Identity SN2 Reactions X−+CH3X→XCH3+X− (X=F, Cl, Br, and I) in Vacuum and in Aqueous Solution: A Valence Bond Study

Promotion Energy Analysis Predicts Reaction Modes: Nucleophilic and Electrophilic Aromatic Substitution Reactions

To develop an approach to pre-emptively predict the existence of major reaction modes associated with a chemical system, based on exclusive consideration of reactant properties, we build herein on the valence bond perspective of chemical reactivity. In this perspective, elementary chemical reactions are conceptualized as crossovers between individual diabatic/semilocalized states. As demonstrated, the spacings between the main diabatic states in the reactant geometries-the so-called promotion energies-contain predictive information about which types of crossings are likely to occur on a potential energy surface, facilitating the identification of potential transition states and products. As an added bonus, promotion energy analysis provides direct insight into the impact of environmental effects, e.g., the presence of (polar) solvents and/or (local) electric fields, on a mechanistic landscape. We illustrate the usefulness of our approach by focusing on model nucleophilic and electrophilic aromatic substitution reactions. Overall, we envision our analysis to be useful not only as a tool for conceptualizing individual mechanistic landscapes but also as a facilitator of systematic reaction-network exploration efforts. Because the emerging VB descriptors are computationally inexpensive (and can alternatively be inferred through machine learning), they could be evaluated on-the-fly as part of an exploration algorithm. The so-predicted reaction modes could subsequently be examined in detail through computationally more-demanding methods.

A Unified Framework for Understanding Nucleophilicity and Protophilicity in the SN 2/E2 Competition

The concepts of nucleophilicity and protophilicity are fundamental and ubiquitous in chemistry. A case in point is bimolecular nucleophilic substitution (SN 2) and base-induced elimination (E2). A Lewis base acting as a strong nucleophile is needed for SN 2 reactions, whereas a Lewis base acting as a strong protophile (i.e., base) is required for E2 reactions. A complicating factor is, however, the fact that a good nucleophile is often a strong protophile. Nevertheless, a sound, physical model that explains, in a transparent manner, when an electron-rich Lewis base acts as a protophile or a nucleophile, which is not just phenomenological, is currently lacking in the literature. To address this fundamental question, the potential energy surfaces of the SN 2 and E2 reactions of X- +C2 H5 Y model systems with X, Y = F, Cl, Br, I, and At, are explored by using relativistic density functional theory at ZORA-OLYP/TZ2P. These explorations have yielded a consistent overview of reactivity trends over a wide range in reactivity and pathways. Activation strain analyses of these reactions reveal the factors that determine the shape of the potential energy surfaces and hence govern the propensity of the Lewis base to act as a nucleophile or protophile. The concepts of "characteristic distortivity" and "transition state acidity" of a reaction are introduced, which have the potential to enable chemists to better understand and design reactions for synthesis.

NBO/NRT Two-State Theory of Bond-Shift Spectral Excitation

We show that natural bond orbital (NBO) and natural resonance theory (NRT) analysis methods provide both optimized Lewis-structural bonding descriptors for ground-state electronic properties as well as suitable building blocks for idealized "diabatic" two-state models of the associated spectroscopic excitations. Specifically, in the framework of single-determinant Hartree-Fock or density functional methods for a resonance-stabilized molecule or supramolecular complex, we employ NBO/NRT descriptors of the ground-state determinant to develop a qualitative picture of the associated charge-transfer excitation that dominates the valence region of the electronic spectrum. We illustrate the procedure for the elementary bond shifts of SN2-type halide exchange reaction as well as the more complex bond shifts in a series of conjugated cyanine dyes. In each case, we show how NBO-based descriptors of resonance-type 3-center, 4-electron (3c/4e) interactions provide simple estimates of spectroscopic excitation energy, bond orders, and other vibronic details of the excited-state PES that anticipate important features of the full multi-configuration description. The deep 3c/4e connections to measurable spectral properties also provide evidence for NBO-based estimates of ground-state donor-acceptor stabilization energies (sometimes criticized as "too large" compared to alternative analysis methods) that are also found to be of proper magnitude to provide useful estimates of excitation energies and structure-dependent spectral shifts.

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.

