulations using the coordination number of the oxygen atoms of THF to each of the Mg atoms as CVs (Figure 6). Three low-energy solvation structures were obtained. The lowest in energy, D₁₁^ClMe, has two tetrahedral-coordinated Mg centers bridged by a Cl atom and a methyl group (Figure 6a). This structure is favored over the other ones (Figure 6b–d) by about 3 kcal mol^–1. The two other major structures are dinuclear species with three coordinated solvent molecules, D₂₁^ClMe and D₁₁^ClMeTHF. In the former species, the additional THF is bound to the Mg–Cl moiety, while in the latter, THF bridges the two Mg centers (Figure 6). The free energies of triply bridged species D₁₁^ClMeTHF and the asymmetrically solvated D₂₁^ClMe differ by only 0.5 kcal mol^–1, separated by a barrier on the order of 2kT. A well corresponding to the asymmetric structure with two THF molecules coordinated to the Mg–CH₃ moiety (D₁₂^ClMe) was also obtained about 5 kcal mol^–1 above D_11.^ClMe Overall, fast interchange between D₂₁^ClMe, D₁₁^ClMeTHF, and D₁₂^ClMe is observed with low activation energy barriers of around 4 kcal mol^–1.

Figure 6. FES for the methyl bridged dimer D^ClMe equilibria using the THF coordination number to Mg¹ (CV1) and the THF coordination number to Mg² (CV2) as variables, together with the most representative species obtained for wells a–d.

All D^ClMe structures show tetrahedral and trigonal-bipyramidal geometries for the Mg centers solvated by one and two THF molecules, respectively. The bridging methyl (μ-CH₃) interacts differently with the two Mg atoms in the ClMg(μ-CH₃)(μ-Cl)MgCH₃ dimer. This is due to the asymmetric distribution of the ligands at the two Mg atoms because Mg¹ has a terminal chloride while Mg² has a terminal methyl group. Moreover, the two Mg atoms can have different solvation states at room temperature, as shown by the FES in Figure 6. In order to quantify the way the bridging CH₃ group interacts with the two Mg centers in the different structures, the direction of the bridging p_z orbital axis relative to the two C–Mg directions was monitored (Figure 7).

Figure 7. Orientation of the methyl group in D^ClMe as a function of the solvation state, represented by φ₁ and φ₂. A larger φ angle is indicative of a stronger Mg–CH₃ interaction.

In both D₁₁^ClMe and D₁₂^ClMe, the p_z orbital is oriented toward the Mg¹–Cl moiety, with average angles φ₁ of approximately 141 and 149°, respectively. In these two structures, φ₂ has average values of 127 and 128°, indicating a poorer interaction of the bridging methyl with the Mg² p_z orbital. In D₁₁^ClMeTHF, the μ-CH₃ bridging group is more equally shared between the two Mg centers, as indicated by the values of φ₁ and φ₂ that oscillate around 145 and 136°, respectively. A larger solvation for the Mg bound to the terminal Cl than the other Mg atom (D₂₁^ClMe) results in practically equal sharing of the bridging methyl between the two Mg centers. In this case, both angles φ₁ and φ₂ oscillate around an average value of ∼137°.

The orientation of the bridging methyl group is thus highly sensitive to the chemical groups and the solvation at each Mg center. For equal solvation, the methyl interacts more with the more electron deficient Mg¹ center, that is, the one with the terminal chloride. Increasing solvation of Mg¹ by either bridging or terminal THF results in an increased interaction of the bridging methyl group with Mg² bearing the terminal methyl group. In this way, the solvent helps the bridging methyl group weaken its interaction with Mg¹ and increase that to Mg², assisting the transformation of CH₃MgCl into MgCl₂ and Mg(CH₃)₂.

Geometry optimizations on the PES with DFT methods of the minima D₁₁^ClMe, D₁₂^ClMe, D₁₁^ClMeTHF, and D₂₁^ClMe on the FES gave minima with similar structures, as indicated in Table 2. In all cases, trigonal-bipyramid geometries were found on the pentacoordinated Mg atoms with the bridging CH₃ and a terminal THF in the axial positions. NBO analysis on the optimized structures showed slightly higher electron donation of the bridged CH₃ lone pair to the Mg of the Mg–Cl moiety (χ^Mg1 = 5.7, 5.2, and 4.6%) compared to that for the Mg–CH₃ moiety (χ^Mg2 = 3.7, 3.8, and 3.6%) for D₁₁^ClMe, D₁₂^ClMe, and D₁₁^ClMeTHF, respectively. With increasing solvation of Mg¹, as in D₂₁^ClMe, donation of the bridging methyl group to the two Mg centers becomes equivalent (χ^Mg1 = 4.3%; χ^Mg2 = 4.2%), consistent with the distribution of the φ₁ and φ₂ angles during AIMD simulations (Figure 8). Although small, the increased electron donation of the Me group to Mg², which already bears the other methyl group, is in agreement with D₂₁^ClMe being the most prone of the methyl chloride bridged dimers to yield the final products MgCl₂ and Mg(CH₃)₂.

Table 2. Average angles (α^dyn, β₁^dyn, and β₂^dyn, in degrees) with the Standard Deviations (in parentheses) Obtained from Cluster Analysis of the Metadynamics Trajectory and Optimized Angles from DFT Calculations with Implicit Solvent (α^st, β₁^st, and β₂^st, in degrees)

	α^dyn	α^st	β₁^dyn	β₁^st	β₂^dyn	β₂^st
D₁₁^ClMe	167(11)	175.6	101(10)	103.7	94(7)	100.0
D₁₂^ClMe	166(8)	179.4	102(7)	110.6	89(7)	93.2
D₁₁^ClMeTHF	165(6)	154.4	103(7)	102.0	96(7)	99.6
D₂₁^ClMe	161(7)	172.3	94(7)	100.4	101(7)	102.5

Figure 8. Intermediates involved in the Schlenk equilibrium according to dynamic simulations. Arrows indicate the chemical transformations along the main pathway leading from monomeric reactants to products (inside of solid squares). The most stable dichloride and methyl chloride bridged dinuclear species are inside of dashed squares.

Reaction Pathway of the Schlenk Equilibrium

The computational results presented above allow reconstruction of the full reaction pathway of the Schlenk equilibrium in a THF solution. Figure 8 presents the set of structures, localized as minima on the FES, that are involved in the transformation of the reactants CH₃MgCl(THF)₂ to the products Mg(CH₃)₂(THF)₂ and MgCl₂(THF)_n (n = 2–4). The scheme also highlights the key role played by the solvent in assisting the Cl/CH₃ ligand exchange.

The Schlenk equilibrium starts by dimerization of (CH₃)MgCl(THF)₂ via the two chlorides to form the dichloride bridged species D₂₂^ClCl. Static calculations show that this reaction is slightly endoergic by 4.9 kcal mol^–1, consistent with experimental results. (22, 76)

The coordination geometry of the pentacoordinated Mg atoms in D₂₂^ClCl was found to be distorted square-pyramidal when exploring the FES but trigonal-bipyramidal when performing ab initio geometry optimizations on the PES. Such discrepancy evidences a strong influence of the surrounding solvent molecules on the structural geometry of D₂₂^ClCl. THF exchange on the Mg atom may occur through addition of one THF to form an octahedral species. (77-79) These last transient structures are very short lived and thus have not been included in Figure 8.

Desolvation of D₂₂^ClCl by one THF molecule yields an asymmetrical dinuclear complex (D₁₂^ClCl) with tetrahedral and pyramidal-trigonal geometries for Mg¹ and Mg², respectively. This trisolvated species can lose one THF molecule to produce the disolvated (D₁₁^ClCl), which was found to be the most stable species in solution. Tetrahedral coordination of Mg is also the one preferred in the solid state, as shown by reported crystallographic structures of related Mg₂X₂R₂ species. (28, 80) The difference in energy between D₁₁^ClCl and the least stable intermediate D₁₂^ClCl is 2.7 kcal/mol^–1 with an activation energy barrier of less than 5 kcal mol^–1 (Figure 4). Therefore, all D₁₁^ClCl, D₁₂^ClCl, and D₂₂^ClCl species are expected to coexist and undergo interconversion at room temperature.

Interestingly, not all species favor the Mg–Cl bond cleavage required for the Cl/Me ligand exchange. Analysis of the Mg–Cl bond distances in D₁₁^ClCl, D₂₂^ClCl, and D₁₂^ClCl (Figure 5 top) shows that the formation of monochloride bridged species takes place preferentially from D₁₂^ClCl. NBO analysis indicates that asymmetric solvation of D₁₂^ClCl favors Mg²–Cl^ax bond cleavage (step (ii) in Figure 8). In this complex, the higher solvation on Mg² weakens the Mg²–Cl bond, while the lower solvation on Mg¹ makes it prone to accept an extra anionic ligand during the Cl/CH₃ exchange process. Analysis on several trajectories, such as the one represented in Figure 9, reaffirms that the chloride involved in the cleavage is the one located in the axial position of Mg² (Figure 5 bottom). The monobridged species generated by Mg–Cl bond cleavage (snapshot 2 in Figure 9) is short-lived and rapidly evolves into methyl chloride bridged structures (D^ClMe). The methyl group occupying the bridging position comes from Mg¹, as shown in snapshot 3; this is consistent with the higher electron density on the MgCl(THF)(μ-Cl) fragment compared to that on Mg(THF)₂(μ-Cl) calculated for the structure shown in snapshot 2.

Figure 9. Snapshots for the methyl transfer reaction in D₁₂^ClCl (Mg¹ on the left-hand side and Mg² on the right for all snapshots): (1) initial D₁₂^ClCl structure, (2) transition state of the transmetalation reaction, (3) D₁₂^ClMe, (4) solvent loss to form D₁₁^ClMe, and (5) solvent addition to form D₂₁^ClMe and (6) D₁₁^ClMeTHF. The atoms for the Grignard reagent and the coordinating THF molecules are depicted as balls and/or sticks and colored according to standard color codes. Selected neighboring solvent molecules are drawn with thin lines.

The first D^ClMe species generated after Mg–Cl bond cleavage is the D₁₂^ClMe complex (snapshot 3 in Figure 9). This species is however the least stable of the four solvation states observed by AIMD, with a free energy difference of +5 kcal mol^–1 (Figure 4) over the most stable solvation structure. As in the case of D^ClCl species, the most stable D^ClMe complex is the disolvated D₁₁^ClMe, in which both Mg atoms have tetrahedral coordination geometry. However, D^ClMe incorporates other trisolvated species, D₁₁^ClMeTHF and D₂₁^ClMe, which are both 3 kcal mol^–1 above D₁₁^ClMe. Exchange between these species has low activation energy barriers (smaller than 4 kcal mol^–1) and involves the addition of an external THF either at the bridging position (D₁₁^ClMe → D₁₁^ClMeTHF) or at the terminal position of Mg¹(D₁₁^ClMe → D₂₁^ClMe). Internal rearrangement of THF from bridging to terminal is also observed (D₁₁^ClMeTHF → D₂₁^ClMe) with an even lower energy barrier (<0.5 kcal mol^–1). The higher stability of D₂₁^ClMe compared to that of D₁₂^ClMe is consistent with the higher solvation of the most electrophilic Mg atom (Mg¹), that is, the one with a terminal chloride.

In order to form the final products, both Mg²–Cl and Mg¹–CH₃ bonds need to be cleaved. This however does not take place simultaneously but consecutively, and solvation plays an important role. Because Cl is a much better ligand than CH₃, (28) the Mg–CH₃ bond is the first to be broken. Analysis of the orientation of the formal lone pair in the bridging methyl ligand shows that at equal solvation of Mg atoms in D^ClMe, μ-CH₃ is more strongly bonded to Mg¹ than to Mg² because Mg¹ is more electrophilic (Figure 7). This preference is however modified by increasing the solvation of Mg¹ relative to Mg². Thus, in D₂₁^ClMe, the methyl is equally bonded to Mg¹ and Mg². In addition, in this species, the axial position occupied by the bridged methyl group in the coordination sphere of Mg¹ also favors the Mg¹–C^axH₃ bond cleavage. An increase in solvation of Mg¹ thus yields the preproduct of the Schlenk equilibrium (P₂₁ and minimum E in Figure 3), consisting of a Mg¹Cl₂ species bridged by way of a single chloride to Mg²(CH₃)₂. An increase in solvation of both Mg centers is expected to favor the final release of the mononuclear MgCl₂ and Mg(CH₃)₂ products. The dissociation energy from P₂₁ to CH₃MgCl(THF)₂ and the most stable MgCl₂(THF)₃ has been estimated to be −8.7 kcal mol^–1 in this study (see Figure S4 for further details).

Despite their relatively low abundance in solution, as also experimentally observed, (22) formation of dimeric adducts is key to the evolution of the Schlenk equilibrium reaction. The reaction pathway identified in this study highlights the crucial role of the solvent in assisting Cl/Me exchange in the Schlenk equilibrium. Most importantly, it shows that the tetracoordinated Mg species proposed in most computational studies (28, 81, 82) are indeed the most stable structures but are not on the reactive pathway. Instead, asymmetric solvation on Mg atoms is needed to promote the Mg–Cl and Mg–CH₃ bond cleavage to go from MgCH₃Cl to Mg(CH₃)₂ and MgCl₂. These tetra/pentacoordinated Mg dimers (D₁₂^ClCl and D₂₁^ClMe) are transient intermediates that interchange with the most stable solvation structures at room temperature. In addition, the bridging ligand involved in the bond-breaking process is located always in the axial position of the pentacoordinated Mg atom. This detailed information on the Schlenk equilibrium mechanism will be useful for a better understanding of the reactivity of the Grignard reagents. In addition, this study may help to better understand other transmetalation processes, such as those involved in the Kumada and Negishi cross-coupling reactions, (4, 83-86) which are also assisted by solvent.

Conclusions

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The here presented AIMD study of the Schlenk equilibrium reaction, in which two molecules of CH₃MgCl exchange methyl and chloride groups to yield Mg(CH₃)₂ and MgCl₂, showed how the ether solvent (THF here) has a crucial role in assisting the reaction. Although coordination of the solvent is needed for stabilizing the various mono- and dinuclear Mg complexes, the stabilizing effect is not the only factor at work.

The reaction goes via the formation of a dinuclear (CH₃)Mg(μ-Cl)₂Mg(CH₃) intermediate whose most stable solvated form (with a single THF at each Mg) is unreactive. The chloride/methyl exchange is promoted by making the two Mg atoms electronically different. The calculations show that these differences are created by different solvations of the two Mg centers. The cleavage of the Mg–Cl bond and associated shift of the methyl group from the terminal to bridging position is assisted by increasing the solvation at the Mg involved in the bond cleavage while keeping the other Mg less solvated.

A similar process occurs at the dinuclear (CH₃)Mg(μ-CH₃)(μ-Cl)MgCl; the cleavage of the bond between Mg and the bridging CH₃ group to form solvated Mg(CH₃)₂ and MgCl₂ requires the chloride-rich Mg atom to be more solvated than the methyl-rich Mg one. Increasing solvation at one Mg favors bond cleavage, while decreasing solvation on the other one favors the formation of new terminal bonds.

The species selected by the dynamics to be on the reaction pathway are not necessarily minima on the PES, which emphasizes the need for the former method. Our findings highlight the need of including explicit solvent dynamics in the modeling of such reactions because this is crucial in allowing the Cl/CH₃ group exchange to occur with a low energy barrier.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b02716.

Metadynamics parameters, natural bond orbital analysis, DFT optimized geometries, and solvation properties for different sizes of the simulation box (PDF)

jp7b02716_si_001.pdf (774.55 kb)

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Author Information

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Corresponding Authors
- Ainara Nova - Department of Chemistry and Centre for Theoretical and Computational Chemistry (CTCC), University of Oslo, Postbox 1033 Blindern, 0315 Oslo, Norway; Email: [email protected]
- Michele Cascella - Department of Chemistry and Centre for Theoretical and Computational Chemistry (CTCC), University of Oslo, Postbox 1033 Blindern, 0315 Oslo, Norway; Email: [email protected]
Authors
- Raphael M. Peltzer - Department of Chemistry and Centre for Theoretical and Computational Chemistry (CTCC), University of Oslo, Postbox 1033 Blindern, 0315 Oslo, Norway
- Odile Eisenstein - Department of Chemistry and Centre for Theoretical and Computational Chemistry (CTCC), University of Oslo, Postbox 1033 Blindern, 0315 Oslo, Norway; Institut Charles Gerhardt, UMR 5253 CNRS-Université de Montpellier, Université de Montpellier, cc 1501, Place E. Bataillon, 34095 Montpellier, France; http://orcid.org/0000-0001-5056-0311
Notes
The authors declare no competing financial interest.

Acknowledgment

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This work was supported by the Research Council of Norway (RCN) through the CoE Centre for Theoretical and Computational Chemistry (CTCC) Grant No. 179568/V30 and 171185/V30 and by the Norwegian Supercomputing Program (NOTUR) (Grant No. NN4654K). A.N. thanks the RCN for Grants 221801/F20 and 250044/F20. The authors thank Elisa Rebolini for enlightening discussion.

References

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This article references 86 other publications.

