Hybrid Quantum Mechanical/Molecular Mechanics Study of the SN2 Reaction of CH3Cl+OH– in Water

"Marriage" of Inorganic to Organic Chemistry as Motivation for a Theoretical Study of Chloroform Hydrolysis Mechanisms

Incorporation of chlorides in coordination complexes, prepared by reactions in CHCl3, stimulated MP2 and DFT studies of its complete hydrolysis mechanisms. In excellent agreement with previous experimental results, the most important mechanism for CHCl3 basic hydrolysis at room temperature is the radical one producing :CCl2. The latter inserts into the H-O bond of H2O yielding dichloromethanol (1). The hydrolysis mechanism of α-H-lacking PhCCl3 to the corresponding dichloro(phenyl)methanol (3) was also studied. 1 decomposes by H2O to formyl chloride (2) and HCl. 2, following a variety of pathways, leads to known CHCl3 hydrolysis products, such as CO (4) and formic acid (6), via the intermediates chloromethanediol (5), s-cis, s-trans-dihydroxycarbene (ct-7), and s-trans, s-trans-dihydroxycarbene (tt-7). Interestingly, both ct-7 and tt-7 intermediates have recently been implicated in the reduction of CO2 with H2 to 6. The conversion of CO to HCOOH was studied. Most of the reactions studied are asynchronous concerted processes, the radical mechanism being a multistep one. The synthetic utility of this mechanism is briefly mentioned. To avoid chloride ions when performing reactions in CHCl3, we should use the solvent at room temperature even in the presence of water. This has been verified further by coordination chemistry reactions in progress.

Benchmark ab initio characterization of the complex potential energy surfaces of the HOO- + CH3Y [Y = F, Cl, Br, I] reactions

The α-effect is a well-known phenomenon in organic chemistry, and is related to the enhanced reactivity of nucleophiles involving one or more lone-pair electrons adjacent to the nucleophilic center. The gas-phase bimolecular nucleophilic substitution (SN2) reactions of α-nucleophile HOO- with methyl halides have been thoroughly investigated experimentally and theoretically; however, these investigations have mainly focused on identifying and characterizing the α-effect of HOO-. Here, we perform the first comprehensive high-level ab initio mapping for the HOO- + CH3Y [Y = F, Cl, Br and I] reactions utilizing the modern explicitly-correlated CCSD(T)-F12b method with the aug-cc-pVnZ [n = 2-4] basis sets. The present ab initio characterization considers five distinct product channels of SN2: (CH3OOH + Y-), proton abstraction (CH2Y- + H2O2), peroxide ion substitution (CH3OO- + HY), SN2-induced elimination (CH2O + HY + HO-) and SN2-induced rearrangement (CH2(OH)O- + HY). Moreover, besides the traditional back-side attack Walden inversion, the pathways of front-side attack, double inversion and halogen-bond complex formation have also been explored for SN2. With regard to the Walden inversion of HOO- + CH3Cl, the previously unaddressed discrepancies concerning the geometry of the corresponding transition state are clarified. For the HOO- + CH3F reaction, the recently identified SN2-induced elimination is found to be more exothermic than the SN2 channel, submerged by ∼36 kcal mol-1. The accuracy of our high-level ab initio calculations performed in the present study is validated by the fact that our new benchmark 0 K reaction enthalpies show excellent agreement with the experimental data in nearly all cases.

Vibrational mode-specificity in the dynamics of the OH- + CH3I multi-channel reaction

We report a comprehensive characterization of the vibrational mode-specific dynamics of the OH- + CH3I reaction. Quasi-classical trajectory simulations are performed at four different collision energies on our previously-developed full-dimensional high-level ab initio potential energy surface in order to examine the impact of four different normal-mode excitations in the reactants. Considering the 11 possible pathways of OH- + CH3I, pronounced mode-specificity is observed in reactivity: In general, the excitations of the OH- stretching and CH stretching exert the greatest influence on the channels. For the SN2 and proton-abstraction products, the reactant initial attack angle and the product scattering angle distributions do not show major mode-specific features, except for SN2 at higher collision energies, where forward scattering is promoted by the CI stretching and CH stretching excitations. The post-reaction energy flow is also examined for SN2 and proton abstraction, and it is unveiled that the excess vibrational excitation energies rather transfer into the product vibrational energy because the translational and rotational energy distributions of the products do not represent significant mode-specificity. Moreover, in the course of proton abstraction, the surplus vibrational energy in the OH- reactant mostly remains in the H2O product owing to the prevailing dominance of the direct stripping mechanism.