Accelerated computation of free energy profile at ab initio quantum mechanical/molecular mechanical accuracy via a semi-empirical reference potential. II. Recalibrating semi-empirical parameters with force matching

An efficient and accurate reference potential simulation protocol is proposed for producing ab initio quantum mechanical/molecular mechanical (AI-QM/MM) quality free energy profiles for chemical reactions in a solvent or macromolecular environment. This protocol involves three stages: (a) using force matching to recalibrate a semi-empirical quantum mechanical (SE-QM) Hamiltonian for the specific reaction under study; (b) employing the recalibrated SE-QM Hamiltonian (in combination with molecular mechanical force fields) as the reference potential to drive umbrella samplings along the reaction pathway; and (c) computing AI-QM/MM energy values for collected configurations from the sampling and performing weighted thermodynamic perturbation to acquire an AI-QM/MM corrected reaction free energy profile. For three model reactions (identity SN2 reaction, Menshutkin reaction, and glycine proton transfer reaction) in aqueous solution and one enzyme reaction (Claisen arrangement in chorismate mutase), our simulations using recalibrated PM3 SE-QM Hamiltonians well reproduced QM/MM free energy profiles at the B3LYP/6-31G* level of theory all within 1 kcal mol-1 with a 20 to 45 fold reduction in the computer time.

QM/MM Calculations for the Cl- + CH3Cl SN2 Reaction in Water Using CM5 Charges and Density Functional Theory

The prototypical S_N2 reaction of chloride ion with methyl chloride has been reinvestigated in aqueous solution using QM/MM methodology featuring MO6-2X/6-31+G(d) calculations with the TIP4P water model, and partial charges were computed with the CM5 method. Though the DFT method yields excellent gas-phase energetics for the reaction, the QM/MM approach is found to yield overestimation of the activation barrier by ca. 12 kcal/mol. The discrepancy is traced to underestimate of the magnitude of the partial charges on the chlorine atoms in the transition structure. When CM1 or CM3 charges based on semiempirical wave functions are used instead, the agreement with experiment is much improved. The findings emphasize the sensitivity of the results of QM/MM calculations to the choice of QM method, the MM force field, and implementation of the QM/MM interface.

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.

Multilevel Quantum Mechanics Theories and Molecular Mechanics Calculations of the Cl- + CH3I Reaction in Water

The Cl^- + CH₃I → CH₃Cl + I^- reaction in water was studied using combined multilevel quantum mechanism theories and molecular mechanics with an explicit water solvent model. The study shows a significant influence of aqueous solution on the structures of the stationary points along the reaction pathway. A detailed, atomic-level evolution of the reaction mechanism shows a concerted one-bond-broken and one-bond-formed mechanism, as well as a synchronized charge-transfer process. The potentials of mean force calculated with the CCSD(T) and DFT treatments of the solute produce a free activation barrier at 24.5 and 19.0 kcal/mol, respectively, which agrees with the experimental one at 22.0 kcal/mol. The solvent effects have also been quantitatively analyzed: in total, the solvent effects raise the activation energy by 20.2 kcal/mol, which shows a significant impact on this reaction in water.

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.

Dynamical Bifurcation in Gas-Phase XH- + CH3 Y SN 2 Reactions: The Role of Energy Flow and Redistribution in Avoiding the Minimum Energy Path

The gas-phase reactions of XH^- (X=O, S) + CH₃ Y (Y=F, Cl, Br) span nearly the whole range of S_N 2 pathways, and show an intrinsic reaction coordinate (IRC) (minimum energy path) with a deep well owing to the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) hydrogen-bonded postreaction complex. MP2 quasiclassical-type direct dynamics starting at the [HX⋅⋅⋅CH₃ ⋅⋅⋅Y]^- transition-state (TS) structure reveal distinct mechanistic behaviors. Trajectories that yield the separated CH₃ XH+Y^- (or CH₃ S^- +HF) products directly are non-IRC, whereas those that sample the CH₃ XH⋅⋅⋅Y^- (or CH₃ S^- ⋅⋅⋅HF) complex are IRC. The IRCIRC/non-IRC ratios of 90:10, 40:60, 25:75, 2:98, 0:100, and 0:100 are obtained for (X, Y)=(S, F), (O, F), (S, Cl), (S, Br), (O, Cl), and (O, Br), respectively. The properties of the energy profiles after the TS cannot provide a rationalization of these results. Analysis of the energy flow in dynamics shows that the trajectories cross a dynamical bifurcation, and that the inability to follow the minimum energy path arises from long vibration periods of the X-C⋅⋅⋅Y bending mode. The partition of the available energy to the products into vibrational, rotational, and translational energies reveals that if the vibrational contribution is more than 80 %, non-IRC behavior dominates, unless the relative fraction of the rotational and translational components is similar, in which case a richer dynamical mechanism is shown, with an IRC/non-IRC ratio that correlates to this relative fraction.