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Journal of the American Chemical Society (2016), 138 (14), 4796-4806CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Grignard reagents that are at the simplest level described as "RMgX" (where R is an org. substituent and X a halide) are one of the most widely utilized classes of synthetic reagents. Lately, esp. Grignard reagents with amido ligands of the type R1R2NMgX, so-called Hauser bases, and their Turbo analog R1R2NMgX·LiCl play an outranging role in modern synthetic chem. However, because of their complex soln. behavior, where Schlenk-type equil. are involved, very little is known about their structure in soln. Esp. the impact of LiCl on the Schlenk-equil. was still obscured by complexity and limited anal. access. Herein, we present unprecedented insights into the soln. structure of the Hauser base iPr2NMgCl 1 and the Turbo-Hauser base iPr2NMgCl·LiCl 2 at various temps. in THF-d8 soln. by employing a newly elaborated diffusion ordered spectroscopy (DOSY) NMR method hand-in-hand with theor. calcns.
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Journal of the American Chemical Society (1968), 90 (20), 5375-8CODEN: JACSAT; ISSN:0002-7863.
An x-ray diffraction study of the Et Grignard reagent in Et2O was undertaken to establish the structure of this reagent in the solid state. Crystals of EtMgBr.2Et2O are monoclinic with space group P21/c and 4 formula units per cell of dimensions a 13.18, b 10.27, c 11.42 A., and β 103.3°. The structure consists of the packing of discrete monomer units with a Br atom, an Et group, and 2 ether groups tetrahedrally coordinated to a Mg atom.
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Vallino, M. Structure Cristalline de CH₃MgBr·3 C₄H₈O J. Organomet. Chem. 1969, 20, 1– 10 DOI: 10.1016/S0022-328X(00)80080-7
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Crystalline structure of CH3MgBr.3C4H8O[methylmagnesium bromide-tritetrahydrofuran complex]
Vallino, Maurice
Journal of Organometallic Chemistry (1969), 20 (1), 1-10CODEN: JORCAI; ISSN:0022-328X.
The structure of MeMgBr.-3C4H8O was solved by single crystal x-ray diffraction techniques. The 5-coordinate Mg is at the center of a trigonal bipyramid. Me and Br are disordered and tetrahydrofuran rings distorded. A rigid body least squares refinement program is described.
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Toney, J.; Stucky, G. D. The Stereochemistry of Polynuclear Compounds of the Main Group Elements [C₂H₅Mg₂Cl₃(C₄H₈O)₃]₂, a Tetrameric Grignard Reagent J. Organomet. Chem. 1971, 28, 5– 20 DOI: 10.1016/S0022-328X(00)81569-7
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Stereochemistry of polynuclear compounds of the main group elements [C2H5Mg2Cl3(C4H8O)3]2, a tetrameric Grignard reagent
Stucky, Galen D.; Toney, Joe D.
Journal of Organometallic Chemistry (1971), 28 (1), 5-20CODEN: JORCAI; ISSN:0022-328X.
Reaction of EtCl with Mg in THF yielded a compd. which was detd. by a single-crystal x-ray diffraction study to be a tetrameric Grignard reagent, [EtMg2Cl3(THF)3]2. This organometallic complex crystallizes into the space group P21/c with Z = 2. The cell dimensions are: a = 12.128(3), b = 16.750(4), c = 10.972(3) Å, β = 104.02(2)°. A full matrix least-squares refinement based upon 919 obsd. reflections measured by diffractometer techniques yielded a final unweighted R factor of 0.102. The mol. lies on a crystallog. inversion center and contains a total of 5 4-membered bridging units consisting of Mg and Cl atoms. The 2 independent Mg atoms in [EtMg2Cl3(THF)3]2 exhibit 5 and 6 coordination. Two 3-coordinated bridging Cl atoms are also present in the mol.
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Blasberg, F.; Bolte, M.; Wagner, M.; Lerner, H.-W. An Approach to Pin Down the Solid-State Structure of the “Turbo Grignard Organometallics 2012, 31, 1001– 1005 DOI: 10.1021/om201080t
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An Approach to Pin Down the Solid-State Structure of the "Turbo Grignard"
Blasberg, Florian; Bolte, Michael; Wagner, Matthias; Lerner, Hans-Wolfram
Organometallics (2012), 31 (3), 1001-1005CODEN: ORGND7; ISSN:0276-7333. (American Chemical Society)
Single crystals of [iPrMgCl(THF)]2[MgCl2(THF)2]2 were obtained by layering a THF soln. of the "turbo Grignard" iPrMgCl·LiCl with Et2O at ambient temp. The isolated 1:1 Grignard-MgCl2 adduct is isostructural with cryst. compds. which were obtained from pure RMgCl solns. (R = Me, tBu, Ph, Bn). The structure of [iPrMgCl(THF)]2[MgCl2(THF)2]2 reveals an open-cube motif (monoclinic, P21/c). When dioxane was added to a THF soln. of iPrMgCl·LiCl, single crystals of [LiCl(THF)2]2 and [iPr2Mg(dioxane)]∞ (monoclinic, C2/c) were isolated. From 1:1 mixts. of (Me3Si)2CHMgCl (DisylMgCl) and LiCl (prepd. analogously to iPrMgCl·LiCl) two different Grignard compds., the monomer [DisylMgCl(THF)2] (monoclinic, P21) and the dimer [DisylMgCl(THF)]2 (monoclinic, P21/c), were isolated as single crystals. During studies, two oxidn. products of iPrMgCl and DisylMgCl, resp., resulting from oxygen insertion, were obtained and structurally characterized. Colorless plates of [iPrMg(OiPr)]4 (monoclinic, P21/m) grew from a THF/benzene soln. The dimeric alkoxide {[DisylOMgCl][LiCl(THF)2]}2 (monoclinic, C2/c), which was obtained from DisylMgCl·LiCl by oxidn. through residual oxygen, displays the only structure in which incorporation of LiCl in the mol. framework of a Mg alkoxide was obsd.
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Smith, M. B.; Becker, W. E. The constitution of the grignard reagent—III:The reaction between R₂Mg and MgX₂ in tetrahydrofuran Tetrahedron 1967, 23, 4215– 4227 DOI: 10.1016/S0040-4020(01)88819-0
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Smith, M. B.; Becker, W. E. The constitution of the Grignard Reagent - I. The reaction between diethyl magnesium and magnesium bromide in diethyl ether Tetrahedron Lett. 1965, 6, 3843– 3847 DOI: 10.1016/S0040-4039(01)89135-8
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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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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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Schlenk, W.; Schlenk, W. Über die Konstitution der Grignardschen Magnesiumverbindungen Ber. Dtsch. Chem. Ges. B 1929, 62, 920– 924 DOI: 10.1002/cber.19290620422
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The constitution of the Grignard magnesium derivatives
Schlenk, W.; Schlenk, Wilh., Jr.
Berichte der Deutschen Chemischen Gesellschaft [Abteilung] B: Abhandlungen (1929), 62B (), 920-4CODEN: BDCBAD; ISSN:0365-9488.
Several Grignard compds. have been prepd., then fractionally pptd. from their Et2O soln. by means of O(CH2CH2)2O. The Mg:X ratios of the fractions have been examd. Grignard compds. must be represented by 2RMgX .dblharw. MgR2 + MgX2. For EtI, the compn. of the Grignard deriv. would be: 6EtMgI + 4MgEt2 + 4MgI2. For PhBr: PhMgBr + 0.115MgPh2 + 0.115MgBr2.
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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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Sobota, P.; Duda, B. Influence of MgCl₂ on Grignard Reagent Composition in Tetrahydrofuran. III J. Organomet. Chem. 1987, 332, 239– 245 DOI: 10.1016/0022-328X(87)85090-8
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Influence of magnesium chloride on Grignard reagent composition in tetrahydrofuran. III
Sobota, Piotr; Duda, Barbara
Journal of Organometallic Chemistry (1987), 332 (3), 239-45CODEN: JORCAI; ISSN:0022-328X.
Reaction of [MgCl2(THF)2] with [NBu4][BF4] yields the compds. [NBu4][MgCl4] (I) and [Mg(THF)6][BF4]2. After addn. of dioxane (C4H8O2) the reaction equil. shifts in the opposite direction. The formation of [MgCl2(C4H8O2)2] in soln. does not require the presence of MgCl2. This compd. may be formed in the reaction of dioxane with the ionic or mol. species formed by the magnesium atom in soln. The [NBu4][BF4] salt also reacts with the Grignard reagent to produce I which confirms that there is a new equil. between [Mg(R)X(THF)n] and [MgR2(THF)2], [MgCl4]2-, and [Mg(THF6)]2+. Bis(tetrahydrofuran)magnesium dichloride, because of its reactivity is only stable in Grignard reagent. For that reason the compn. of the Grignard reagent in soln. is best described as an equil. between [Mg(R)X(THF)n] and [(THF)4Mg(μ-Cl)2MgR2] and [RMg2(μ-Cl)3(THF)5] rather than as a Schlenk equil.
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Sakamoto, S.; Imamoto, T.; Yamaguchi, K. Constitution of Grignard Reagent RMgCl in Tetrahydrofuran Org. Lett. 2001, 3, 1793– 1795 DOI: 10.1021/ol010048x
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Constitution of Grignard Reagent RMgCl in Tetrahydrofuran
Sakamoto, Shigeru; Imamoto, Tsuneo; Yamaguchi, Kentaro
Organic Letters (2001), 3 (12), 1793-1795CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)
The constitution of Grignard reagent, RMgCl (R = Me, tBu, Ph, benzyl), was investigated in the solid state by x-ray crystallog. and in THF by coldspray ionization mass spectrometry (CSI-MS). Three types of crystal structures, (a) [Mg2(μ-Cl3)(THF)6]+[RMgCl2(THF)]-, (b) R2Mg4Cl6(THF)6, and (c) [2Mg2(μ-Cl3)(THF)6]+[R4Mg2Cl2]2-, were identified, and MeMg2(μ-Cl3)(THF)4-6 were detected as major species of MeMgCl in soln.
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Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas Phys. Rev. B 1964, 136, 864– 871 DOI: 10.1103/PhysRev.136.B864
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Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects Phys. Rev. A 1965, 140, 1133– 1138 DOI: 10.1103/PhysRev.140.A1133
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Jiménez-Halla, J. O. C.; Bickelhaupt, F. M.; Solà, M. Organomagnesium clusters: Structure, stability, and bonding in archetypal models J. Organomet. Chem. 2011, 696, 4104– 4111 DOI: 10.1016/j.jorganchem.2011.06.014
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Organomagnesium clusters: Structure, stability, and bonding in archetypal models
Jimenez-Halla, J. Oscar C.; Bickelhaupt, F. Matthias; Sola, Miquel
Journal of Organometallic Chemistry (2011), 696 (25), 4104-4111CODEN: JORCAI; ISSN:0022-328X. (Elsevier B.V.)
The mol. structure and the nature of the chem. bond in the monomers and tetramers of the Grignard reagent CH3MgCl as well as MgX2 (X = H, Cl, and CH3) were studied at the BP86/TZ2P level of theory. For the tetramers, the stability of three possible mol. structures of C2h, D2h, and Td symmetry are discussed. The most stable structure for (MgCl2)4 is D2h, the one for (MgH2)4 is C2h, and that of (CH3MgCl)4 is Td. The latter is 38 kcal/mol more stable with chlorines in bridge positions and Me groups coordinated to a Mg vertex than vice versa. Through a quant. energy decompn. anal. (EDA) that the tetramerization energy is predominantly composed of electrostatic attraction ΔVelstat (60% of all bonding terms ΔVelstat + ΔEoi) although the orbital interaction ΔEoi also provides an important contribution (40%) were found.
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Lioe, H.; White, J. M.; O’Hair, R. A. J. Preference for bridging versus terminal ligands in magnesium dimers J. Mol. Model. 2011, 17, 1325– 1334 DOI: 10.1007/s00894-010-0834-1
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Preference for bridging versus terminal ligands in magnesium dimers
Lioe, Hadi; White, Jonathan M.; O'Hair, Richard A. J.
Journal of Molecular Modeling (2011), 17 (6), 1325-1334CODEN: JMMOFK; ISSN:0948-5023. (Springer)
Magnesium dimers play important roles in inorg. and organometallic chem. This study evaluates the inherent bridging ability of a range of different ligands in magnesium dimers. In the first part, the Cambridge Structural Database is interrogated to establish the frequency of different types of ligands found in bridging vs. terminal positions in two key structural motifs: one in which there are two bridging ligands (the D 2h "Mg2(μ-X2)" structure); the other in which there are three bridging ligands (the C 3v "Mg2(μ-X3)" structure). The most striking finding from the database search is the overwhelming preference for magnesium dimers possessing two bridging ligands. The most common bridging ligands are C-, N-, and O-based. In the second part, DFT calcns. (at the B3LYP/6-311+G(d) level of theory) are carried out to examine a wider range of structural types for dimers consisting of the stoichiometries Mg2Cl3R and Mg2Cl2R2, where R = CH3, SiH3, NH2, PH2, OH, SH, CH2CH3, CH=CH2, C CH, Ph, OAc, F and Br. Consistent with the database search, the most stable magnesium dimers are those that contain two bridging ligands. Furthermore, it was demonstrated that the electronic effect of the bridging ligands is important in influencing the stability of the magnesium dimers. The preference for a bridging ligand, which reflects its ability to stabilize a magnesium dimer, follows the order: OH > NH2 > C CH > SH > Ph > Br > PH2 = CH=CH2 > CH2CH3 > CH3 > SiH3. Finally, the role that the ether solvent Me2O has on the stability of isomeric Mg2Cl2Me2 dimers was studied. It was found that the first solvent mol. stabilizes the dimers, while the second solvent mol. can either have a stabilizing or destabilizing effect, depending on the isomer structure.
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Henriques, A. M.; Barbosa, A. G. H. Chemical Bonding and the Equilibrium Composition of Grignard Reagents in Ethereal Solutions 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
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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Ramirez, F.; Sarma, R.; Chaw, F.; McCaffrey, T. M. Magnesium bromide-tetrahydrofuran complexes: bis(tetrahydrofuran)magnesium bromide, tris(tetrahydrofuran)magnesium bromide, tetrakis(tetrahydrofuran)magnesium bromide, and diaquotetrakis(tetrahydrofuran)magnesium bromide. A reagent for the preparation of anhydrous magnesium phosphodiester salts J. Am. Chem. Soc. 1977, 99, 5285– 5289 DOI: 10.1021/ja00458a010
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Pirinen, S.; Koshevoy, I. O.; Denifl, P.; Pakkanen, T. T. A Single-Crystal Model for MgCl₂ – Electron Donor Support Materials: [Mg₃Cl₅(THF)₄Bu]₂ (Bu = n-Butyl) Organometallics 2013, 32, 4208– 4213 DOI: 10.1021/om400407p
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Ashby, E. C.; Becker, W. E. Concerning the Structure of the Grignard Reagent J. Am. Chem. Soc. 1963, 85, 118– 119 DOI: 10.1021/ja00884a032
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The structure of the Grignard reagent
Ashby, E. C.; Becker, W. E.
Journal of the American Chemical Society (1963), 85 (), 118-19CODEN: JACSAT; ISSN:0002-7863.
cf. Dessy, et al., CA 51, 16283e. The observation that the Grignard reagent [prepd. by the action of alkyl halide with Mg in tetrahydrofuran (THF) or ether; in THF the soln. prepd. from EtCl and Mg was identical to the soln. prepd. from Et2Mg and MgCl2 with respect to infrared spectra, conductance and dipole moment], although dimeric in Et2O, was monomeric in THF, and fractional crystn. of EtMgCl in THF produced EtMg2Cl3 and Et2Mg in quant. yield, proved that there was alkyl exchange in Grignard solns., and the predominant species in soln. was RMgX, as formulated by Schlenk and Schlenk (CA 23, 5159). The equil. could be extended as: 3RMgX .rdblhar. 3/2 R2Mg + 3/2 MgX2 .rdblhar. RMg2X3 + R2Mg. RMg2X3 was formed on crystn. through a combination of RMgX and MgX2 in THF-C6H6 system. Out of the two most logical dimeric structures I and II, in view of the above results I was preferred, though the work of Dessy (CA 55, 10303h, D. and Jones, CA 55, 11009d, D., et al., loc. cit.) leads to preference of II. This was supported by detn. of mol. aggregation (found to be dimeric) of mesitylmagnesium bromide in Et2O. If Grignard compds. in Et2O soln. existed as II, a severe steric problem would arise from a Mg atom surrounded by two mesityl groups and two Br atoms. Thus, it would appear that the equil. which existed in Et2O was similar to that in THF.
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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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Tobisu, M.; Chatani, N. Cross-Couplings Using Aryl Ethers via C–O Bond Activation Enabled by Nickel Catalysts Acc. Chem. Res. 2015, 48, 1717– 1726 DOI: 10.1021/acs.accounts.5b00051
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Cross-Couplings Using Aryl Ethers via C-O Bond Activation Enabled by Nickel Catalysts
Tobisu, Mamoru; Chatani, Naoto
Accounts of Chemical Research (2015), 48 (6), 1717-1726CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
A review. Arene synthesis has been revolutionized by the invention of catalytic cross-coupling reactions, wherein aryl halides can be coupled with organometallic and org. nucleophiles. Although the replacement of aryl halides with phenol derivs. would lead to more economical and ecol. methods, success has been primarily limited to activated phenol derivs. such as triflates. Aryl ethers arguably represent one of the most ideal substrates in terms of availability, cost, safety, and atom efficiency. However, the robust nature of the C(aryl)-O bonds of aryl ethers renders it extremely difficult to use them in catalytic reactions among the phenol derivs. In 1979, Wenkert reported a seminal work on the nickel-catalyzed cross-coupling of aryl ethers with Grignard reagents. However, it was not until 2004 that the unique ability of a low-valent nickel species to activate otherwise unreactive C(aryl)-O bonds was appreciated with Dankwardt's identification of the Ni(0)/PCy3 system, which significantly expanded the efficiency of the Wenkert reaction. Application of the nickel catalyst to cross-couplings with other nucleophiles was first accomplished in 2008 by the authors' group using organoboron reagents. Later on, several other nucleophiles, including organozinc reagents, amines, hydrosilane, and hydrogen were shown to be coupled with aryl ethers under nickel catalysis. Despite these advances, progress in this field is relatively slow because of the low reactivity of benzene derivs. (e.g., anisole) compared with polyarom. substrates (e.g., methoxynaphthalene), particularly when less reactive and synthetically useful nucleophiles are used. The "naphthalene problem" has been overcome by the use of N-heterocyclic carbene (NHC) ligands bearing bulky N-alkyl substituents, which enables a wide range of aryl ethers to be coupled with organoboron nucleophiles. Moreover, the use of N-alkyl-substituted NHC ligands allows the use of alkynylmagnesium reagents, thereby realizing the first Sonogashira-type reaction of anisoles. From a mechanistic perspective, nickel-catalyzed cross-couplings of aryl ethers are at a nascent stage, in particular regarding the mode of activation of C(aryl)-O bonds. Oxidative addn. is one plausible pathway, although such a process has not been fully verified exptl. Nickel-catalyzed reductive cleavage of aryl ethers in the absence of an external reducing agent provides strong support for this oxidative addn. process. Several other mechanisms have also been proposed. For example, Martin demonstrated a new possibility of the involvement of a Ni(I) species, which could mediate the cleavage of the C(aryl)-O bond via a redox-neutral pathway. The tolerance of aryl ethers under commonly used synthetic conditions enables alkoxy groups to serve as a platform for late-stage elaboration of complex mols. without any tedious protecting group manipulations. Aryl ethers are therefore not mere economical alternatives to aryl halides but also enable nonclassical synthetic strategies.