Quasi-classical trajectory study of the OH- + CH3I reaction: theory meets experiment

Regarding OH^- + CH₃I, several studies have focused on the dynamics of the reaction. Here, high-level quasi-classical trajectory simulations are carried out at four different collision energies on our recently developed potential energy surface. In all, more than half a million trajectories are performed, and for the first time, the detailed quasi-classical trajectory results are compared with the reanalysed crossed-beam ion imaging experiments. Concerning the previously reported direct dynamics study of OH^- + CH₃I, a better agreement can be obtained between the revised experiment and our novel theoretical results. Furthermore, in the present work, the benchmark geometries, frequencies and relative energies of the stationary points are also determined for the OH^- + CH₃I proton-abstraction channel along with the earlier characterized S_N2 channel.

Unconventional SN2 retention pathways induced by complex formation: High-level dynamics investigation of the NH2 - + CH3I polyatomic reaction

Investigations on the dynamics of chemical reactions have been a hot topic for experimental and theoretical studies over the last few decades. Here, we carry out the first high-level dynamical characterization for the polyatom-polyatom reaction between NH₂ ^- and CH₃I. A global analytical potential energy surface is developed to describe the possible pathways with the quasi-classical trajectory method at several collision energies. In addition to S_N2 and proton abstraction, a significant iodine abstraction is identified, leading to the CH₃ + [NH₂⋯I]^- products. For S_N2, our computations reveal an indirect character as well, promoting the formation of [CH₃⋯NH₂] complexes. Two novel dominant S_N2 retention pathways are uncovered induced by the rotation of the CH₃ fragment in these latter [CH₃⋯NH₂] complexes. Moreover, these uncommon routes turn out to be the most dominant retention paths for the NH₂ ^- + CH₃I S_N2 reaction.

Theoretical investigation of the SN2 mechanism of X- [X = SH, PH2] + CH3Y [Y = F, Cl, Br, I] reactions in water

We investigated the S_N2 Walden-inversion mechanism of X^- (X = SH, PH₂) + CH₃Y (Y = F, Cl, Br, I) reactions in water using multi-level quantum mechanics (ML-QM) and molecular mechanics (MM) methods. The potentials of the mean force were mapped using not only the density functional theory (DFT)/MM method but also a high-level, accurate CCSD(T)/MM method using the aug-cc-pVTZ basis set. In particular, for the PH₂^- + CH₃I reaction, although the backside attack Walden-inversion mechanics were not observed in the gas phase, we found that this mechanism takes place in water. The atomic-level dynamics of the concerted S_N2 mechanism and the stationary points along the reaction paths were characterized. For these reactions in water, their Walden-inversion barriers are higher than their corresponding ones in the gas phase, indicating that the aqueous solution hinders their reactivity. For the reactions with the same nucleophile X^- in water, the reaction barrier heights with different leaving groups are in the order of F > Cl > Br > I. For the same leaving group Y with different nucleophiles SH^- and PH₂^-, the reaction barrier with SH^- is greater than that of PH₂^- due to the former having higher electronegativity than the latter.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

Hybrid Solvation Model with First Solvation Shell for Calculation of Solvation Free Energy

We present a hybrid solvation model with first solvation shell to calculate solvation free energies. This hybrid model combines the quantum mechanics and molecular mechanics methods with the analytical expression based on the Born solvation model to calculate solvation free energies. Based on calculated free energies of solvation and reaction profiles in gas phase, we set up a unified scheme to predict reaction profiles in solution. The predicted solvation free energies and reaction barriers are compared with experimental results for twenty bimolecular nucleophilic substitution reactions. These comparisons show that our hybrid solvation model can predict reliable solvation free energies and reaction barriers for chemical reactions of small molecules in aqueous solution.