Combined Electrostatically Embedded Multiconfiguration Molecular Mechanics and Molecular Mechanical Method: Application to Molecular Dynamics Simulation of a Chemical Reaction in Aqueous Solution with Hybrid Density Functional Theory

We here combine the electrostatically embedded multiconfiguration molecular mechanics (EE-MCMM) method for generating global potential energy surfaces in the presence of an electrostatic potential with molecular mechanics (MM). The resulting EE-MCMM/MM method is illustrated by applying it to carry out a molecular dynamics simulation for the symmetric bimolecular reaction Cl(-) + CH3Cl' → ClCH3 + Cl'(-) in aqueous solution with hybrid density functional theory as the quantum mechanical level. The potential of mean force is calculated, and the free energy barrier is found to be 25.3 kcal/mol, which is in good agreement with previous work. The advantage of the combined EE-MCMM and MM method is that the number of quantum mechanical calculations required for the active subsystem is very small compared to straight direct dynamics.

Valence bond and enzyme catalysis: a time to break down and a time to build up

Understanding enzyme catalysis and developing ability to control of it are two great challenges in biochemistry. A few successful examples of computational-based enzyme design have proved the fantastic potential of computational approaches in this field, however, relatively modest rate enhancements have been reported and the further development of complementary methods is still required. Herein we propose a conceptually simple scheme to identify the specific role that each residue plays in catalysis. The scheme is based on a breakdown of the total catalytic effect into contributions of individual protein residues, which are further decomposed into chemically interpretable components by using valence bond theory. The scheme is shown to shed light on the origin of catalysis in wild-type haloalkane dehalogenase (wt-DhlA) and its mutants. Furthermore, the understanding gained through our scheme is shown to have great potential in facilitating the selection of non-optimal sites for catalysis and suggesting effective mutations to enhance the enzymatic rate.

How valence bond theory can help you understand your (bio)chemical reaction

This Tutorial Review describes modern VB theory, using a didactic example of an S_N2 reaction to illustrate its immediate applications.

A tutorial for understanding chemical reactivity through the valence bond approach

This is a tutorial on the usage of valence bond (VB) diagrams for understanding chemical reactivity in general, and hydrogen atom transfer (HAT) reactivity in particular. The tutorial instructs the reader how to construct the VB diagrams and how to estimate HAT barriers from raw data, starting with the simplest reaction H + H2 and going all the way to HAT in the enzyme cytochrome P450. Other reactions are treated as well, and some unifying principles are outlined. The tutorial projects the unity of reactivity treatments, following Coulson's dictum "give me insight, not numbers", albeit with its modern twist: giving numbers and insight.

Quantum mechanical study of solvent effects in a prototype SN2 reaction in solution: Cl- attack on CH3Cl

The nucleophilic attack of a chloride ion on methyl chloride is an important prototype SN2 reaction in organic chemistry that is known to be sensitive to the effects of the surrounding solvent. Herein, we develop a highly accurate Specific Reaction Parameter (SRP) model based on the Austin Model 1 Hamiltonian for chlorine to study the effects of solvation into an aqueous environment on the reaction mechanism. To accomplish this task, we apply high-level quantum mechanical calculations to study the reaction in the gas phase and combined quantum mechanical/molecular mechanical simulations with TIP3P and TIP4P-ew water models and the resulting free energy profiles are compared with those determined from simulations using other fast semi-empirical quantum models. Both gas phase and solution results with the SRP model agree very well with experiment and provide insight into the specific role of solvent on the reaction coordinate. Overall, the newly parameterized SRP Hamiltonian is able to reproduce both the gas phase and solution phase barriers, suggesting it is an accurate and robust model for simulations in the aqueous phase at greatly reduced computational cost relative to comparably accurate ab initio and density functional models.

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.

Type-I dyotropic reactions: understanding trends in barriers

To understand the factors that control the activation barrier of type-I 1,2-dyotropic reactions (X-EH(2)-CH(2)-X*→X*-EH(2)-CH(2)-X, with E=C and Si, X=H, CH(3), SiH(3), F to I) and trends therein as a function of the migrating groups X, we have explored ten archetypal model reactions of this class using relativistic density functional theory (DFT) at ZORA-OLYP/TZ2P. The main trends in reactivity are rationalized using the activation strain model of chemical reactivity, which had to be extended from bimolecular to unimolecular reactions. Thus, the above type-I dyotropic reactions can be conceived as a relative rotation of the CH(2)CH(2) and [X···X] fragments in X-CH(2)-CH(2)-X. The picture that emerges from these analyses is that reduced C-X bonding in the transition state is the origin of the reaction barrier. Also the trends in reactivity on variation of X can be understood in terms of how sensitive the C-X interaction is towards adopting the transition-state geometry. A valence bond analysis complements the analyses and confirms the picture emerging from the activation strain model.