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Cahiez, G.; Moyeux, A.; Cossy, J. Grignard Reagents and Non-Precious Metals: Cheap and Eco-Friendly Reagents for Developing Industrial Cross-Couplings. A Personal Account Adv. Synth. Catal. 2015, 357, 1983– 1989 DOI: 10.1002/adsc.201400654
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Tasker, S. Z.; Standley, E. A.; Jamison, T. F. Recent Advances in Homogeneous Nickel Catalysis Nature 2014, 509, 299– 309 DOI: 10.1038/nature13274
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Recent advances in homogeneous nickel catalysis
Tasker, Sarah Z.; Standley, Eric A.; Jamison, Timothy F.
Nature (London, United Kingdom) (2014), 509 (7500), 299-309CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
A review. Tremendous advances have been made in nickel catalysis over the past decade. Several key properties of nickel, such as facile oxidative addn. and ready access to multiple oxidn. states, have allowed the development of a broad range of innovative reactions. In recent years, these properties have been increasingly understood and used to perform transformations long considered exceptionally challenging. Here we discuss some of the most recent and significant developments in homogeneous nickel catalysis, with an emphasis on both synthetic outcome and mechanism.
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Laio, A.; Parrinello, M. Escaping Free-Energy Minima Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 12562– 12566 DOI: 10.1073/pnas.202427399
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Escaping free-energy minima
Laio, Alessandro; Parrinello, Michele
Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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Iannuzzi, M.; Laio, A.; Parrinello, M. Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics Phys. Rev. Lett. 2003, 90, 23– 26 DOI: 10.1103/PhysRevLett.90.238302
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Vuilleumier, R.; Sprik, M. Electronic Properties of Hard and Soft Ions in Solution: Aqueous Na⁺ and Ag⁺ Compared J. Chem. Phys. 2001, 115, 3454– 3468 DOI: 10.1063/1.1388901
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Electronic properties of hard and soft ions in solution: Aqueous Na+ and Ag+ compared
Vuilleumier, Rodolphe; Sprik, Michiel
Journal of Chemical Physics (2001), 115 (8), 3454-3468CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The electronic structure of model aq. solns. of Na+ and Ag+ is investigated using ab initio mol.-dynamics methods. We compute a no. of electronic response coeffs. in soln., such as global hardness and nuclear Fukui functions. The nuclear Fukui functions are found to be particularly sensitive to the chem. nature of the component species giving for Ag+ a susceptibility 3.5 times the value for a H2O mol. while the result for Na+ is more than a factor of 4 smaller compared to a solvent mol. The electronic structure of the soln. is further characterized by construction of effective MOs and energies. This anal. reveals that the effective HOMO (HOMO) of the hard cation, Na+, remains buried in the valence bands of the solvent, whereas the HOMO of Ag+ is found to mix with the lone pair electrons of its four ligand H2O mols. to form the (global) HOMO of the soln. This observation, highlighting the importance of the electronic structure of the solvent, is used to rationalize the results for the electronic response.
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Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G. A First Principles Molecular Dynamics Simulation of the Hydrated Magnesium Ion Chem. Phys. Lett. 2001, 343, 549– 555 DOI: 10.1016/S0009-2614(01)00735-7
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A first principles molecular dynamics simulation of the hydrated magnesium ion
Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G.
Chemical Physics Letters (2001), 343 (5,6), 549-555CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
First principles Car-Parrinello mol. dynamics has been used to investigate the solvation of Mg2+ in water. In agreement with expt., we find that the first solvation shell around Mg2+ contains six water mols. in an octahedral arrangement. The electronic structure of first solvation shell water mols. has been examd. with a localized orbital anal. We find that water mols. tend to asym. coordinate Mg2+ through one of the oxygen lone pair orbitals and that the first solvation shell dipole moments increase by 0.2 Debye relative to pure liq. water.
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Bernasconi, L.; Baerends, E. J.; Sprik, M. Long-Range Solvent Effects on the Orbital Interaction Mechanism of Water Acidity Enhancement in Metal Ion Solutions: A Comparative Study of the Electronic Structure of Aqueous Mg and Zn Dications J. Phys. Chem. B 2006, 110, 11444– 11453 DOI: 10.1021/jp0609941
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Long-Range Solvent Effects on the Orbital Interaction Mechanism of Water Acidity Enhancement in Metal Ion Solutions: A Comparative Study of the Electronic Structure of Aqueous Mg and Zn Dications
Bernasconi, Leonardo; Baerends, Evert Jan; Sprik, Michiel
Journal of Physical Chemistry B (2006), 110 (23), 11444-11453CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
We study the dissocn. of water coordinated to a divalent metal ion center, M2+ = Mg2+, Zn2+ using d. functional theory (DFT) and ab initio mol. dynamics (AIMD) simulations. First, the proton affinity of a coordinated OH- group is computed from gas-phase M2+(H2O)5(OH-), which yields a relative higher gas-phase acidity for a Zn2+-coordinated as compared to a Mg2+-coordinated water mol., ΔpKagp = 5.3. We explain this difference on the basis of a gain in stabilization energy of the Zn2+(H2O)5(OH-) system arising from direct orbital interaction between the coordinated OH- and the empty 4s state of the cation. Next, we compute the acidity of coordinated water mols. in soln. using free-energy thermodn. integration with constrained AIMD. This approach yields pKa Mg2+ = 11.2 and pKa Zn2+ = 8.4, which compare favorably to exptl. data. Finally, we examine the factors responsible for the apparent decrease in the relative Zn2+-coordinated water acidity in going from the gas-phase (ΔpKagp = 5.3) to the solvated (ΔpKa = 2.8) regime. We propose two simultaneously occurring solvation-induced processes affecting the relative stability of Zn2+(H2O)5(OH-), namely: (a) redn. of the Zn 4s character in soln. states near the bottom of the conduction band; (b) hybridization between OH- orbitals and valence-band states of the solvent. Both effects contribute to hindering the OH- → Zn2+ charge transfer, either by making it energetically unfavorable or by delocalizing the ligand charge d. over several water mols.
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Blumberger, J.; Bernasconi, L.; Tavernelli, I.; Vuilleumier, R.; Sprik, M. Electronic Structure and Solvation of Copper and Silver Ions: A Theoretical Picture of a Model Aqueous Redox Reaction J. Am. Chem. Soc. 2004, 126, 3928– 3938 DOI: 10.1021/ja0390754
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Electronic Structure and Solvation of Copper and Silver Ions: A Theoretical Picture of a Model Aqueous Redox Reaction
Blumberger, Jochen; Bernasconi, Leonardo; Tavernelli, Ivano; Vuilleumier, Rodolphe; Sprik, Michiel
Journal of the American Chemical Society (2004), 126 (12), 3928-3938CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Electronic states and solvation of Cu and Ag aqua ions are investigated by comparing the Cu2+ + e- → Cu+ and Ag2+ + e- → Ag+ redox reactions using d. functional-based computational methods. The coordination no. of aq. Cu2+ is found to fluctuate between 5 and 6 and reduces to 2 for Cu+, which forms a tightly bound linear dihydrate. Redn. of Ag2+ changes the coordination no. from 5 to 4. The energetics of the oxidn. reactions is analyzed by comparing vertical ionization potentials, relaxation energies, and vertical electron affinities. The model is validated by a computation of the free energy of the full redox reaction Ag2+ + Cu+ → Ag+ + Cu2+. Investigation of the one-electron states shows that the redox active frontier orbitals are confined to the energy gap between occupied and empty states of the pure solvent and localized on the metal ion hydration complex. The effect of solvent fluctuations on the electronic states is highlighted in a computation of the UV absorption spectrum of Cu+ and Ag+.
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Guido, C. A.; Pietrucci, F.; Gallet, G. A.; Andreoni, W. The Fate of a Zwitterion in Water from Ab Initio Molecular Dynamics: Monoethanolamine (MEA)-CO₂ J. Chem. Theory Comput. 2013, 9, 28– 32 DOI: 10.1021/ct301071b
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The Fate of a Zwitterion in Water from ab Initio Molecular Dynamics: Monoethanolamine (MEA)-CO2
Guido, Ciro A.; Pietrucci, Fabio; Gallet, Gregoire A.; Andreoni, Wanda
Journal of Chemical Theory and Computation (2013), 9 (1), 28-32CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Understanding the fundamental reactions accompanying the capture of carbon dioxide in amine solns. is crit. for the design of high-performance solvents and requires an accurate modeling of the solute-solvent interaction. As a first step toward this goal, using ab initio mol. dynamics (Car-Parrinello) simulations, we investigate a zwitterionic carbamate, a species long proposed as intermediate in the formation of a stable carbamate, in a dil. aq. soln. CO2 release and deprotonation are competitive routes for its dissocn. and are both characterized by free-energy barriers of 6-8 kcal/mol. Water mols. play a crucial role in both pathways, resulting in large entropic effects. This is esp. true in the case of CO2 release, which is accompanied by a strong reorganization of the solvent beyond the first coordination shell, leading to the formation of a water cage entrapping the solute (hydrophobic effect). Our results contrast with the assumptions of implicit solvent models.
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Boero, M.; Ikeshoji, T.; Liew, C. C.; Terakura, K.; Parrinello, M.; Boero, M.; Ikeshoji, T.; Liew, C. C.; Terakura, K. Hydrogen Bond Driven Chemical Reactions: Beckmann Rearrangement of Cyclohexanone Oxime into ε-Caprolactam in Supercritical Water Hydrogen Bond Driven Chemical Reactions: Beckmann Rearrangement of Cyclohexanone Oxime into E-Caprolactam in Supercritical J. Am. Chem. Soc. 2004, 126, 6280– 6286 DOI: 10.1021/ja049363f
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Vidossich, P.; Lledós, A.; Ujaque, G. Realistic Simulation of Organometallic Reactivities in Solution by Means of First-Principles Molecular Dynamics. In Computational Studies in Organometallic Chemistry; Macgregor, S. A.; Eisenstein, O., Eds.; Structure and Bonding; Springer International Publishing: Berlin, Germany, 2016; Vol. 167, pp 81– 106.
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Vidossich, P.; Lledós, A.; Ujaque, G. First-Principles Molecular Dynamics Studies of Organometallic Complexes and Homogeneous Catalytic Processes Acc. Chem. Res. 2016, 49, 1271– 1278 DOI: 10.1021/acs.accounts.6b00054
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First-Principles Molecular Dynamics Studies of Organometallic Complexes and Homogeneous Catalytic Processes
Vidossich, Pietro; Lledos, Agusti; Ujaque, Gregori
Accounts of Chemical Research (2016), 49 (6), 1271-1278CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
A review. Computational chem. is a valuable aid to complement exptl. studies of organometallic systems and their reactivity. It allows probing mechanistic hypotheses and investigating mol. structures, shedding light on the behavior and properties of mol. assemblies at the at. scale. When approaching a chem. problem, the computational chemist has to decide on the theor. approach needed to describe electron/nuclear interactions and the compn. of the model used to approx. the actual system. Both factors det. the reliability of the modeling study. The community dedicated much effort to developing and improving the performance and accuracy of theor. approaches for electronic structure calcns., on which the description of (inter)at. interactions rely. Here, the importance of the model system used in computational studies is highlighted through examples from our recent research focused on organometallic systems and homogeneous catalytic processes. We show how the inclusion of explicit solvent allows the characterization of mol. events that would otherwise not be accessible in reduced model systems (clusters). These include the stabilization of nascent charged fragments via microscopic solvation (notably, hydrogen bonding), transfer of charge (protons) between distant fragments mediated by solvent mols., and solvent coordination to unsatd. metal centers. Furthermore, when weak interactions are involved, we show how conformational and solvation properties of organometallic complexes are also affected by the explicit inclusion of solvent mols. Such extended model systems may be treated under periodic boundary conditions, thus removing the cluster/continuum (or vacuum) boundary, and require a statistical mechanics simulation technique to sample the accessible configurational space. First-principles mol. dynamics, in which at. forces are computed from electronic structure calcns. (namely, d. functional theory), is certainly the technique of choice to investigate chem. events in soln. This methodol. is well established and thanks to advances in both algorithms and computational resources simulation times required for the modeling of chem. events are nowadays accessible, though the computational requirements use to be high. Specific applications reviewed here include mechanistic studies of the Shilov and Wacker processes, speciation in Pd chem., hydrogen bonding to metal centers, and the dynamics of agostic interactions.
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Laio, A.; VandeVondele, J.; Rothlisberger, U. A Hamiltonian Electrostatic Coupling Scheme for Hybrid Car–Parrinello Molecular Dynamics Simulations J. Chem. Phys. 2002, 116, 6941– 6947 DOI: 10.1063/1.1462041
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A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations
Laio, Alessandro; VandeVondele, Joost; Rothlisberger, Ursula
Journal of Chemical Physics (2002), 116 (16), 6941-6947CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We present a fully Hamiltonian and computationally efficient scheme to include the electrostatic effects due to the classical environment in a Car-Parrinello mixed quantum mechanics/mol. mechanics (QM/MM) method. The polarization due to the MM atoms close to the quantum system is described by a Coulombic potential modified at short range. The functional form of this potential has to be chosen carefully in order to obtain the correct interaction properties and to prevent an unphys. escape of the electronic d. to the MM atoms (the so-called spill-out effect). The interaction between the QM system and the more distant MM atoms is modeled by a Hamiltonian term explicitly coupling the multipole moments of the quantum charge distribution with the classical point charges. Our approach remedies some of the well known deficiencies of current electrostatic coupling schemes in QM/MM methods, allowing mol. dynamics simulations of mixed systems within a fully consistent and energy conserving approach.
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Moret, M.-E.; Tavernelli, I.; Chergui, M.; Rothlisberger, U. Electron Localization Dynamics in the Triplet Excited State of [Ru(bpy)₃]²⁺ in Aqueous Solution Chem. - Eur. J. 2010, 16, 5889– 5894 DOI: 10.1002/chem.201000184
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Electron localization dynamics in the triplet excited state of [Ru(bpy)3]2+ in aqueous solution
Moret, Marc-Etienne; Tavernelli, Ivano; Chergui, Majed; Rothlisberger, Ursula
Chemistry - A European Journal (2010), 16 (20), 5889-5894, S5889/1-S5889/9CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
Hybrid DFT/classical mol. dynamics of the long-lived triplet excited state of [Ru(bpy)3]2+ (bpy=2,2'-bipyridine) in aq. soln. is used to investigate the solvent-mediated electron localization and dynamics in the triplet metal-to-ligand charge-transfer (MLCT) state. Our studies reveal a solvent-induced breaking of the coordination symmetry with consequent localization of the photoexcited electron on one or two bipyridine units for the entire length of our simulation, which amts. to several picoseconds. Frequent electronic "hops" between the ligands constituting the pair are obsd. with a characteristic time of approx. half a picosecond.
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Dal Peraro, M.; Llarrull, L. I.; Rothlisberger, U.; Vila, A. J.; Carloni, P. Water-Assisted Reaction Mechanism of Monozinc β-Lactamases J. Am. Chem. Soc. 2004, 126, 12661– 12668 DOI: 10.1021/ja048071b
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Water-Assisted Reaction Mechanism of Monozinc β-Lactamases
Dal Peraro, Matteo; Llarrull, Leticia I.; Rothlisberger, Ursula; Vila, Alejandro J.; Carloni, Paolo
Journal of the American Chemical Society (2004), 126 (39), 12661-12668CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Hybrid Car-Parrinello QM/MM calcns. are used to investigate the reaction mechanism of hydrolysis of a common β-lactam substrate (cefotaxime) by the monozinc β-lactamase from Bacillus cereus (BcII). The calcns. suggest a fundamental role for an active site water in the catalytic mechanism. This water mol. binds the zinc ion in the first step of the reaction, expanding the zinc coordination no. and providing a proton donor adequately oriented for the second step. The free energy barriers of the two reaction steps are similar and consistent with the available exptl. data. The conserved hydrogen bond network in the active site, defined by Asp-120, Cys-221, and His-263, not only contributes to orient the nucleophile (as already proposed), but it also guides the second catalytic water mol. to the zinc ion after the substrate is bound. The hydrolysis reaction in water has a relatively high free energy barrier, which is consistent with the stability of cefotaxime in water soln. The modeled Michaelis complexes for other substrates are also characterized by the presence of an ordered water mol. in the same position, suggesting that this mechanism might be general for the hydrolysis of different β-lactam substrates.
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Dal Peraro, M.; Vila, A. J.; Carloni, P.; Klein, M. L. Role of Zinc Content on the Catalytic Efficiency of B1Metallo β-Lactamases J. Am. Chem. Soc. 2007, 129, 2808– 2816 DOI: 10.1021/ja0657556
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Role of Zinc Content on the Catalytic Efficiency of B1 Metallo β-Lactamases
Dal Peraro, Matteo; Vila, Alejandro J.; Carloni, Paolo; Klein, Michael L.
Journal of the American Chemical Society (2007), 129 (10), 2808-2816CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Metallo β-lactamases (MβL) are enzymes naturally evolved by bacterial strains under the evolutionary pressure of β-lactam antibiotic clin. use. They have a broad substrate spectrum and are resistant to all the clin. useful inhibitors, representing a potential risk of infection if massively disseminated. The MβL scaffold is designed to accommodate one or two zinc ions able to activate a nucleophilic hydroxide for the hydrolysis of the β-lactam ring. The role of zinc content on the binding and reactive mechanism of action has been the subject of debate and still remains an open issue despite the large amt. of data acquired. We report herein a study of the reaction pathway for binuclear CcrA from Bacteroides fragilis using d. functional theory based quantum mechanics-mol. mechanics dynamical modeling. CcrA is the prototypical binuclear enzyme belonging to the B1 MβL family, which includes several harmful chromosomally encoded and transferable enzymes. The involvement of a second zinc ion in the catalytic mechanism lowers the energetic barrier for β-lactam hydrolysis, preserving the essential binding features found in mononuclear B1 enzymes (BcII from Bacillus cereus) while providing a more efficient single-step mechanism. Overall, this study suggests that uptake of a second equiv. zinc ion is evolutionary favored.