Multilevel Quantum Mechanics and Molecular Mechanics Study of the Double-Inversion Mechanism at Nitrogen: F- + NH2Cl in Aqueous Solution

We employ a multilevel quantum mechanics and molecular mechanics method to investigate the double-inversion mechanism of the nucleophilic substitution reaction at the N center: the F^- + NH₂Cl reaction in aqueous solution. We find that the structures of the stationary points along the reaction path are quite different from the ones in the gas phase owing to the hydrogen-bond interactions between the solute and the surrounding water molecules. The atomic-level evolutions of the structures and charge transfer along the reaction path show that this double-inversion mechanism consists of an upside-down proton inversion process and a Walden-inversion process. The computed potential of mean force at the coupled-cluster singles and doubles with perturbative triples (CCSD(T))/molecular mechanics (MM) level of theory has the two-inversion barrier heights, and reaction free energy at 11.7, 29.6, and 12.6 kcal/mol, agreeing well with the predicted ones at 12.6, 32.5, and 12.2 kcal/mol obtained on the basis of the gas-phase reaction path and the solvation free energies of the stationary points.

Rethinking the X− + CH3Y [X = OH, SH, CN, NH2, PH2; Y = F, Cl, Br, I] SN2 reactions

Explicitly-correlated ab initio computations reveal novel inversion and retention pathways for several S_N2 reactions with different nucleophiles and leaving groups.

Ion-Pair SN 2 Reaction of OH- and CH3 Cl: Activation Strain Analyses of Counterion and Solvent Effects

We have theoretically studied the non-identity S_N 2 reactions of M_n OH^(n-1) +CH₃ Cl (M⁺ =Li⁺ , Na⁺ , K⁺ , and MgCl⁺ ; n=0, 1) in the gas phase and in THF solution at the OLYP/6-31++G(d,p) level using polarizable continuum model (PCM) implicit solvation. We want to explore and understand the effect of the metal counterion M⁺ and solvation on the reaction profile and the stereoselectivity of these processes. To this end, we have explored the potential energy surfaces of the backside (S_N 2-b) and frontside (S_N 2-f) pathways. To explain the computed trends, we have carried out analyses with an extended activation strain model (ASM) of chemical reactivity that includes the treatment of solvation effects.

Catalytic Effect of Aqueous Solution in Water-Assisted Proton-Transfer Mechanism of 8-Hydroxy Guanine Radical

Water-assisted proton-transfer process is a key step in guanine damage reaction by hydroxyl radical in aqueous solution. In this article, we quantitatively determine the solvent effect in water-assisted proton-transfer mechanism of 8-hydroxy guanine radical using combined quantum mechanics and molecular mechanism with an explicit solvation model. Atomic-level reaction pathway was mapped, which shows a synchronized two-proton-transfer mechanism between the assistant water molecule and 8-hydroxy guanine radical. The transition-state dipole moment is the largest along the reaction pathway, which electrostatically stabilizes the proton-transfer transition-state complex. The free-energy reaction barrier for this water-assisted proton-transfer reaction was calculated at 19.2 kcal/mol with the density functional theory/M08-SO/cc-pVTZ+/molecular mechanics level of theory. The solvent effect not only has a big impact on geometries, but also dramatically changes the energetics along the reaction pathway. Among the solvent effect contributions to the transition state, the solvent energy contribution is -28.5 kcal/mol and the polarization effect contribution is 19.9 kcal/mol. In total, the solvent effect contributes -8.6 kcal/mol to the free-energy barrier height, which means that the presence of aqueous solution has a catalytic effect on the reaction mechanism and enhances the proton-transfer reactivity in aqueous solution.