The valence bond way: reactivity patterns of cytochrome P450 enzymes and synthetic analogs

The preceding decade has witnessed an immense surge of activity in the bioinorganic chemistry of transition metal enzymes and synthetic analogs that model their operation. The wide range of research covers both experimental and theoretical investigations of structure and reactivity patterns. Theory, and especially density functional theory (DFT), has become a very useful tool, an important partner of experiment in resolving structural and mechanistic issues. This flare of activity has generated a great deal of knowledge on intermediates, transition states, barriers, rate constants, rate-equilibrium relationships, stereoselectivity, and so forth. This abundance of acquired knowledge has created the need for establishing order, namely, the outlining of broad generalizations, as well as the creation of a more-intuitive interface between experimental and theoretical data. The valence bond (VB) diagram model, originally developed for organic reactions, is such a theoretical framework that has the potential to guide the requisite generalizations in the field of bioinorganic chemical reactivity. In this Account, we briefly describe the principles of construction of VB diagrams for bioinorganic reactions, detailing applications in the booming research area of heme enzyme (specifically cytochrome P450) reactivity, and particularly two archetypal reactions of these enzymes, alkane hydroxylation and thioether sulfoxidation. For congruence with the lingua franca of bioinorganic chemistry, the VB model is formulated to create bridges to (i) the molecular orbital (MO) description, (ii) the oxidation state formulation of transition metal complexes, and (iii) widely used concepts such as the Bell-Evans-Polanyi (BEP) principle. The VB diagram model reveals the origins of the barrier, describes the formation of transition states and reaction intermediates, and allows the prediction of barrier heights and structure-reactivity relationships. Thus, from the VB diagram model, we can rationalize the mechanistic selection during alkane hydroxylation compared with thioether sulfoxidation, as well as the different behaviors of the spin states during the reactions with the active species of P450, the high-valent iron oxo species called compound I (Cpd I). Furthermore, the VB model leads to expressions that enable us to estimate barrier heights from easily accessible reactant properties, such as bond energies, ionization potential, and electron affinities. We further show that the model is not limited to these archetypal processes: its applicability is wider and more general. Accordingly, we outline the potential applications of these principles to other reactions of P450 (such as olefin epoxidation and arene hydroxylation) and to similar reactions of nonheme enzymes and synthetic models. The VB diagram model leads to a unified understanding of complex bioinorganic transformations, creates order in the data, and provides an important framework for making useful predictions.

Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase S(N)2 Reaction of Acetate Ion with 1,2-Dichloroethane

Diabatic models are widely employed for studying chemical reactivity in condensed phases and enzymes, but there has been little discussion of the pros and cons of various diabatic representations for this purpose. Here we discuss and contrast six different schemes for computing diabatic potentials for a charge rearrangement reaction. They include (i) the variational diabatic configurations (VDC) constructed by variationally optimizing individual valence bond structures and (ii) the consistent diabatic configurations (CDC) obtained by variationally optimizing the ground-state adiabatic energy, both in the nonorthogonal molecular orbital valence bond (MOVB) method, along with the orthogonalized (iii) VDC-MOVB and (iv) CDC-MOVB models. In addition, we consider (v) the fourfold way (based on diabatic molecular orbitals and configuration uniformity), and (vi) empirical valence bond (EVB) theory. To make the considerations concrete, we calculate diabatic electronic states and diabatic potential energies along the reaction path that connects the reactant and the product ion-molecule complexes of the gas-phase bimolecular nucleophilic substitution (S(N)2) reaction of 1,2-dichloethane (DCE) with acetate ion, which is a model reaction corresponding to the reaction catalyzed by haloalkane dehalogenase. We utilize ab initio block-localized molecular orbital theory to construct the MOVB diabatic states and ab initio multi-configuration quasidegenerate perturbation theory to construct the fourfold-way diabatic states; the latter are calculated at reaction path geometries obtained with the M06-2X density functional. The EVB diabatic states are computed with parameters taken from the literature. The MOVB and fourfold-way adiabatic and diabatic potential energy profiles along the reaction path are in qualitative but not quantitative agreement with each other. In order to validate that these wave-function-based diabatic states are qualitatively correct, we show that the reaction energy and barrier for the adiabatic ground state, obtained with these methods, agree reasonably well with the results of high-level calculations using the composite G3SX and G3SX(MP3) methods and the BMC-CCSD multi-coefficient correlation method. However, a comparison of the EVB gas-phase adiabatic ground-state reaction path with those obtained from MOVB and with the fourfold way reveals that the EVB reaction path geometries show a systematic shift towards the products region, and that the EVB lowest-energy path has a much lower barrier. The free energies of solvation and activation energy in water reported from dynamical calculations based on EVB also imply a low activation barrier in the gas phase. In addition, calculations of the free energy of solvation using the recently proposed SM8 continuum solvation model with CM4M partial atomic charges lead to an activation barrier in reasonable agreement with experiment only when the geometries and the gas-phase barrier are those obtained from electronic structure calculations, i.e., methods i-v. These comparisons show the danger of basing the diabatic states on molecular mechanics without the explicit calculation of electronic wave functions. Furthermore, comparison of schemes i-v with one another shows that significantly different quantitative results can be obtained by using different methods for extracting diabatic states from wave function calculations, and it is important for each user to justify the choice of diabatization method in the context of its intended use.