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Cascella, M.; Magistrato, A.; Tavernelli, I.; Carloni, P.; Rothlisberger, U. Role of Protein Frame and Solvent for the Redox Properties of Azurin from Pseudomonas Aeruginosa Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 19641– 19646 DOI: 10.1073/pnas.0607890103
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Role of protein frame and solvent for the redox properties of azurin from Pseudomonas aeruginosa
Cascella, Michele; Magistrato, Alessandra; Tavernelli, Ivano; Carloni, Paolo; Rothlisberger, Ursula
Proceedings of the National Academy of Sciences of the United States of America (2006), 103 (52), 19641-19646CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
We have coupled hybrid quantum mechanics (d. functional theory; Car-Parrinello)/mol. mechanics mol. dynamics simulations to a grand-canonical scheme, to calc. the in situ redox potential of the Cu2+ + - → Cu+ half reaction in azurin from Pseudomonas aeruginosa. An accurate description at atomistic level of the environment surrounding the metal-binding site and finite-temp. fluctuations of the protein structure are both essential for a correct quant. description of the electronic properties of this system. We report a redox potential shift with respect to copper in water of 0.2 eV (exptl. 0.16 eV) and a reorganization free energy λ = 0.76 eV (exptl. 0.6-0.8 eV). The electrostatic field of the protein plays a crucial role in fine tuning the redox potential and detg. the structure of the solvent. The inner-sphere contribution to the reorganization energy is negligible. The overall small value is mainly due to solvent rearrangement at the protein surface.
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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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Gossens, C.; Tavernelli, I.; Rothlisberger, U. Rational Design of Organo-Ruthenium Anticancer Compounds Chimia 2005, 59, 81– 84 DOI: 10.2533/000942905777676795
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Metz, D. J.; Glines, A. Density, Viscosity, and Dielectric Constant of Tetrahydrofuran between −78 and 30° J. Phys. Chem. 1967, 71, 1158– 1158 DOI: 10.1021/j100863a067
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Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions Phys. Rev. A: At., Mol., Opt. Phys. 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. Nose–Hoover chains: The Canonical Ensemble via Continuous Dynamics J. Chem. Phys. 1992, 97, 2635– 2643 DOI: 10.1063/1.463940
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Nosé, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods J. Chem. Phys. 1984, 81, 511– 519 DOI: 10.1063/1.447334
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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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Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868 DOI: 10.1103/PhysRevLett.77.3865
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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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Lippert, G.; Hutter, J.; Parrinello, M. The Gaussian and Augmented-Plane-Wave Density Functional Method for Ab Initio Molecular Dynamics Simulations Theor. Chem. Acc. 1999, 103, 124– 140 DOI: 10.1007/s002140050523
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The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations
Lippert, Gerald; Hutter, Jurg; Parrinello, Michele
Theoretical Chemistry Accounts (1999), 103 (2), 124-140CODEN: TCACFW; ISSN:1432-881X. (Springer-Verlag)
A new algorithm for d.-functional-theory-based ab initio mol. dynamics simulations is presented. The Kohn-Sham orbitals are expanded in Gaussian-type functions and an APW-type approach is used to represent the electronic d. This extends previous work of ours where the d. was expanded only in plane waves. We describe the total d. in a smooth extended part which we represent in plane waves as in our previous work and parts localized close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localized and extended part can be treated sep., achieving a computational cost for the calcn. of the Kohn-Sham matrix that scales with the system size N as O(N log N). Furthermore, we are able to reduce drastically the size of the plane-wave basis. In addn., we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calcns. and for ab initio mol. dynamics simulations.
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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: Condens. Matter Mater. Phys. 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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Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. Atomistic Simulations of Condensed Matter Systems WIREs 2014, 4, 15– 25 DOI: 10.1002/wcms.1159
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cp2k: atomistic simulations of condensed matter systems
Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
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Laio, A.; Gervasio, F. L. Metadynamics: a Method to Simulate Rare Events and Reconstruct the Free Energy in Biophysics, Chemistry and Material Science Rep. Prog. Phys. 2008, 71, 126601 DOI: 10.1088/0034-4885/71/12/126601
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Metadynamics: a method to stimulate rare events and reconstruct the free energy in biophysics, chemistry and material science
Laio, Alessandro; Gervasio, Francesco L.
Reports on Progress in Physics (2008), 71 (12), 126601/1-126601/22CODEN: RPPHAG; ISSN:0034-4885. (Institute of Physics Publishing)
A review. Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local min. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.
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Laio, A.; Rodriguez-Fortea, A.; Gervasio, F. L.; Ceccarelli, M.; Parrinello, M. Assessing the Accuracy of Metadynamics J. Phys. Chem. B 2005, 109, 6714– 6721 DOI: 10.1021/jp045424k
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Assessing the Accuracy of Metadynamics
Laio, Alessandro; Rodriguez-Fortea, Antonio; Gervasio, Francesco Luigi; Ceccarelli, Matteo; Parrinello, Michele
Journal of Physical Chemistry B (2005), 109 (14), 6714-6721CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
Metadynamics is a powerful technique that has been successfully exploited to explore the multidimensional free energy surface of complex polyat. systems and predict transition mechanisms in very different fields, ranging from chem. and solid-state physics to biophysics. We here derive an explicit expression for the accuracy of the methodol. and provide a way to choose the parameters of the method in order to optimize its performance.
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Vandevondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. r. Quickstep: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach Comput. Phys. Commun. 2005, 167, 103– 128 DOI: 10.1016/j.cpc.2004.12.014
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QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
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Krack, M.; Parrinello, M. In QUICKSTEP: Make the Atoms Dance; NIC Series; Forschungszentrum Jülich, 2004; p 29.
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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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Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Gaussian 09; Gaussian, Inc.: Wallingford, CT, 2009.
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Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules J. Chem. Phys. 1972, 56, 2257– 2261 DOI: 10.1063/1.1677527
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Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules
Hehre, W. J.; Ditchfield, R.; Pople, J. A.
Journal of Chemical Physics (1972), 56 (5), 2257-61CODEN: JCPSA6; ISSN:0021-9606.
Two extended basis sets (termed 5-31G and 6-31G) consisting of AO expressed as fixed linear combinations of Gaussian functions are presented for the 1st row atoms C to F. These basis functions are similar to the 4-31G set in that each valence shell is split into inner and outer parts described by 3 and 1 Gaussian function, resp. Inner shells are represented by a single basis function taken as a sum of 5 (5-31G) or 6 (6-31G) Guassians. Studies with a no. of polyat. mols. indicate a substantial lowering of calcd. total energies over the 4-31G set. Calcd. relative energies and equil. geometries do not appear to be altered significantly.
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Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. R. Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set for First-Row Elements, Li–F J. Comput. Chem. 1983, 4, 294– 301 DOI: 10.1002/jcc.540040303
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Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21 + G basis set for first-row elements, lithium to fluorine
Clark, Timothy; Chandrasekhar, Jayaraman; Spitznagel, Guenther W.; Schleyer, Paul v. R.
Journal of Computational Chemistry (1983), 4 (3), 294-301CODEN: JCCHDD; ISSN:0192-8651.
The relatively small diffuse function-augmented basis set, 3-21+G, describes anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.
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Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-Consistent Molecular Orbital Methods 25. Supplementary Functions for Gaussian Basis Sets J. Chem. Phys. 1984, 80, 3265 DOI: 10.1063/1.447079
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Self-consistent molecular orbital methods. 25. Supplementary functions for Gaussian basis sets
Frisch, Michael J.; Pople, John A.; Binkley, J. Stephen
Journal of Chemical Physics (1984), 80 (7), 3265-9CODEN: JCPSA6; ISSN:0021-9606.
Std. sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6-31G and 6-311G basis sets. Preliminary applications of the modified basis sets to the calcn. of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.
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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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(a) Glendening, E. D.; Landis, C. R.; Weinhold, F. NBO 6.0: Natural Bond Orbital Analysis Program J. Comput. Chem. 2013, 34, 1429– 1437 DOI: 10.1002/jcc.23266
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NBO 6.0: Natural bond orbital analysis program
Glendening, Eric D.; Landis, Clark R.; Weinhold, Frank
Journal of Computational Chemistry (2013), 34 (16), 1429-1437CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
We describe principal features of the newly released version, NBO 6.0, of the natural bond orbital anal. program, that provides novel "link-free" interactivity with host electronic structure systems, improved search algorithms and labeling conventions for a broader range of chem. species, and new anal. options that significantly extend the range of chem. applications. We sketch the motivation and implementation of program changes and describe newer anal. options with illustrative applications. © 2013 Wiley Periodicals, Inc.
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(b) Glendening, E. D., Jr.; Badenhoop, K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F.NBO 6.0; Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2013.
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Weinhold, F.; Landis, C. R. Discovering Chemistry with Natural Bond Orbitals; Wiley, 2012.
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Silverman, G. S.; Rakita, P. E. Handbook of Grignard Reagents; CRC Press: New York, 1996.
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Vestergren, M.; Eriksson, J.; Håkansson, M. Absolute Asymmetric Synthesis of “Chiral-at-Metal” Grignard Reagents and Transfer of the Chirality to Carbon Chem. - Eur. J. 2003, 9, 4678– 4686 DOI: 10.1002/chem.200305003
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Absolute asymmetric synthesis of "chiral-at-metal" Grignard reagents and transfer of the chirality to carbon
Vestergren, Marcus; Eriksson, Johan; Hakansson, Mikael
Chemistry--A European Journal (2003), 9 (19), 4678-4686CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
Two new six-coordinate Grignard reagents, cis-[(p-CH3C6H4)MgBr(dme)2] (1) and cis-[MgCH3(THF)(dme)2]I (2), were synthesized and their crystal structures were detd. Both reagents are cis-octahedral and therefore chiral. They crystallize as conglomerates and racemize rapidly in soln. By using these properties, the abs. asym. synthesis of specifically the Δ or the Λ enantiomer was achieved for both Grignard reagents. Enantiopure 1 and 2 were then reacted with butyraldehyde or benzaldehyde to give the corresponding alc. in up to 22% enantiomeric excess. At -60°, the Grignard reagents crystallize as racemic phases instead of conglomerates. Consequently, the crystal structures of rac-cis-[(p-CH3C6H4)MgBr(dme)2].DME (3) and rac-cis-[MgCH3(THF)(dme)2]I (4) could be detd.
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Vestergren, M.; Eriksson, J.; Håkansson, M. Chiral cis-Octahedral Grignard reagents J. Organomet. Chem. 2003, 681, 215– 224 DOI: 10.1016/S0022-328X(03)00616-8
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Chiral cis-octahedral Grignard reagents
Vestergren, Marcus; Eriksson, Johan; Hakansson, Mikael
Journal of Organometallic Chemistry (2003), 681 (1-2), 215-224CODEN: JORCAI; ISSN:0022-328X. (Elsevier Science B.V.)
Three chiral cis-octahedral Grignard reagents were synthesized and structurally characterized by x-ray diffraction methods. Crystals of cis-[PrMgBr(dme)2] (1), cis-[(i-Pr)MgBr(dme)2] (2) and cis-[(allyl)MgBr(dme)2] (3) were prepd. from neat 1,2-dimethoxyethane (DME) and are all racemic. Synthesis and structural characterization of trans-[MgBr2(tmeda)2] (4) and cis-[MgBr2(dme)2] (5) indicated that bidentate tertiary amino ligands may be less well suited for the prepn. of cis-octahedral Grignard reagents. However, the crystal structures of cis-[MgBr2(trigly)] (6) and [Mg2(μ-Br)2(trigly)2][Mg2(μ-Me)2Br4] (7; trigly = triglyme), suggest that the triglyme ligand may be ideally suited for this purpose.
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Vestergren, M.; Gustafsson, B.; Davidsson, Ö.; Håkansson, M. Octahedral Grignard Reagents Can Be Chiral at Magnesium Angew. Chem., Int. Ed. 2000, 39, 3435– 3437 DOI: 10.1002/1521-3773(20001002)39:19<3435::AID-ANIE3435>3.0.CO;2-A
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Harrison-Marchand, A.; Mongin, F. Mixed AggregAte (MAA): A Single Concept for All Dipolar Organometallic Aggregates. 1. Structural Data Chem. Rev. 2013, 113, 7470– 7562 DOI: 10.1021/cr300295w
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Mixed AggregAte (MAA): A Single Concept for All Dipolar Organometallic Aggregates. 1. Structural Data
Harrison-Marchand, Anne; Mongin, Florence
Chemical Reviews (Washington, DC, United States) (2013), 113 (10), 7470-7562CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. This review will focus on structures of organo(bi)metallic species for which the ligands mainly realize nucleophilic transfers for addn. or deprotonation purposes.
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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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Hölzer, B.; Hoffmann, R. W. Kumada-Corriu Coupling of Grignard reagents, Probed with a Chiral Grignard Reagent Chem. Commun. 2003, 2, 732– 733 DOI: 10.1039/b300033h
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King, A. O.; Okukado, N.; Negishi, E.-i. Highly General Stereo-, Regio-, and Chemo-Selective Synthesis of Terminal and Internal Conjugated Enynes by the Pd-Catalysed Reaction of Alkynylzinc Reagents with Alkenyl Halides J. Chem. Soc., Chem. Commun. 1977, 683– 684 DOI: 10.1039/c39770000683
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Highly general stereo-, regio-, and chemo-selective synthesis of terminal and internal conjugated enynes by the palladium-catalyzed reaction of alkynylzinc reagents with alkenyl halides
King, Anthony O.; Okukado, Nobuhisa; Negishi, Eiichi
Journal of the Chemical Society, Chemical Communications (1977), (19), 683-4CODEN: JCCCAT; ISSN:0022-4936.
RC≡CZnCl [R = H, Bu, (CH2)4Me], prepd. by reaction of RC≡CLi with ZnCl2, underwent palladium phosphine complex-catalyzed condensation with R1CR2:CHR3 (R1 = H, R2 = Bu, R3 = I; R1 = Bu, R2 = H, Et, R3 = I; R1 = CO2Me, R1 = Me, R3 = Br) to give ≥65% R1CR2:CHC≡CR, the stereospecificity of the reaction being ≥97%.
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Negishi, E.-i. Palladium- or Nickel-Catalyzed Cross Coupling. A New Selective Method for Carbon-Carbon Bond Formation Acc. Chem. Res. 1982, 15, 340– 348 DOI: 10.1021/ar00083a001
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Palladium- or nickel-catalyzed cross coupling. A new selective method for carbon-carbon bond formation
Negishi, Eiichi
Accounts of Chemical Research (1982), 15 (11), 340-8CODEN: ACHRE4; ISSN:0001-4842.
A review with 88 refs.
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García-Melchor, M.; Fuentes, B.; Lledós, A.; Casares, J. A.; Ujaque, G.; Espinet, P. Cationic Intermediates in the Pd-Catalyzed Negishi Coupling. Kinetic and Density Functional Theory Study of Alternative Transmetalation Pathways in the Me–Me Coupling of ZnMe₂ and trans-[PdMeCl(PMePh₂)₂] J. Am. Chem. Soc. 2011, 133, 13519– 13526 DOI: 10.1021/ja204256x
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Cationic Intermediates in the Pd-Catalyzed Negishi Coupling. Kinetic and Density Functional Theory Study of Alternative Transmetalation Pathways in the Me-Me Coupling of ZnMe2 and trans-[PdMeCl(PMePh2)2]
Garcia-Melchor, Max; Fuentes, Beatriz; Lledos, Agusti; Casares, Juan A.; Ujaque, Gregori; Espinet, Pablo
Journal of the American Chemical Society (2011), 133 (34), 13519-13526CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The complexity of the transmetalation step in a Pd-catalyzed Negishi reaction has been investigated by combining expt. and theor. calcns. The reaction between trans-[PdMeCl(PMePh2)2] and ZnMe2 in THF as solvent was analyzed. The results reveal some unexpected and relevant mechanistic aspects not obsd. for ZnMeCl as nucleophile. The operative reaction mechanism is not the same when the reaction is carried out in the presence or in the absence of an excess of phosphine in the medium. In the absence of added phosphine an ionic intermediate with THF as ligand ([PdMe(PMePh2)2(THF)]+) opens ionic transmetalation pathways. In contrast, an excess of phosphine retards the reaction because of the formation of a very stable cationic complex with three phosphines ([PdMe(PMePh2)3]+) that sequesters the catalyst. These ionic intermediates had never been obsd. or proposed in palladium Negishi systems and warn on the possible detrimental effect of an excess of good ligand (as PMePh2) for the process. In contrast, the ionic pathways via cationic complexes with one solvent (or a weak ligand) can be noticeably faster and provide a more rapid reaction than the concerted pathways via neutral intermediates. Theor. calcns. on the real mols. reproduce well the exptl. rate trends obsd. for the different mechanistic pathways.
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The Journal of Physical Chemistry B