A new, double-inversion mechanism of the F- + CH3Cl SN2 reaction in aqueous solution

Atomic-level, bimolecular nucleophilic substitution reaction mechanisms have been studied mostly in the gas phase, but the gas-phase results cannot be expected to reliably describe condensed-phase chemistry. As a novel, double-inversion mechanism has just been found for the F^- + CH₃Cl S_N2 reaction in the gas phase [Nat. Commun., 2015, 6, 5972], here, using multi-level quantum mechanics methods combined with the molecular mechanics method, we discovered a new, double-inversion mechanism for this reaction in aqueous solution. However, the structures of the stationary points along the reaction path show significant differences from those in the gas phase due to the strong influence of solvent and solute interactions, especially due to the hydrogen bonds formed between the solute and the solvent. More importantly, the relationship between the two double-inversion transition states is not clear in the gas phase, but, here we revealed a novel intermediate complex serving as a "connecting link" between the two transition states of the abstraction-induced inversion and the Walden-inversion mechanisms. A detailed reaction path was constructed to show the atomic-level evolution of this novel double reaction mechanism in aqueous solution. The potentials of mean force were calculated and the obtained Walden-inversion barrier height agrees well with the available experimental value.

Multi-level Quantum Mechanics and Molecular Mechanics Study of Ring Opening Process of Guanine Damage by Hydroxyl Radical in Aqueous Solution

Combining multi-level quantum mechanics theories and molecular mechanics with an explicit water model, we investigated the ring opening process of guanine damage by hydroxyl radical in aqueous solution. The detailed, atomic-level ring-opening mechanism along the reaction pathway was revealed in aqueous solution at the CCSD(T)/MM levels of theory. The potentials of mean force in aqueous solution were calculated at both the DFT/MM and CCSD(T)/MM levels of the theory. Our study found that the aqueous solution has a significant effect on this reaction in solution. In particular, by comparing the geometries of the stationary points between in gas phase and in aqueous solution, we found that the aqueous solution has a tremendous impact on the torsion angles much more than on the bond lengths and bending angles. Our calculated free-energy barrier height 31.6 kcal/mol at the CCSD(T)/MM level of theory agrees well with the one obtained based on gas-phase reaction profile and free energies of solvation. In addition, the reaction path in gas phase was also mapped using multi-level quantum mechanics theories, which shows a reaction barrier at 19.2 kcal/mol at the CCSD(T) level of theory, agreeing very well with a recent ab initio calculation result at 20.8 kcal/mol.

Multi-level quantum mechanics theories and molecular mechanics study of the double-inversion mechanism of the F- + CH3I reaction in aqueous solution

A double-inversion mechanism of the F^- + CH₃I reaction was discovered in aqueous solution using combined multi-level quantum mechanics theories and molecular mechanics. The stationary points along the reaction path show very different structures to the ones in the gas phase due to the interactions between the solvent and solute, especially strong hydrogen bonds. An intermediate complex, a minimum on the potential of mean force, was found to serve as a connecting-link between the abstraction-induced inversion transition state and the Walden-inversion transition state. The potentials of mean force were calculated with both the DFT/MM and CCSD(T)/MM levels of theory. Our calculated free energy barrier of the abstraction-induced inversion is 69.5 kcal mol^-1 at the CCSD(T)/MM level of theory, which agrees with the one at 72.9 kcal mol^-1 calculated using the Born solvation model and gas-phase data; and our calculated free energy barrier of the Walden inversion is 24.2 kcal mol^-1, which agrees very well with the experimental value at 25.2 kcal mol^-1 in aqueous solution. The calculations show that the aqueous solution makes significant contributions to the potentials of mean force and exerts a big impact on the molecular-level evolution along the reaction pathway.

A multi-level quantum mechanics and molecular mechanics study of SN2 reaction at nitrogen: NH2Cl + OH(-) in aqueous solution

We employed a multi-level quantum mechanics and molecular mechanics approach to study the reaction NH2Cl + OH(-) in aqueous solution. The multi-level quantum method (including the DFT method with both the B3LYP and M06-2X exchange-correlation functionals and the CCSD(T) method, and both methods with the aug-cc-pVDZ basis set) was used to treat the quantum reaction region in different stages of the calculation in order to obtain an accurate potential of mean force. The obtained free energy activation barriers at the DFT/MM level of theory yielded a big difference of 21.8 kcal mol(-1) with the B3LYP functional and 27.4 kcal mol(-1) with the M06-2X functional respectively. Nonetheless, the barrier heights become very close when shifted from DFT to CCSD(T): 22.4 kcal mol(-1) and 22.9 kcal mol(-1) at CCSD(T)(B3LYP)/MM and CCSD(T)(M06-2X)/MM levels of theory, respectively. The free reaction energy obtained using CCSD(T)(M06-2X)/MM shows an excellent agreement with the one calculated using the available gas-phase data. Aqueous solution plays a significant role in shaping the reaction profile. In total, the water solution contributes 13.3 kcal mol(-1) and 14.6 kcal mol(-1) to the free energy barrier heights at CCSD(T)(B3LYP)/MM and CCSD(T)(M06-2X)/MM respectively. The title reaction at nitrogen is a faster reaction than the corresponding reaction at carbon, CH3Cl + OH(-).