An Effective Hamiltonian Molecular Orbital-Valence Bond (MOVB) Approach for Chemical Reactions Applied to the Nucleophilic Substitution Reaction of Hydrosulfide Ion and Chloromethane

An effective Hamiltonian mixed molecular orbital and valence bond (EH-MOVB) method is described to obtain an accurate potential energy surface for chemical reactions. Building upon previous results on the construction of diabatic and adiabatic potential surfaces using ab initio MOVB theory, we introduce a diabatic-coupling scaling factor to uniformly scale the ab initio off-diagonal matrix element H(12) such that the computed energy of reaction from the EH-MOVB method is in agreement with the target value. The scaling factor is very close to unity, resulting in minimal alteration of the potential energy surface of the original MOVB model. Furthermore, the relative energy between the reactant and product diabatic states in the EH-MOVB method can be improved to match the experimental energy of reaction. A key ingredient in the EH-MOVB theory is that the off-diagonal matrix elements are functions of all degrees of freedom of the system and the overlap matrix is explicitly evaluated. The EH-MOVB method has been applied to the nucleophilic substitution reaction between hydrosulfide and chloromethane to illustrate the methodology and the results were matched to reproduce the results from ab initio valence bond self-consistent valence bond (VBSCF) calculations. The diabatic coupling (the off-diagonal matrix element in the generalized secular equation) has small variations along the minimum energy reaction path in the EH-MOVB model, whereas it shows a maximum value at the transition state and has nearly zero values in the regions of the ion-dipole complexes from VBSCF calculations. The difference in the diabatic coupling stabilization is attributed to the large overlap integral in the computationally efficient MOVB method.

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.

Ab initio calculations of free-energy reaction barriers

The theoretical description of chemical reactions was until recently limited to a 'static' approach in which important parameters such as the rate constant are deduced from the local topology of the potential energy surface close to minima and saddle points. Such an approach has, however, serious limitations. The growing computational power allows us now to use advanced simulation techniques to determine entropic effects accurately for medium-sized systems at ab initio level. Recently, we have implemented free-energy simulation techniques based on molecular dynamics, in particular on the blue-moon ensemble technique and on metadynamics, in the popular DFT code VASP. In the thermodynamic integration (blue-moon ensemble) technique, the free-energy profile is calculated as the path integral over the restoring forces along a parametrized reaction coordinate. In metadynamics, an image of the free-energy surface is constructed on the fly during the simulation by adding small repulsive Gaussian-shaped hills to the Lagrangian driving the dynamics. The two methods are tested on a simple chemical reaction-the nucleophilic substitution of methyl chloride by a chlorine anion.

The rates of S(N)2 reactions and their relation to molecular and solvent properties

The energy barriers of symmetrical methyl exchanges in the gas phase have been calculated with the reaction path of the intersecting/interacting-state model (ISM). Reactive bond lengths increase down a column of the Periodic Table and compensate for the decrease in the force constants, which explains the near constancy of the intrinsic barriers in the following series of nucleophiles: F(-) approximately Cl(-) approximately Br(-) approximately I(-). This compensation is absent along the rows of the Periodic Table and the trend in the reactivity is dominated by the increase in the electrophilicity index of the nucleophile in the series C<N<O<F. Solvent effects have been quantitatively incorporated into the ISM model through a correlation between electrophilicity and the solvent acceptor number. This correlation is transferable between nucleophiles and solvents and allows the methyl transfer rate constants in solution to be calculated with remarkable simplicity and accuracy. The relationship between the S(N)2 and electron-transfer mechanisms is clarified and it is shown that smaller solvent static effects should be expected for electron transfer in the absence of a thermodynamic driving force.