Cite this: J. Phys. Chem. B 2017, 121, 16, 4226–4237

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https://doi.org/10.1021/acs.jpcb.7b02716

Published March 30, 2017

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Abstract
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Scheme 1
Scheme 1. Schlenk Equilibria
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Figure 1
Figure 1. Simulation box used in this study. The atoms of the Grignard reagent are represented by spheres and the THF solvent molecules by sticks in licorice and red. Hydrogen atoms of THF are not shown for clarity.
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Figure 2
Figure 2. Most likely solvation structures for MgCl₂ (left), Mg(CH₃)₂ (middle), and (CH₃)MgCl (right). The dotted black lines represent coordination of the ligands to the Mg center.
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Figure 3
Figure 3. FES of the Schlenk equilibrium. The CVs for this representation are the difference in Mg–CH₃ coordination number between Mg² and Mg¹ (CV1) and the THF coordination number to Mg¹ (CV2). The chemical structures drawn in the figure depict the most representative species obtained for wells A–E.
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Figure 4
Figure 4. Solvated D^ClCl structures found by metadynamics simulations (left) and the corresponding FES (right). CV1 and CV2 are defined as the coordination numbers of THF at Mg¹ and Mg², respectively, following eq 1. The two minima b correspond to the chemically equivalent D₁₂^ClCl and D₂₁^ClCl structures. Only D₁₂^ClCl is shown for simplicity.
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Figure 5
Figure 5. (Top) Mg–Cl distance distributions in D^ClCl dimeric structures. (Bottom) Mg¹–Cl (blue) and Mg²–Cl (red) distance distributions in D₁₂^ClCl. Mg–Cl bond cleavage is observed when the Mg–Cl distance is larger than 3.7 Å.
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Figure 6
Figure 6. FES for the methyl bridged dimer D^ClMe equilibria using the THF coordination number to Mg¹ (CV1) and the THF coordination number to Mg² (CV2) as variables, together with the most representative species obtained for wells a–d.
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Figure 7
Figure 7. Orientation of the methyl group in D^ClMe as a function of the solvation state, represented by φ₁ and φ₂. A larger φ angle is indicative of a stronger Mg–CH₃ interaction.
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Figure 8
Figure 8. Intermediates involved in the Schlenk equilibrium according to dynamic simulations. Arrows indicate the chemical transformations along the main pathway leading from monomeric reactants to products (inside of solid squares). The most stable dichloride and methyl chloride bridged dinuclear species are inside of dashed squares.
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Figure 9
Figure 9. Snapshots for the methyl transfer reaction in D₁₂^ClCl (Mg¹ on the left-hand side and Mg² on the right for all snapshots): (1) initial D₁₂^ClCl structure, (2) transition state of the transmetalation reaction, (3) D₁₂^ClMe, (4) solvent loss to form D₁₁^ClMe, and (5) solvent addition to form D₂₁^ClMe and (6) D₁₁^ClMeTHF. The atoms for the Grignard reagent and the coordinating THF molecules are depicted as balls and/or sticks and colored according to standard color codes. Selected neighboring solvent molecules are drawn with thin lines.
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References
This article references 86 other publications.
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  Regioselective double alkylation of styrenes with alkyl Grignard reagents and alkyl bromides having a heteroatom functional group at the β-position has been achieved by the use of a titanocene catalyst in THF. When ether was used instead of THF as a solvent, monoalkylation by substitution of a vinylic hydrogen atom with an alkyl group proceeded under similar conditions. These reactions involve the addn. of alkyl radicals to styrenes to form benzylic radical intermediates.
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  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtl2ltrjK&md5=982dc11ef55a2051938892f3997965d3
10. 10
  Jana, R.; Pathak, T. P.; Sigman, M. S. Advances in Transition Metal (Pd,Ni,Fe)-Catalyzed Cross-Coupling Reactions Using Alkyl-organometallics as Reaction Partners Chem. Rev. 2011, 111, 1417– 1492 DOI: 10.1021/cr100327p
  10
  Advances in Transition Metal (Pd, Ni, Fe)-Catalyzed Cross-Coupling Reactions Using Alkyl-organometallics as Reaction Partners
  Jana, Ranjan; Pathak, Tejas P.; Sigman, Matthew S.
  Chemical Reviews (Washington, DC, United States) (2011), 111 (3), 1417-1492CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review was given discussing the synthesis, stability, and transition metal-catalyzed(Pd, Ni, Fe) cross-coupling of sp3-organonetallics possessing β-H(s) using alkylzinc (Negishi), allylboron (Suzuki-Miyaura), alkylmagnesium (Kumada), alkyltin (Stille), alkylsilicon (Hiyama), and alkylindium. Besides their detailed development and mechanistic investigations, extension to asym. catalysis and applications in total synthesis were described. Organometallic reagents that cannot undergo β-H- elimination were not reviewed comprehensively.
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11. 11
  Cong, X.; Tang, H.; Zeng, X. Regio- and Chemoselective Kumada–Tamao–Corriu Reaction of Aryl Alkyl Ethers Catalyzed by Chromium Under Mild Conditions J. Am. Chem. Soc. 2015, 137, 14367– 14372 DOI: 10.1021/jacs.5b08621
  11
  Regio- and Chemoselective Kumada-Tamao-Corriu Reaction of Aryl Alkyl Ethers Catalyzed by Chromium Under Mild Conditions
  Cong, Xuefeng; Tang, Huarong; Zeng, Xiaoming
  Journal of the American Chemical Society (2015), 137 (45), 14367-14372CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Acting as an environmentally benign synthetic tool, the cross-coupling reactions with aryl ethers via C-O bond activation have attracted broad interest. However, the functionalizations of C-O bonds are mainly limited to nickel catalysis, and selectivity has long been a prominent challenge when several C-O bonds are present in the one mol. We report here the first chromium-catalyzed selective cross-coupling reactions of aryl ethers with Grignard reagents by the cleavage of C-O(alkyl) bonds. Diverse transformations were achieved using simple, inexpensive chromium(II) precatalyst combining imino auxiliary at room temp. It offers a new avenue for buildup functionalized arom. aldehydes with high efficiency and selectivity.
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12. 12
  Neufeld, R.; Teuteberg, T. L.; Herbst-Irmer, R.; Mata, R. A.; Stalke, D. Solution Structures of Hauser Base iPr₂NMgCl and Turbo-Hauser Base iPr₂NMgCl·LiCl in THF and the Influence of LiCl on the Schlenk-Equilibrium J. Am. Chem. Soc. 2016, 138, 4796– 4806 DOI: 10.1021/jacs.6b00345
  12
  Solution Structures of Hauser Base iPr2NMgCl and Turbo-Hauser Base iPr2NMgCl·LiCl in THF and the Influence of LiCl on the Schlenk-Equilibrium
  Neufeld, Roman; Teuteberg, Thorsten L.; Herbst-Irmer, Regine; Mata, Ricardo A.; Stalke, Dietmar
  Journal of the American Chemical Society (2016), 138 (14), 4796-4806CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Grignard reagents that are at the simplest level described as "RMgX" (where R is an org. substituent and X a halide) are one of the most widely utilized classes of synthetic reagents. Lately, esp. Grignard reagents with amido ligands of the type R1R2NMgX, so-called Hauser bases, and their Turbo analog R1R2NMgX·LiCl play an outranging role in modern synthetic chem. However, because of their complex soln. behavior, where Schlenk-type equil. are involved, very little is known about their structure in soln. Esp. the impact of LiCl on the Schlenk-equil. was still obscured by complexity and limited anal. access. Herein, we present unprecedented insights into the soln. structure of the Hauser base iPr2NMgCl 1 and the Turbo-Hauser base iPr2NMgCl·LiCl 2 at various temps. in THF-d8 soln. by employing a newly elaborated diffusion ordered spectroscopy (DOSY) NMR method hand-in-hand with theor. calcns.
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13. 13
  Seyferth, D. The grignard reagents Organometallics 2009, 28, 1598– 1605 DOI: 10.1021/om900088z
  13
  The Grignard Reagents
  Seyferth, Dietmar
  Organometallics (2009), 28 (6), 1598-1605CODEN: ORGND7; ISSN:0276-7333. (American Chemical Society)
  A review of prepn. and reactions of Grignard reagents.
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14. 14
  Guggenberger, L. J.; Rundle, R. E. Crystal Structure of the Ethyl Grignard Reagent, Ethylmagnesium Bromide Dietherate J. Am. Chem. Soc. 1968, 90, 5375– 5378 DOI: 10.1021/ja01022a007
  14
  Crystal structure of the ethyl Grignard reagent, ethylmagnesium bromide dietherate
  Guggenberger, L. J.; Rundle, R. E.
  Journal of the American Chemical Society (1968), 90 (20), 5375-8CODEN: JACSAT; ISSN:0002-7863.
  An x-ray diffraction study of the Et Grignard reagent in Et2O was undertaken to establish the structure of this reagent in the solid state. Crystals of EtMgBr.2Et2O are monoclinic with space group P21/c and 4 formula units per cell of dimensions a 13.18, b 10.27, c 11.42 A., and β 103.3°. The structure consists of the packing of discrete monomer units with a Br atom, an Et group, and 2 ether groups tetrahedrally coordinated to a Mg atom.
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15. 15
  Vallino, M. Structure Cristalline de CH₃MgBr·3 C₄H₈O J. Organomet. Chem. 1969, 20, 1– 10 DOI: 10.1016/S0022-328X(00)80080-7
  15
  Crystalline structure of CH3MgBr.3C4H8O[methylmagnesium bromide-tritetrahydrofuran complex]
  Vallino, Maurice
  Journal of Organometallic Chemistry (1969), 20 (1), 1-10CODEN: JORCAI; ISSN:0022-328X.
  The structure of MeMgBr.-3C4H8O was solved by single crystal x-ray diffraction techniques. The 5-coordinate Mg is at the center of a trigonal bipyramid. Me and Br are disordered and tetrahydrofuran rings distorded. A rigid body least squares refinement program is described.
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16. 16
  Toney, J.; Stucky, G. D. The Stereochemistry of Polynuclear Compounds of the Main Group Elements [C₂H₅Mg₂Cl₃(C₄H₈O)₃]₂, a Tetrameric Grignard Reagent J. Organomet. Chem. 1971, 28, 5– 20 DOI: 10.1016/S0022-328X(00)81569-7
  16
  Stereochemistry of polynuclear compounds of the main group elements [C2H5Mg2Cl3(C4H8O)3]2, a tetrameric Grignard reagent
  Stucky, Galen D.; Toney, Joe D.
  Journal of Organometallic Chemistry (1971), 28 (1), 5-20CODEN: JORCAI; ISSN:0022-328X.
  Reaction of EtCl with Mg in THF yielded a compd. which was detd. by a single-crystal x-ray diffraction study to be a tetrameric Grignard reagent, [EtMg2Cl3(THF)3]2. This organometallic complex crystallizes into the space group P21/c with Z = 2. The cell dimensions are: a = 12.128(3), b = 16.750(4), c = 10.972(3) Å, β = 104.02(2)°. A full matrix least-squares refinement based upon 919 obsd. reflections measured by diffractometer techniques yielded a final unweighted R factor of 0.102. The mol. lies on a crystallog. inversion center and contains a total of 5 4-membered bridging units consisting of Mg and Cl atoms. The 2 independent Mg atoms in [EtMg2Cl3(THF)3]2 exhibit 5 and 6 coordination. Two 3-coordinated bridging Cl atoms are also present in the mol.
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17. 17
  Blasberg, F.; Bolte, M.; Wagner, M.; Lerner, H.-W. An Approach to Pin Down the Solid-State Structure of the “Turbo Grignard Organometallics 2012, 31, 1001– 1005 DOI: 10.1021/om201080t
  17
  An Approach to Pin Down the Solid-State Structure of the "Turbo Grignard"
  Blasberg, Florian; Bolte, Michael; Wagner, Matthias; Lerner, Hans-Wolfram
  Organometallics (2012), 31 (3), 1001-1005CODEN: ORGND7; ISSN:0276-7333. (American Chemical Society)
  Single crystals of [iPrMgCl(THF)]2[MgCl2(THF)2]2 were obtained by layering a THF soln. of the "turbo Grignard" iPrMgCl·LiCl with Et2O at ambient temp. The isolated 1:1 Grignard-MgCl2 adduct is isostructural with cryst. compds. which were obtained from pure RMgCl solns. (R = Me, tBu, Ph, Bn). The structure of [iPrMgCl(THF)]2[MgCl2(THF)2]2 reveals an open-cube motif (monoclinic, P21/c). When dioxane was added to a THF soln. of iPrMgCl·LiCl, single crystals of [LiCl(THF)2]2 and [iPr2Mg(dioxane)]∞ (monoclinic, C2/c) were isolated. From 1:1 mixts. of (Me3Si)2CHMgCl (DisylMgCl) and LiCl (prepd. analogously to iPrMgCl·LiCl) two different Grignard compds., the monomer [DisylMgCl(THF)2] (monoclinic, P21) and the dimer [DisylMgCl(THF)]2 (monoclinic, P21/c), were isolated as single crystals. During studies, two oxidn. products of iPrMgCl and DisylMgCl, resp., resulting from oxygen insertion, were obtained and structurally characterized. Colorless plates of [iPrMg(OiPr)]4 (monoclinic, P21/m) grew from a THF/benzene soln. The dimeric alkoxide {[DisylOMgCl][LiCl(THF)2]}2 (monoclinic, C2/c), which was obtained from DisylMgCl·LiCl by oxidn. through residual oxygen, displays the only structure in which incorporation of LiCl in the mol. framework of a Mg alkoxide was obsd.
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18. 18
  Smith, M. B.; Becker, W. E. The constitution of the grignard reagent—III:The reaction between R₂Mg and MgX₂ in tetrahydrofuran Tetrahedron 1967, 23, 4215– 4227 DOI: 10.1016/S0040-4020(01)88819-0
  There is no corresponding record for this reference.
19. 19
  Smith, M. B.; Becker, W. E. The constitution of the Grignard Reagent - I. The reaction between diethyl magnesium and magnesium bromide in diethyl ether Tetrahedron Lett. 1965, 6, 3843– 3847 DOI: 10.1016/S0040-4039(01)89135-8
  There is no corresponding record for this reference.
20. 20
  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
  20
  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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21. 21
  Schlenk, W.; Schlenk, W. Über die Konstitution der Grignardschen Magnesiumverbindungen Ber. Dtsch. Chem. Ges. B 1929, 62, 920– 924 DOI: 10.1002/cber.19290620422
  21
  The constitution of the Grignard magnesium derivatives
  Schlenk, W.; Schlenk, Wilh., Jr.
  Berichte der Deutschen Chemischen Gesellschaft [Abteilung] B: Abhandlungen (1929), 62B (), 920-4CODEN: BDCBAD; ISSN:0365-9488.
  Several Grignard compds. have been prepd., then fractionally pptd. from their Et2O soln. by means of O(CH2CH2)2O. The Mg:X ratios of the fractions have been examd. Grignard compds. must be represented by 2RMgX .dblharw. MgR2 + MgX2. For EtI, the compn. of the Grignard deriv. would be: 6EtMgI + 4MgEt2 + 4MgI2. For PhBr: PhMgBr + 0.115MgPh2 + 0.115MgBr2.
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22. 22
  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
  22
  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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23. 23
  Sobota, P.; Duda, B. Influence of MgCl₂ on Grignard Reagent Composition in Tetrahydrofuran. III J. Organomet. Chem. 1987, 332, 239– 245 DOI: 10.1016/0022-328X(87)85090-8
  23
  Influence of magnesium chloride on Grignard reagent composition in tetrahydrofuran. III
  Sobota, Piotr; Duda, Barbara
  Journal of Organometallic Chemistry (1987), 332 (3), 239-45CODEN: JORCAI; ISSN:0022-328X.
  Reaction of [MgCl2(THF)2] with [NBu4][BF4] yields the compds. [NBu4][MgCl4] (I) and [Mg(THF)6][BF4]2. After addn. of dioxane (C4H8O2) the reaction equil. shifts in the opposite direction. The formation of [MgCl2(C4H8O2)2] in soln. does not require the presence of MgCl2. This compd. may be formed in the reaction of dioxane with the ionic or mol. species formed by the magnesium atom in soln. The [NBu4][BF4] salt also reacts with the Grignard reagent to produce I which confirms that there is a new equil. between [Mg(R)X(THF)n] and [MgR2(THF)2], [MgCl4]2-, and [Mg(THF6)]2+. Bis(tetrahydrofuran)magnesium dichloride, because of its reactivity is only stable in Grignard reagent. For that reason the compn. of the Grignard reagent in soln. is best described as an equil. between [Mg(R)X(THF)n] and [(THF)4Mg(μ-Cl)2MgR2] and [RMg2(μ-Cl)3(THF)5] rather than as a Schlenk equil.
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24. 24
  Sakamoto, S.; Imamoto, T.; Yamaguchi, K. Constitution of Grignard Reagent RMgCl in Tetrahydrofuran Org. Lett. 2001, 3, 1793– 1795 DOI: 10.1021/ol010048x
  24
  Constitution of Grignard Reagent RMgCl in Tetrahydrofuran
  Sakamoto, Shigeru; Imamoto, Tsuneo; Yamaguchi, Kentaro
  Organic Letters (2001), 3 (12), 1793-1795CODEN: ORLEF7; ISSN:1523-7060. (American Chemical Society)
  The constitution of Grignard reagent, RMgCl (R = Me, tBu, Ph, benzyl), was investigated in the solid state by x-ray crystallog. and in THF by coldspray ionization mass spectrometry (CSI-MS). Three types of crystal structures, (a) [Mg2(μ-Cl3)(THF)6]+[RMgCl2(THF)]-, (b) R2Mg4Cl6(THF)6, and (c) [2Mg2(μ-Cl3)(THF)6]+[R4Mg2Cl2]2-, were identified, and MeMg2(μ-Cl3)(THF)4-6 were detected as major species of MeMgCl in soln.
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25. 25
  Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas Phys. Rev. B 1964, 136, 864– 871 DOI: 10.1103/PhysRev.136.B864
  There is no corresponding record for this reference.
26. 26
  Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects Phys. Rev. A 1965, 140, 1133– 1138 DOI: 10.1103/PhysRev.140.A1133
  There is no corresponding record for this reference.
27. 27
  Jiménez-Halla, J. O. C.; Bickelhaupt, F. M.; Solà, M. Organomagnesium clusters: Structure, stability, and bonding in archetypal models J. Organomet. Chem. 2011, 696, 4104– 4111 DOI: 10.1016/j.jorganchem.2011.06.014