Investigation of the CH3Cl + CN(-) reaction in water: Multilevel quantum mechanics/molecular mechanics study

The CH3Cl + CN(-) reaction in water was studied using a multilevel quantum mechanics/molecular mechanics (MM) method with the multilevels, electrostatic potential, density functional theory (DFT) and coupled-cluster single double triple (CCSD(T)), for the solute region. The detailed, back-side attack SN2 reaction mechanism was mapped along the reaction pathway. The potentials of mean force were calculated under both the DFT and CCSD(T) levels for the reaction region. The CCSD(T)/MM level of theory presents a free energy activation barrier height at 20.3 kcal/mol, which agrees very well with the experiment value at 21.6 kcal/mol. The results show that the aqueous solution has a dominant role in shaping the potential of mean force. The solvation effect and the polarization effect together increase the activation barrier height by ∼11.4 kcal/mol: the solvation effect plays a major role by providing about 75% of the contribution, while polarization effect only contributes 25% to the activation barrier height. Our calculated potential of mean force under the CCSD(T)/MM also has a good agreement with the one estimated using data from previous gas-phase studies.

Tuning the reactivity of Fe(V)(O) toward C-H bonds at room temperature: effect of water

The presence of an Fe(V)(O) species has been postulated as the active intermediate for the oxidation of both C-H and C═C bonds in the Rieske dioxygenase family of enzymes. Understanding the reactivity of these high valent iron-oxo intermediates, especially in an aqueous medium, would provide a better understanding of these enzymatic reaction mechanisms. The formation of an Fe(V)(O) complex at room temperature in an aqueous CH3CN mixture that contains up to 90% water using NaOCl as the oxidant is reported here. The stability of Fe(V)(O) decreases with increasing water concentration. We show that the reactivity of Fe(V)(O) toward the oxidation of C-H bonds, such as those in toluene, can be tuned by varying the amount of water in the H2O/CH3CN mixture. Rate acceleration of up to 60 times is observed for the oxidation of toluene upon increasing the water concentration. The role of water in accelerating the rate of the reaction has been studied using kinetic measurements, isotope labeling experiments, and density functional theory (DFT) calculations. A kinetic isotope effect of ∼13 was observed for the oxidation of toluene and d8-toluene showing that C-H abstraction was involved in the rate-determining step. Activation parameters determined for toluene oxidation in H2O/CH3CN mixtures on the basis of Eyring plots for the rate constants show a gain in enthalpy with a concomitant loss in entropy. This points to the formation of a more-ordered transition state involving water molecules. To further understand the role of water, we performed a careful DFT study, concentrating mostly on the rate-determining hydrogen abstraction step. The DFT-optimized structure of the starting Fe(V)(O) and the transition state indicates that the rate enhancement is due to the transition state's favored stabilization over the reactant due to enhanced hydrogen bonding with water.

Recent advances in QM/MM free energy calculations using reference potentials

Background

Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way.

Scope of review

Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field.

Major conclusions

The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed.

General significance

As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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We present some of the advances to accelerate high-level QM/MM calculations.

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Quantitative limitations of low-level methods can be overcome by these approaches.

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Reference potentials make free energy simulations feasible for large systems.

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Automated fitting reduces the need of expensive sampling of high-level approaches.

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Application of reference potentials can be extended to a wide range of processes.