  27
  Organomagnesium clusters: Structure, stability, and bonding in archetypal models
  Jimenez-Halla, J. Oscar C.; Bickelhaupt, F. Matthias; Sola, Miquel
  Journal of Organometallic Chemistry (2011), 696 (25), 4104-4111CODEN: JORCAI; ISSN:0022-328X. (Elsevier B.V.)
  The mol. structure and the nature of the chem. bond in the monomers and tetramers of the Grignard reagent CH3MgCl as well as MgX2 (X = H, Cl, and CH3) were studied at the BP86/TZ2P level of theory. For the tetramers, the stability of three possible mol. structures of C2h, D2h, and Td symmetry are discussed. The most stable structure for (MgCl2)4 is D2h, the one for (MgH2)4 is C2h, and that of (CH3MgCl)4 is Td. The latter is 38 kcal/mol more stable with chlorines in bridge positions and Me groups coordinated to a Mg vertex than vice versa. Through a quant. energy decompn. anal. (EDA) that the tetramerization energy is predominantly composed of electrostatic attraction ΔVelstat (60% of all bonding terms ΔVelstat + ΔEoi) although the orbital interaction ΔEoi also provides an important contribution (40%) were found.
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28. 28
  Lioe, H.; White, J. M.; O’Hair, R. A. J. Preference for bridging versus terminal ligands in magnesium dimers J. Mol. Model. 2011, 17, 1325– 1334 DOI: 10.1007/s00894-010-0834-1
  28
  Preference for bridging versus terminal ligands in magnesium dimers
  Lioe, Hadi; White, Jonathan M.; O'Hair, Richard A. J.
  Journal of Molecular Modeling (2011), 17 (6), 1325-1334CODEN: JMMOFK; ISSN:0948-5023. (Springer)
  Magnesium dimers play important roles in inorg. and organometallic chem. This study evaluates the inherent bridging ability of a range of different ligands in magnesium dimers. In the first part, the Cambridge Structural Database is interrogated to establish the frequency of different types of ligands found in bridging vs. terminal positions in two key structural motifs: one in which there are two bridging ligands (the D 2h "Mg2(μ-X2)" structure); the other in which there are three bridging ligands (the C 3v "Mg2(μ-X3)" structure). The most striking finding from the database search is the overwhelming preference for magnesium dimers possessing two bridging ligands. The most common bridging ligands are C-, N-, and O-based. In the second part, DFT calcns. (at the B3LYP/6-311+G(d) level of theory) are carried out to examine a wider range of structural types for dimers consisting of the stoichiometries Mg2Cl3R and Mg2Cl2R2, where R = CH3, SiH3, NH2, PH2, OH, SH, CH2CH3, CH=CH2, C CH, Ph, OAc, F and Br. Consistent with the database search, the most stable magnesium dimers are those that contain two bridging ligands. Furthermore, it was demonstrated that the electronic effect of the bridging ligands is important in influencing the stability of the magnesium dimers. The preference for a bridging ligand, which reflects its ability to stabilize a magnesium dimer, follows the order: OH > NH2 > C CH > SH > Ph > Br > PH2 = CH=CH2 > CH2CH3 > CH3 > SiH3. Finally, the role that the ether solvent Me2O has on the stability of isomeric Mg2Cl2Me2 dimers was studied. It was found that the first solvent mol. stabilizes the dimers, while the second solvent mol. can either have a stabilizing or destabilizing effect, depending on the isomer structure.
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29. 29
  Henriques, A. M.; Barbosa, A. G. H. Chemical Bonding and the Equilibrium Composition of Grignard Reagents in Ethereal Solutions J. Phys. Chem. A 2011, 115, 12259– 12270 DOI: 10.1021/jp202762p
  29
  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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30. 30
  Ramirez, F.; Sarma, R.; Chaw, F.; McCaffrey, T. M. Magnesium bromide-tetrahydrofuran complexes: bis(tetrahydrofuran)magnesium bromide, tris(tetrahydrofuran)magnesium bromide, tetrakis(tetrahydrofuran)magnesium bromide, and diaquotetrakis(tetrahydrofuran)magnesium bromide. A reagent for the preparation of anhydrous magnesium phosphodiester salts J. Am. Chem. Soc. 1977, 99, 5285– 5289 DOI: 10.1021/ja00458a010
  There is no corresponding record for this reference.
31. 31
  Pirinen, S.; Koshevoy, I. O.; Denifl, P.; Pakkanen, T. T. A Single-Crystal Model for MgCl₂ – Electron Donor Support Materials: [Mg₃Cl₅(THF)₄Bu]₂ (Bu = n-Butyl) Organometallics 2013, 32, 4208– 4213 DOI: 10.1021/om400407p
  There is no corresponding record for this reference.
32. 32
  Ashby, E. C.; Becker, W. E. Concerning the Structure of the Grignard Reagent J. Am. Chem. Soc. 1963, 85, 118– 119 DOI: 10.1021/ja00884a032
  32
  The structure of the Grignard reagent
  Ashby, E. C.; Becker, W. E.
  Journal of the American Chemical Society (1963), 85 (), 118-19CODEN: JACSAT; ISSN:0002-7863.
  cf. Dessy, et al., CA 51, 16283e. The observation that the Grignard reagent [prepd. by the action of alkyl halide with Mg in tetrahydrofuran (THF) or ether; in THF the soln. prepd. from EtCl and Mg was identical to the soln. prepd. from Et2Mg and MgCl2 with respect to infrared spectra, conductance and dipole moment], although dimeric in Et2O, was monomeric in THF, and fractional crystn. of EtMgCl in THF produced EtMg2Cl3 and Et2Mg in quant. yield, proved that there was alkyl exchange in Grignard solns., and the predominant species in soln. was RMgX, as formulated by Schlenk and Schlenk (CA 23, 5159). The equil. could be extended as: 3RMgX .rdblhar. 3/2 R2Mg + 3/2 MgX2 .rdblhar. RMg2X3 + R2Mg. RMg2X3 was formed on crystn. through a combination of RMgX and MgX2 in THF-C6H6 system. Out of the two most logical dimeric structures I and II, in view of the above results I was preferred, though the work of Dessy (CA 55, 10303h, D. and Jones, CA 55, 11009d, D., et al., loc. cit.) leads to preference of II. This was supported by detn. of mol. aggregation (found to be dimeric) of mesitylmagnesium bromide in Et2O. If Grignard compds. in Et2O soln. existed as II, a severe steric problem would arise from a Mg atom surrounded by two mesityl groups and two Br atoms. Thus, it would appear that the equil. which existed in Et2O was similar to that in THF.
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33. 33
  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
  33
  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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34. 34
  Tobisu, M.; Chatani, N. Cross-Couplings Using Aryl Ethers via C–O Bond Activation Enabled by Nickel Catalysts Acc. Chem. Res. 2015, 48, 1717– 1726 DOI: 10.1021/acs.accounts.5b00051
  34
  Cross-Couplings Using Aryl Ethers via C-O Bond Activation Enabled by Nickel Catalysts
  Tobisu, Mamoru; Chatani, Naoto
  Accounts of Chemical Research (2015), 48 (6), 1717-1726CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  A review. Arene synthesis has been revolutionized by the invention of catalytic cross-coupling reactions, wherein aryl halides can be coupled with organometallic and org. nucleophiles. Although the replacement of aryl halides with phenol derivs. would lead to more economical and ecol. methods, success has been primarily limited to activated phenol derivs. such as triflates. Aryl ethers arguably represent one of the most ideal substrates in terms of availability, cost, safety, and atom efficiency. However, the robust nature of the C(aryl)-O bonds of aryl ethers renders it extremely difficult to use them in catalytic reactions among the phenol derivs. In 1979, Wenkert reported a seminal work on the nickel-catalyzed cross-coupling of aryl ethers with Grignard reagents. However, it was not until 2004 that the unique ability of a low-valent nickel species to activate otherwise unreactive C(aryl)-O bonds was appreciated with Dankwardt's identification of the Ni(0)/PCy3 system, which significantly expanded the efficiency of the Wenkert reaction. Application of the nickel catalyst to cross-couplings with other nucleophiles was first accomplished in 2008 by the authors' group using organoboron reagents. Later on, several other nucleophiles, including organozinc reagents, amines, hydrosilane, and hydrogen were shown to be coupled with aryl ethers under nickel catalysis. Despite these advances, progress in this field is relatively slow because of the low reactivity of benzene derivs. (e.g., anisole) compared with polyarom. substrates (e.g., methoxynaphthalene), particularly when less reactive and synthetically useful nucleophiles are used. The "naphthalene problem" has been overcome by the use of N-heterocyclic carbene (NHC) ligands bearing bulky N-alkyl substituents, which enables a wide range of aryl ethers to be coupled with organoboron nucleophiles. Moreover, the use of N-alkyl-substituted NHC ligands allows the use of alkynylmagnesium reagents, thereby realizing the first Sonogashira-type reaction of anisoles. From a mechanistic perspective, nickel-catalyzed cross-couplings of aryl ethers are at a nascent stage, in particular regarding the mode of activation of C(aryl)-O bonds. Oxidative addn. is one plausible pathway, although such a process has not been fully verified exptl. Nickel-catalyzed reductive cleavage of aryl ethers in the absence of an external reducing agent provides strong support for this oxidative addn. process. Several other mechanisms have also been proposed. For example, Martin demonstrated a new possibility of the involvement of a Ni(I) species, which could mediate the cleavage of the C(aryl)-O bond via a redox-neutral pathway. The tolerance of aryl ethers under commonly used synthetic conditions enables alkoxy groups to serve as a platform for late-stage elaboration of complex mols. without any tedious protecting group manipulations. Aryl ethers are therefore not mere economical alternatives to aryl halides but also enable nonclassical synthetic strategies.
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35. 35
  Cahiez, G.; Moyeux, A.; Cossy, J. Grignard Reagents and Non-Precious Metals: Cheap and Eco-Friendly Reagents for Developing Industrial Cross-Couplings. A Personal Account Adv. Synth. Catal. 2015, 357, 1983– 1989 DOI: 10.1002/adsc.201400654
  There is no corresponding record for this reference.
36. 36
  Tasker, S. Z.; Standley, E. A.; Jamison, T. F. Recent Advances in Homogeneous Nickel Catalysis Nature 2014, 509, 299– 309 DOI: 10.1038/nature13274
  36
  Recent advances in homogeneous nickel catalysis
  Tasker, Sarah Z.; Standley, Eric A.; Jamison, Timothy F.
  Nature (London, United Kingdom) (2014), 509 (7500), 299-309CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  A review. Tremendous advances have been made in nickel catalysis over the past decade. Several key properties of nickel, such as facile oxidative addn. and ready access to multiple oxidn. states, have allowed the development of a broad range of innovative reactions. In recent years, these properties have been increasingly understood and used to perform transformations long considered exceptionally challenging. Here we discuss some of the most recent and significant developments in homogeneous nickel catalysis, with an emphasis on both synthetic outcome and mechanism.
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37. 37
  Laio, A.; Parrinello, M. Escaping Free-Energy Minima Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 12562– 12566 DOI: 10.1073/pnas.202427399
  37
  Escaping free-energy minima
  Laio, Alessandro; Parrinello, Michele
  Proceedings of the National Academy of Sciences of the United States of America (2002), 99 (20), 12562-12566CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  We introduce a powerful method for exploring the properties of the multidimensional free energy surfaces (FESs) of complex many-body systems by means of coarse-grained non-Markovian dynamics in the space defined by a few collective coordinates. A characteristic feature of these dynamics is the presence of a history-dependent potential term that, in time, fills the min. in the FES, allowing the efficient exploration and accurate detn. of the FES as a function of the collective coordinates. We demonstrate the usefulness of this approach in the case of the dissocn. of a NaCl mol. in water and in the study of the conformational changes of a dialanine in soln.
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38. 38
  Iannuzzi, M.; Laio, A.; Parrinello, M. Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics Phys. Rev. Lett. 2003, 90, 23– 26 DOI: 10.1103/PhysRevLett.90.238302
  There is no corresponding record for this reference.
39. 39
  Vuilleumier, R.; Sprik, M. Electronic Properties of Hard and Soft Ions in Solution: Aqueous Na⁺ and Ag⁺ Compared J. Chem. Phys. 2001, 115, 3454– 3468 DOI: 10.1063/1.1388901
  39
  Electronic properties of hard and soft ions in solution: Aqueous Na+ and Ag+ compared
  Vuilleumier, Rodolphe; Sprik, Michiel
  Journal of Chemical Physics (2001), 115 (8), 3454-3468CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The electronic structure of model aq. solns. of Na+ and Ag+ is investigated using ab initio mol.-dynamics methods. We compute a no. of electronic response coeffs. in soln., such as global hardness and nuclear Fukui functions. The nuclear Fukui functions are found to be particularly sensitive to the chem. nature of the component species giving for Ag+ a susceptibility 3.5 times the value for a H2O mol. while the result for Na+ is more than a factor of 4 smaller compared to a solvent mol. The electronic structure of the soln. is further characterized by construction of effective MOs and energies. This anal. reveals that the effective HOMO (HOMO) of the hard cation, Na+, remains buried in the valence bands of the solvent, whereas the HOMO of Ag+ is found to mix with the lone pair electrons of its four ligand H2O mols. to form the (global) HOMO of the soln. This observation, highlighting the importance of the electronic structure of the solvent, is used to rationalize the results for the electronic response.
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40. 40
  Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G. A First Principles Molecular Dynamics Simulation of the Hydrated Magnesium Ion Chem. Phys. Lett. 2001, 343, 549– 555 DOI: 10.1016/S0009-2614(01)00735-7
  40
  A first principles molecular dynamics simulation of the hydrated magnesium ion
  Lightstone, F. C.; Schwegler, E.; Hood, R. Q.; Gygi, F.; Galli, G.
  Chemical Physics Letters (2001), 343 (5,6), 549-555CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
  First principles Car-Parrinello mol. dynamics has been used to investigate the solvation of Mg2+ in water. In agreement with expt., we find that the first solvation shell around Mg2+ contains six water mols. in an octahedral arrangement. The electronic structure of first solvation shell water mols. has been examd. with a localized orbital anal. We find that water mols. tend to asym. coordinate Mg2+ through one of the oxygen lone pair orbitals and that the first solvation shell dipole moments increase by 0.2 Debye relative to pure liq. water.
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41. 41
  Bernasconi, L.; Baerends, E. J.; Sprik, M. Long-Range Solvent Effects on the Orbital Interaction Mechanism of Water Acidity Enhancement in Metal Ion Solutions: A Comparative Study of the Electronic Structure of Aqueous Mg and Zn Dications J. Phys. Chem. B 2006, 110, 11444– 11453 DOI: 10.1021/jp0609941
  41
  Long-Range Solvent Effects on the Orbital Interaction Mechanism of Water Acidity Enhancement in Metal Ion Solutions: A Comparative Study of the Electronic Structure of Aqueous Mg and Zn Dications
  Bernasconi, Leonardo; Baerends, Evert Jan; Sprik, Michiel
  Journal of Physical Chemistry B (2006), 110 (23), 11444-11453CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
  We study the dissocn. of water coordinated to a divalent metal ion center, M2+ = Mg2+, Zn2+ using d. functional theory (DFT) and ab initio mol. dynamics (AIMD) simulations. First, the proton affinity of a coordinated OH- group is computed from gas-phase M2+(H2O)5(OH-), which yields a relative higher gas-phase acidity for a Zn2+-coordinated as compared to a Mg2+-coordinated water mol., ΔpKagp = 5.3. We explain this difference on the basis of a gain in stabilization energy of the Zn2+(H2O)5(OH-) system arising from direct orbital interaction between the coordinated OH- and the empty 4s state of the cation. Next, we compute the acidity of coordinated water mols. in soln. using free-energy thermodn. integration with constrained AIMD. This approach yields pKa Mg2+ = 11.2 and pKa Zn2+ = 8.4, which compare favorably to exptl. data. Finally, we examine the factors responsible for the apparent decrease in the relative Zn2+-coordinated water acidity in going from the gas-phase (ΔpKagp = 5.3) to the solvated (ΔpKa = 2.8) regime. We propose two simultaneously occurring solvation-induced processes affecting the relative stability of Zn2+(H2O)5(OH-), namely: (a) redn. of the Zn 4s character in soln. states near the bottom of the conduction band; (b) hybridization between OH- orbitals and valence-band states of the solvent. Both effects contribute to hindering the OH- → Zn2+ charge transfer, either by making it energetically unfavorable or by delocalizing the ligand charge d. over several water mols.
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42. 42
  Blumberger, J.; Bernasconi, L.; Tavernelli, I.; Vuilleumier, R.; Sprik, M. Electronic Structure and Solvation of Copper and Silver Ions: A Theoretical Picture of a Model Aqueous Redox Reaction J. Am. Chem. Soc. 2004, 126, 3928– 3938 DOI: 10.1021/ja0390754
  42
  Electronic Structure and Solvation of Copper and Silver Ions: A Theoretical Picture of a Model Aqueous Redox Reaction
  Blumberger, Jochen; Bernasconi, Leonardo; Tavernelli, Ivano; Vuilleumier, Rodolphe; Sprik, Michiel
  Journal of the American Chemical Society (2004), 126 (12), 3928-3938CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Electronic states and solvation of Cu and Ag aqua ions are investigated by comparing the Cu2+ + e- → Cu+ and Ag2+ + e- → Ag+ redox reactions using d. functional-based computational methods. The coordination no. of aq. Cu2+ is found to fluctuate between 5 and 6 and reduces to 2 for Cu+, which forms a tightly bound linear dihydrate. Redn. of Ag2+ changes the coordination no. from 5 to 4. The energetics of the oxidn. reactions is analyzed by comparing vertical ionization potentials, relaxation energies, and vertical electron affinities. The model is validated by a computation of the free energy of the full redox reaction Ag2+ + Cu+ → Ag+ + Cu2+. Investigation of the one-electron states shows that the redox active frontier orbitals are confined to the energy gap between occupied and empty states of the pure solvent and localized on the metal ion hydration complex. The effect of solvent fluctuations on the electronic states is highlighted in a computation of the UV absorption spectrum of Cu+ and Ag+.
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43. 43
  Guido, C. A.; Pietrucci, F.; Gallet, G. A.; Andreoni, W. The Fate of a Zwitterion in Water from Ab Initio Molecular Dynamics: Monoethanolamine (MEA)-CO₂ J. Chem. Theory Comput. 2013, 9, 28– 32 DOI: 10.1021/ct301071b
  43
  The Fate of a Zwitterion in Water from ab Initio Molecular Dynamics: Monoethanolamine (MEA)-CO2
  Guido, Ciro A.; Pietrucci, Fabio; Gallet, Gregoire A.; Andreoni, Wanda
  Journal of Chemical Theory and Computation (2013), 9 (1), 28-32CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Understanding the fundamental reactions accompanying the capture of carbon dioxide in amine solns. is crit. for the design of high-performance solvents and requires an accurate modeling of the solute-solvent interaction. As a first step toward this goal, using ab initio mol. dynamics (Car-Parrinello) simulations, we investigate a zwitterionic carbamate, a species long proposed as intermediate in the formation of a stable carbamate, in a dil. aq. soln. CO2 release and deprotonation are competitive routes for its dissocn. and are both characterized by free-energy barriers of 6-8 kcal/mol. Water mols. play a crucial role in both pathways, resulting in large entropic effects. This is esp. true in the case of CO2 release, which is accompanied by a strong reorganization of the solvent beyond the first coordination shell, leading to the formation of a water cage entrapping the solute (hydrophobic effect). Our results contrast with the assumptions of implicit solvent models.
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44. 44
  Boero, M.; Ikeshoji, T.; Liew, C. C.; Terakura, K.; Parrinello, M.; Boero, M.; Ikeshoji, T.; Liew, C. C.; Terakura, K. Hydrogen Bond Driven Chemical Reactions: Beckmann Rearrangement of Cyclohexanone Oxime into ε-Caprolactam in Supercritical Water Hydrogen Bond Driven Chemical Reactions: Beckmann Rearrangement of Cyclohexanone Oxime into E-Caprolactam in Supercritical J. Am. Chem. Soc. 2004, 126, 6280– 6286 DOI: 10.1021/ja049363f
  There is no corresponding record for this reference.
45. 45
  Vidossich, P.; Lledós, A.; Ujaque, G. Realistic Simulation of Organometallic Reactivities in Solution by Means of First-Principles Molecular Dynamics. In Computational Studies in Organometallic Chemistry; Macgregor, S. A.; Eisenstein, O., Eds.; Structure and Bonding; Springer International Publishing: Berlin, Germany, 2016; Vol. 167, pp 81– 106.
  There is no corresponding record for this reference.
46. 46
  Vidossich, P.; Lledós, A.; Ujaque, G. First-Principles Molecular Dynamics Studies of Organometallic Complexes and Homogeneous Catalytic Processes Acc. Chem. Res. 2016, 49, 1271– 1278 DOI: 10.1021/acs.accounts.6b00054
  46
  First-Principles Molecular Dynamics Studies of Organometallic Complexes and Homogeneous Catalytic Processes
  Vidossich, Pietro; Lledos, Agusti; Ujaque, Gregori
  Accounts of Chemical Research (2016), 49 (6), 1271-1278CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  A review. Computational chem. is a valuable aid to complement exptl. studies of organometallic systems and their reactivity. It allows probing mechanistic hypotheses and investigating mol. structures, shedding light on the behavior and properties of mol. assemblies at the at. scale. When approaching a chem. problem, the computational chemist has to decide on the theor. approach needed to describe electron/nuclear interactions and the compn. of the model used to approx. the actual system. Both factors det. the reliability of the modeling study. The community dedicated much effort to developing and improving the performance and accuracy of theor. approaches for electronic structure calcns., on which the description of (inter)at. interactions rely. Here, the importance of the model system used in computational studies is highlighted through examples from our recent research focused on organometallic systems and homogeneous catalytic processes. We show how the inclusion of explicit solvent allows the characterization of mol. events that would otherwise not be accessible in reduced model systems (clusters). These include the stabilization of nascent charged fragments via microscopic solvation (notably, hydrogen bonding), transfer of charge (protons) between distant fragments mediated by solvent mols., and solvent coordination to unsatd. metal centers. Furthermore, when weak interactions are involved, we show how conformational and solvation properties of organometallic complexes are also affected by the explicit inclusion of solvent mols. Such extended model systems may be treated under periodic boundary conditions, thus removing the cluster/continuum (or vacuum) boundary, and require a statistical mechanics simulation technique to sample the accessible configurational space. First-principles mol. dynamics, in which at. forces are computed from electronic structure calcns. (namely, d. functional theory), is certainly the technique of choice to investigate chem. events in soln. This methodol. is well established and thanks to advances in both algorithms and computational resources simulation times required for the modeling of chem. events are nowadays accessible, though the computational requirements use to be high. Specific applications reviewed here include mechanistic studies of the Shilov and Wacker processes, speciation in Pd chem., hydrogen bonding to metal centers, and the dynamics of agostic interactions.
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47. 47
  Laio, A.; VandeVondele, J.; Rothlisberger, U. A Hamiltonian Electrostatic Coupling Scheme for Hybrid Car–Parrinello Molecular Dynamics Simulations J. Chem. Phys. 2002, 116, 6941– 6947 DOI: 10.1063/1.1462041
  47
  A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations
  Laio, Alessandro; VandeVondele, Joost; Rothlisberger, Ursula
  Journal of Chemical Physics (2002), 116 (16), 6941-6947CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We present a fully Hamiltonian and computationally efficient scheme to include the electrostatic effects due to the classical environment in a Car-Parrinello mixed quantum mechanics/mol. mechanics (QM/MM) method. The polarization due to the MM atoms close to the quantum system is described by a Coulombic potential modified at short range. The functional form of this potential has to be chosen carefully in order to obtain the correct interaction properties and to prevent an unphys. escape of the electronic d. to the MM atoms (the so-called spill-out effect). The interaction between the QM system and the more distant MM atoms is modeled by a Hamiltonian term explicitly coupling the multipole moments of the quantum charge distribution with the classical point charges. Our approach remedies some of the well known deficiencies of current electrostatic coupling schemes in QM/MM methods, allowing mol. dynamics simulations of mixed systems within a fully consistent and energy conserving approach.
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48. 48
  Moret, M.-E.; Tavernelli, I.; Chergui, M.; Rothlisberger, U. Electron Localization Dynamics in the Triplet Excited State of [Ru(bpy)₃]²⁺ in Aqueous Solution Chem. - Eur. J. 2010, 16, 5889– 5894 DOI: 10.1002/chem.201000184
  48
  Electron localization dynamics in the triplet excited state of [Ru(bpy)3]2+ in aqueous solution
  Moret, Marc-Etienne; Tavernelli, Ivano; Chergui, Majed; Rothlisberger, Ursula
  Chemistry - A European Journal (2010), 16 (20), 5889-5894, S5889/1-S5889/9CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Hybrid DFT/classical mol. dynamics of the long-lived triplet excited state of [Ru(bpy)3]2+ (bpy=2,2'-bipyridine) in aq. soln. is used to investigate the solvent-mediated electron localization and dynamics in the triplet metal-to-ligand charge-transfer (MLCT) state. Our studies reveal a solvent-induced breaking of the coordination symmetry with consequent localization of the photoexcited electron on one or two bipyridine units for the entire length of our simulation, which amts. to several picoseconds. Frequent electronic "hops" between the ligands constituting the pair are obsd. with a characteristic time of approx. half a picosecond.
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49. 49
  Dal Peraro, M.; Llarrull, L. I.; Rothlisberger, U.; Vila, A. J.; Carloni, P. Water-Assisted Reaction Mechanism of Monozinc β-Lactamases J. Am. Chem. Soc. 2004, 126, 12661– 12668 DOI: 10.1021/ja048071b
  49
  Water-Assisted Reaction Mechanism of Monozinc β-Lactamases
  Dal Peraro, Matteo; Llarrull, Leticia I.; Rothlisberger, Ursula; Vila, Alejandro J.; Carloni, Paolo
  Journal of the American Chemical Society (2004), 126 (39), 12661-12668CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Hybrid Car-Parrinello QM/MM calcns. are used to investigate the reaction mechanism of hydrolysis of a common β-lactam substrate (cefotaxime) by the monozinc β-lactamase from Bacillus cereus (BcII). The calcns. suggest a fundamental role for an active site water in the catalytic mechanism. This water mol. binds the zinc ion in the first step of the reaction, expanding the zinc coordination no. and providing a proton donor adequately oriented for the second step. The free energy barriers of the two reaction steps are similar and consistent with the available exptl. data. The conserved hydrogen bond network in the active site, defined by Asp-120, Cys-221, and His-263, not only contributes to orient the nucleophile (as already proposed), but it also guides the second catalytic water mol. to the zinc ion after the substrate is bound. The hydrolysis reaction in water has a relatively high free energy barrier, which is consistent with the stability of cefotaxime in water soln. The modeled Michaelis complexes for other substrates are also characterized by the presence of an ordered water mol. in the same position, suggesting that this mechanism might be general for the hydrolysis of different β-lactam substrates.
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50. 50
  Dal Peraro, M.; Vila, A. J.; Carloni, P.; Klein, M. L. Role of Zinc Content on the Catalytic Efficiency of B1Metallo β-Lactamases J. Am. Chem. Soc. 2007, 129, 2808– 2816 DOI: 10.1021/ja0657556
  50
  Role of Zinc Content on the Catalytic Efficiency of B1 Metallo β-Lactamases
  Dal Peraro, Matteo; Vila, Alejandro J.; Carloni, Paolo; Klein, Michael L.
  Journal of the American Chemical Society (2007), 129 (10), 2808-2816CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Metallo β-lactamases (MβL) are enzymes naturally evolved by bacterial strains under the evolutionary pressure of β-lactam antibiotic clin. use. They have a broad substrate spectrum and are resistant to all the clin. useful inhibitors, representing a potential risk of infection if massively disseminated. The MβL scaffold is designed to accommodate one or two zinc ions able to activate a nucleophilic hydroxide for the hydrolysis of the β-lactam ring. The role of zinc content on the binding and reactive mechanism of action has been the subject of debate and still remains an open issue despite the large amt. of data acquired. We report herein a study of the reaction pathway for binuclear CcrA from Bacteroides fragilis using d. functional theory based quantum mechanics-mol. mechanics dynamical modeling. CcrA is the prototypical binuclear enzyme belonging to the B1 MβL family, which includes several harmful chromosomally encoded and transferable enzymes. The involvement of a second zinc ion in the catalytic mechanism lowers the energetic barrier for β-lactam hydrolysis, preserving the essential binding features found in mononuclear B1 enzymes (BcII from Bacillus cereus) while providing a more efficient single-step mechanism. Overall, this study suggests that uptake of a second equiv. zinc ion is evolutionary favored.
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51. 51
  Cascella, M.; Magistrato, A.; Tavernelli, I.; Carloni, P.; Rothlisberger, U. Role of Protein Frame and Solvent for the Redox Properties of Azurin from Pseudomonas Aeruginosa Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 19641– 19646 DOI: 10.1073/pnas.0607890103
  51
  Role of protein frame and solvent for the redox properties of azurin from Pseudomonas aeruginosa
  Cascella, Michele; Magistrato, Alessandra; Tavernelli, Ivano; Carloni, Paolo; Rothlisberger, Ursula
  Proceedings of the National Academy of Sciences of the United States of America (2006), 103 (52), 19641-19646CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
  We have coupled hybrid quantum mechanics (d. functional theory; Car-Parrinello)/mol. mechanics mol. dynamics simulations to a grand-canonical scheme, to calc. the in situ redox potential of the Cu2+ + - → Cu+ half reaction in azurin from Pseudomonas aeruginosa. An accurate description at atomistic level of the environment surrounding the metal-binding site and finite-temp. fluctuations of the protein structure are both essential for a correct quant. description of the electronic properties of this system. We report a redox potential shift with respect to copper in water of 0.2 eV (exptl. 0.16 eV) and a reorganization free energy λ = 0.76 eV (exptl. 0.6-0.8 eV). The electrostatic field of the protein plays a crucial role in fine tuning the redox potential and detg. the structure of the solvent. The inner-sphere contribution to the reorganization energy is negligible. The overall small value is mainly due to solvent rearrangement at the protein surface.
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52. 52
  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
  52
  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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53. 53
  Gossens, C.; Tavernelli, I.; Rothlisberger, U. Rational Design of Organo-Ruthenium Anticancer Compounds Chimia 2005, 59, 81– 84 DOI: 10.2533/000942905777676795
  There is no corresponding record for this reference.
54. 54
  Metz, D. J.; Glines, A. Density, Viscosity, and Dielectric Constant of Tetrahydrofuran between −78 and 30° J. Phys. Chem. 1967, 71, 1158– 1158 DOI: 10.1021/j100863a067
  There is no corresponding record for this reference.
55. 55
  Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695– 1697 DOI: 10.1103/PhysRevA.31.1695
  55
  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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56. 56
  Martyna, G. J.; Klein, M. L.; Tuckerman, M. Nose–Hoover chains: The Canonical Ensemble via Continuous Dynamics J. Chem. Phys. 1992, 97, 2635– 2643 DOI: 10.1063/1.463940
  There is no corresponding record for this reference.
57. 57
  Nosé, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods J. Chem. Phys. 1984, 81, 511– 519 DOI: 10.1063/1.447334
  57
  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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58. 58
  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868 DOI: 10.1103/PhysRevLett.77.3865
  58
  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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59. 59
  Lippert, G.; Hutter, J.; Parrinello, M. The Gaussian and Augmented-Plane-Wave Density Functional Method for Ab Initio Molecular Dynamics Simulations Theor. Chem. Acc. 1999, 103, 124– 140 DOI: 10.1007/s002140050523
  59
  The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations
  Lippert, Gerald; Hutter, Jurg; Parrinello, Michele
  Theoretical Chemistry Accounts (1999), 103 (2), 124-140CODEN: TCACFW; ISSN:1432-881X. (Springer-Verlag)
  A new algorithm for d.-functional-theory-based ab initio mol. dynamics simulations is presented. The Kohn-Sham orbitals are expanded in Gaussian-type functions and an APW-type approach is used to represent the electronic d. This extends previous work of ours where the d. was expanded only in plane waves. We describe the total d. in a smooth extended part which we represent in plane waves as in our previous work and parts localized close to the nuclei which are expanded in Gaussians. Using this representation of the charge we show how the localized and extended part can be treated sep., achieving a computational cost for the calcn. of the Kohn-Sham matrix that scales with the system size N as O(N log N). Furthermore, we are able to reduce drastically the size of the plane-wave basis. In addn., we introduce a multiple-cutoff method that improves considerably the performance of this approach. Finally, we demonstrate with a series of numerical examples the accuracy and efficiency of the new algorithm, both for electronic structure calcns. and for ab initio mol. dynamics simulations.