A multilayered-representation, quantum mechanical/molecular mechanics study of the CH3Cl + F− reaction in aqueous solution: the reaction mechanism, solvent effects and potential of mean force

A multi-layered representation, hybrid quantum mechanical and molecular mechanics method study of the CH₃Cl + F⁻ → CH₃F + Cl⁻ reaction in water.

Solvent effects and potential of mean force: a multilayered-representation quantum mechanical/molecular mechanics study of the CH3Br + CN− reaction in aqueous solution

The potential of mean force for the CH₃Br + CN⁻ reaction was obtained at the CCSD(T)/MM level of theory using a multilayered-representation quantum mechanical/molecular mechanics approach, as well as the reactant, transition state and product complexes along the reaction pathway in aqueous solution.

A multilayered-representation quantum mechanical/molecular mechanics study of the S(N)2 reaction of CH3Br + OH(-) in aqueous solution

The bimolecular nucleophilic substitution (S(N)2) reaction of CH(3)Br and OH(-) in aqueous solution was investigated using a multilayered-representation quantum mechanical and molecular mechanics methodology. Reactant complex, transition state, and product complex are identified and characterized in aqueous solution. The potentials of mean force are computed under both the density function theory and coupled-cluster single double (triple) (CCSD(T)) levels of theory for the reaction region. The results show that the aqueous environment has a significant impact on the reaction process. The solvation effect and the polarization effect combined raise the activation barrier height by ~16.2 kcal/mol and the solvation effect is the dominant contribution to the potential of mean force. The CCSD(T)/MM representation presents a free energy activation barrier height of 22.8 kcal/mol and the rate constant at 298 K of 3.7 × 10(-25) cm(3) molecule(-1) s(-1) which agree very well with the experiment values at 23.0 kcal/mol and 2.6 × 10(-25) cm(3) molecule(-1) s(-1), respectively.

Exploring, refining, and validating the paradynamics QM/MM sampling

The performance of the paradynamics (PD) reference potential approach in QM/MM calculations is examined. It is also clarified that, in contrast to some possible misunderstandings, this approach provides a rigorous strategy for QM/MM free energy calculations. In particular, the PD approach provides a gradual and controlled way of improving the evaluation of the free energy perturbation associated with moving from the EVB reference potential to the target QM/MM surface. This is achieved by moving from the linear response approximation to the full free energy perturbation approach in evaluating the free energy changes. We also present a systematic way of improving the reference potential by using Gaussian-based correction potentials along a reaction coordinate. In parallel, we review other recent adaptations of the reference potential approach, emphasizing and demonstrating the advantage of using the EVB potential as a reference potential, relative to semiempirical QM/MM molecular orbital potentials. We also compare the PD results to those obtained by direct calculations of the potentials of the mean force (PMF). Additionally, we propose a way of accelerating the PMF calculations by using Gaussian-based negative potentials along the reaction coordinate (which are also used in the PD refinement). Finally, we discuss performance of the PD and the metadynamics approaches in ab initio QM/MM calculations and emphasize the advantage of using the PD approach.

Hybrid quantum mechanical and molecular mechanics study of the S(N)2 Reaction of CCl4 + OH- in aqueous solution: the potential of mean force, reaction energetics, and rate constants

The bimolecular nucleophilic substitution reaction of CCl(4) and OH(-) in aqueous solution was investigated on the basis of a combined quantum mechanical and molecular mechanics method. A multilayered representation approach is employed to achieve high accuracy results at the CCSD(T) level of theory. The potential of mean force calculations at the DFT level and CCSD(T) level of theory yield reaction barrier heights of 22.7 and 27.9 kcal/mol, respectively. Both the solvation effects and the solvent-induced polarization effect have significant contributions to the reaction energetics, for example, the solvation effect raises the saddle point by 10.6 kcal/mol. The calculated rate constant coefficient is 8.6 × 10(-28) cm(3) molecule(-1) s(-1) at the standard state condition, which is about 17 orders magnitude smaller than that in the gas phase. Among the four chloromethanes (CH(3)Cl, CH(2)Cl(2), CHCl(3), and CCl(4)), CCl(4) has the lowest free energy activation barrier for the reaction with OH(-) in aqueous solution, confirming the trend that substitution of Cl by H in chloromethanes diminishes the reactivity.