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60. 60
  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
  60
  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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61. 61
  Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1703– 1710 DOI: 10.1103/PhysRevB.54.1703
  61
  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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62. 62
  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
  62
  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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63. 63
  Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. Atomistic Simulations of Condensed Matter Systems WIREs 2014, 4, 15– 25 DOI: 10.1002/wcms.1159
  63
  cp2k: atomistic simulations of condensed matter systems
  Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
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64. 64
  Laio, A.; Gervasio, F. L. Metadynamics: a Method to Simulate Rare Events and Reconstruct the Free Energy in Biophysics, Chemistry and Material Science Rep. Prog. Phys. 2008, 71, 126601 DOI: 10.1088/0034-4885/71/12/126601
  64
  Metadynamics: a method to stimulate rare events and reconstruct the free energy in biophysics, chemistry and material science
  Laio, Alessandro; Gervasio, Francesco L.
  Reports on Progress in Physics (2008), 71 (12), 126601/1-126601/22CODEN: RPPHAG; ISSN:0034-4885. (Institute of Physics Publishing)
  A review. Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local min. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.
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65. 65
  Laio, A.; Rodriguez-Fortea, A.; Gervasio, F. L.; Ceccarelli, M.; Parrinello, M. Assessing the Accuracy of Metadynamics J. Phys. Chem. B 2005, 109, 6714– 6721 DOI: 10.1021/jp045424k
  65
  Assessing the Accuracy of Metadynamics
  Laio, Alessandro; Rodriguez-Fortea, Antonio; Gervasio, Francesco Luigi; Ceccarelli, Matteo; Parrinello, Michele
  Journal of Physical Chemistry B (2005), 109 (14), 6714-6721CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
  Metadynamics is a powerful technique that has been successfully exploited to explore the multidimensional free energy surface of complex polyat. systems and predict transition mechanisms in very different fields, ranging from chem. and solid-state physics to biophysics. We here derive an explicit expression for the accuracy of the methodol. and provide a way to choose the parameters of the method in order to optimize its performance.
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66. 66
  Vandevondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. r. Quickstep: Fast and Accurate Density Functional Calculations Using a Mixed Gaussian and Plane Waves Approach Comput. Phys. Commun. 2005, 167, 103– 128 DOI: 10.1016/j.cpc.2004.12.014
  66
  QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
  VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
  Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
  We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
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67. 67
  Krack, M.; Parrinello, M. In QUICKSTEP: Make the Atoms Dance; NIC Series; Forschungszentrum Jülich, 2004; p 29.
  There is no corresponding record for this reference.
68. 68
  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
  68
  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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69. 69
  Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Gaussian 09; Gaussian, Inc.: Wallingford, CT, 2009.
  There is no corresponding record for this reference.
70. 70
  Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules J. Chem. Phys. 1972, 56, 2257– 2261 DOI: 10.1063/1.1677527
  70
  Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules
  Hehre, W. J.; Ditchfield, R.; Pople, J. A.
  Journal of Chemical Physics (1972), 56 (5), 2257-61CODEN: JCPSA6; ISSN:0021-9606.
  Two extended basis sets (termed 5-31G and 6-31G) consisting of AO expressed as fixed linear combinations of Gaussian functions are presented for the 1st row atoms C to F. These basis functions are similar to the 4-31G set in that each valence shell is split into inner and outer parts described by 3 and 1 Gaussian function, resp. Inner shells are represented by a single basis function taken as a sum of 5 (5-31G) or 6 (6-31G) Guassians. Studies with a no. of polyat. mols. indicate a substantial lowering of calcd. total energies over the 4-31G set. Calcd. relative energies and equil. geometries do not appear to be altered significantly.
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71. 71
  Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. R. Efficient Diffuse Function-Augmented Basis Sets for Anion Calculations. III. The 3-21+G Basis Set for First-Row Elements, Li–F J. Comput. Chem. 1983, 4, 294– 301 DOI: 10.1002/jcc.540040303
  71
  Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21 + G basis set for first-row elements, lithium to fluorine
  Clark, Timothy; Chandrasekhar, Jayaraman; Spitznagel, Guenther W.; Schleyer, Paul v. R.
  Journal of Computational Chemistry (1983), 4 (3), 294-301CODEN: JCCHDD; ISSN:0192-8651.
  The relatively small diffuse function-augmented basis set, 3-21+G, describes anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.
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72. 72
  Frisch, M. J.; Pople, J. A.; Binkley, J. S. Self-Consistent Molecular Orbital Methods 25. Supplementary Functions for Gaussian Basis Sets J. Chem. Phys. 1984, 80, 3265 DOI: 10.1063/1.447079
  72
  Self-consistent molecular orbital methods. 25. Supplementary functions for Gaussian basis sets
  Frisch, Michael J.; Pople, John A.; Binkley, J. Stephen
  Journal of Chemical Physics (1984), 80 (7), 3265-9CODEN: JCPSA6; ISSN:0021-9606.
  Std. sets of supplementary diffuse s and p functions, multiple polarization functions (double and triple sets of d functions), and higher angular momentum polarization functions (f functions) are defined for use with the 6-31G and 6-311G basis sets. Preliminary applications of the modified basis sets to the calcn. of the bond energy and hydrogenation energy of N2 illustrate that these functions can be very important in the accurate computation of reaction energies.
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73. 73
  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
  73
  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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74. 74
  (a) Glendening, E. D.; Landis, C. R.; Weinhold, F. NBO 6.0: Natural Bond Orbital Analysis Program J. Comput. Chem. 2013, 34, 1429– 1437 DOI: 10.1002/jcc.23266
  74a
  NBO 6.0: Natural bond orbital analysis program
  Glendening, Eric D.; Landis, Clark R.; Weinhold, Frank
  Journal of Computational Chemistry (2013), 34 (16), 1429-1437CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
  We describe principal features of the newly released version, NBO 6.0, of the natural bond orbital anal. program, that provides novel "link-free" interactivity with host electronic structure systems, improved search algorithms and labeling conventions for a broader range of chem. species, and new anal. options that significantly extend the range of chem. applications. We sketch the motivation and implementation of program changes and describe newer anal. options with illustrative applications. © 2013 Wiley Periodicals, Inc.
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  (b) Glendening, E. D., Jr.; Badenhoop, K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; Landis, C. R.; Weinhold, F.NBO 6.0; Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 2013.
  There is no corresponding record for this reference.
75. 75
  Weinhold, F.; Landis, C. R. Discovering Chemistry with Natural Bond Orbitals; Wiley, 2012.
  There is no corresponding record for this reference.
76. 76
  Silverman, G. S.; Rakita, P. E. Handbook of Grignard Reagents; CRC Press: New York, 1996.
  There is no corresponding record for this reference.
77. 77
  Vestergren, M.; Eriksson, J.; Håkansson, M. Absolute Asymmetric Synthesis of “Chiral-at-Metal” Grignard Reagents and Transfer of the Chirality to Carbon Chem. - Eur. J. 2003, 9, 4678– 4686 DOI: 10.1002/chem.200305003
  77
  Absolute asymmetric synthesis of "chiral-at-metal" Grignard reagents and transfer of the chirality to carbon
  Vestergren, Marcus; Eriksson, Johan; Hakansson, Mikael
  Chemistry--A European Journal (2003), 9 (19), 4678-4686CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Two new six-coordinate Grignard reagents, cis-[(p-CH3C6H4)MgBr(dme)2] (1) and cis-[MgCH3(THF)(dme)2]I (2), were synthesized and their crystal structures were detd. Both reagents are cis-octahedral and therefore chiral. They crystallize as conglomerates and racemize rapidly in soln. By using these properties, the abs. asym. synthesis of specifically the Δ or the Λ enantiomer was achieved for both Grignard reagents. Enantiopure 1 and 2 were then reacted with butyraldehyde or benzaldehyde to give the corresponding alc. in up to 22% enantiomeric excess. At -60°, the Grignard reagents crystallize as racemic phases instead of conglomerates. Consequently, the crystal structures of rac-cis-[(p-CH3C6H4)MgBr(dme)2].DME (3) and rac-cis-[MgCH3(THF)(dme)2]I (4) could be detd.
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78. 78
  Vestergren, M.; Eriksson, J.; Håkansson, M. Chiral cis-Octahedral Grignard reagents J. Organomet. Chem. 2003, 681, 215– 224 DOI: 10.1016/S0022-328X(03)00616-8
  78
  Chiral cis-octahedral Grignard reagents
  Vestergren, Marcus; Eriksson, Johan; Hakansson, Mikael
  Journal of Organometallic Chemistry (2003), 681 (1-2), 215-224CODEN: JORCAI; ISSN:0022-328X. (Elsevier Science B.V.)
  Three chiral cis-octahedral Grignard reagents were synthesized and structurally characterized by x-ray diffraction methods. Crystals of cis-[PrMgBr(dme)2] (1), cis-[(i-Pr)MgBr(dme)2] (2) and cis-[(allyl)MgBr(dme)2] (3) were prepd. from neat 1,2-dimethoxyethane (DME) and are all racemic. Synthesis and structural characterization of trans-[MgBr2(tmeda)2] (4) and cis-[MgBr2(dme)2] (5) indicated that bidentate tertiary amino ligands may be less well suited for the prepn. of cis-octahedral Grignard reagents. However, the crystal structures of cis-[MgBr2(trigly)] (6) and [Mg2(μ-Br)2(trigly)2][Mg2(μ-Me)2Br4] (7; trigly = triglyme), suggest that the triglyme ligand may be ideally suited for this purpose.
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79. 79
  Vestergren, M.; Gustafsson, B.; Davidsson, Ö.; Håkansson, M. Octahedral Grignard Reagents Can Be Chiral at Magnesium Angew. Chem., Int. Ed. 2000, 39, 3435– 3437 DOI: 10.1002/1521-3773(20001002)39:19<3435::AID-ANIE3435>3.0.CO;2-A
  There is no corresponding record for this reference.
80. 80
  Harrison-Marchand, A.; Mongin, F. Mixed AggregAte (MAA): A Single Concept for All Dipolar Organometallic Aggregates. 1. Structural Data Chem. Rev. 2013, 113, 7470– 7562 DOI: 10.1021/cr300295w
  80
  Mixed AggregAte (MAA): A Single Concept for All Dipolar Organometallic Aggregates. 1. Structural Data
  Harrison-Marchand, Anne; Mongin, Florence
  Chemical Reviews (Washington, DC, United States) (2013), 113 (10), 7470-7562CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. This review will focus on structures of organo(bi)metallic species for which the ligands mainly realize nucleophilic transfers for addn. or deprotonation purposes.
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81. 81
  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
  81
  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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82. 82
  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
  82
  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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83. 83
  Hölzer, B.; Hoffmann, R. W. Kumada-Corriu Coupling of Grignard reagents, Probed with a Chiral Grignard Reagent Chem. Commun. 2003, 2, 732– 733 DOI: 10.1039/b300033h
  There is no corresponding record for this reference.
84. 84
  King, A. O.; Okukado, N.; Negishi, E.-i. Highly General Stereo-, Regio-, and Chemo-Selective Synthesis of Terminal and Internal Conjugated Enynes by the Pd-Catalysed Reaction of Alkynylzinc Reagents with Alkenyl Halides J. Chem. Soc., Chem. Commun. 1977, 683– 684 DOI: 10.1039/c39770000683
  84
  Highly general stereo-, regio-, and chemo-selective synthesis of terminal and internal conjugated enynes by the palladium-catalyzed reaction of alkynylzinc reagents with alkenyl halides
  King, Anthony O.; Okukado, Nobuhisa; Negishi, Eiichi
  Journal of the Chemical Society, Chemical Communications (1977), (19), 683-4CODEN: JCCCAT; ISSN:0022-4936.
  RC≡CZnCl [R = H, Bu, (CH2)4Me], prepd. by reaction of RC≡CLi with ZnCl2, underwent palladium phosphine complex-catalyzed condensation with R1CR2:CHR3 (R1 = H, R2 = Bu, R3 = I; R1 = Bu, R2 = H, Et, R3 = I; R1 = CO2Me, R1 = Me, R3 = Br) to give ≥65% R1CR2:CHC≡CR, the stereospecificity of the reaction being ≥97%.
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85. 85
  Negishi, E.-i. Palladium- or Nickel-Catalyzed Cross Coupling. A New Selective Method for Carbon-Carbon Bond Formation Acc. Chem. Res. 1982, 15, 340– 348 DOI: 10.1021/ar00083a001
  85
  Palladium- or nickel-catalyzed cross coupling. A new selective method for carbon-carbon bond formation
  Negishi, Eiichi
  Accounts of Chemical Research (1982), 15 (11), 340-8CODEN: ACHRE4; ISSN:0001-4842.
  A review with 88 refs.
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86. 86
  García-Melchor, M.; Fuentes, B.; Lledós, A.; Casares, J. A.; Ujaque, G.; Espinet, P. Cationic Intermediates in the Pd-Catalyzed Negishi Coupling. Kinetic and Density Functional Theory Study of Alternative Transmetalation Pathways in the Me–Me Coupling of ZnMe₂ and trans-[PdMeCl(PMePh₂)₂] J. Am. Chem. Soc. 2011, 133, 13519– 13526 DOI: 10.1021/ja204256x
  86
  Cationic Intermediates in the Pd-Catalyzed Negishi Coupling. Kinetic and Density Functional Theory Study of Alternative Transmetalation Pathways in the Me-Me Coupling of ZnMe2 and trans-[PdMeCl(PMePh2)2]
  Garcia-Melchor, Max; Fuentes, Beatriz; Lledos, Agusti; Casares, Juan A.; Ujaque, Gregori; Espinet, Pablo
  Journal of the American Chemical Society (2011), 133 (34), 13519-13526CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The complexity of the transmetalation step in a Pd-catalyzed Negishi reaction has been investigated by combining expt. and theor. calcns. The reaction between trans-[PdMeCl(PMePh2)2] and ZnMe2 in THF as solvent was analyzed. The results reveal some unexpected and relevant mechanistic aspects not obsd. for ZnMeCl as nucleophile. The operative reaction mechanism is not the same when the reaction is carried out in the presence or in the absence of an excess of phosphine in the medium. In the absence of added phosphine an ionic intermediate with THF as ligand ([PdMe(PMePh2)2(THF)]+) opens ionic transmetalation pathways. In contrast, an excess of phosphine retards the reaction because of the formation of a very stable cationic complex with three phosphines ([PdMe(PMePh2)3]+) that sequesters the catalyst. These ionic intermediates had never been obsd. or proposed in palladium Negishi systems and warn on the possible detrimental effect of an excess of good ligand (as PMePh2) for the process. In contrast, the ionic pathways via cationic complexes with one solvent (or a weak ligand) can be noticeably faster and provide a more rapid reaction than the concerted pathways via neutral intermediates. Theor. calcns. on the real mols. reproduce well the exptl. rate trends obsd. for the different mechanistic pathways.
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- Metadynamics parameters, natural bond orbital analysis, DFT optimized geometries, and solvation properties for different sizes of the simulation box (PDF)
- jp7b02716_si_001.pdf (774.55 kb)
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How Solvent Dynamics Controls the Schlenk Equilibrium of Grignard Reagents: A Computational Study of CH3MgCl in TetrahydrofuranClick to copy article linkArticle link copied!

The Journal of Physical Chemistry B

Abstract

Introduction

Scheme 1

Computational Methods

System Setup

Monomeric Species

Dimeric Species

Figure 1

Ab Initio Molecular Dynamics Simulations

Free-Energy Calculations

Static Calculations and Electronic Structure Analysis

Results

Monomeric Structures

Figure 2

Dinuclear Structures

Cl/CH3 Exchange Process

Figure 3

Solvation of Dichloride Bridged Structures

Figure 4

Figure 5

Solvation of Methyl Chloride Bridged Structures

Figure 6

Figure 7

Figure 8

Reaction Pathway of the Schlenk Equilibrium

Figure 9

Conclusions

Supporting Information

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Acknowledgment

References

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Abstract

Scheme 1

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

References

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Supporting Information

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How Solvent Dynamics Controls the Schlenk Equilibrium of Grignard Reagents: A Computational Study of CH₃MgCl in Tetrahydrofuran
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Cl/CH₃ Exchange Process