Solvation Effects on the SN2 Reaction between CH3Cl and Cl- in Water

Dataset for quantum-mechanical exploration of conformers and solvent effects in large drug-like molecules

We here introduce the Aquamarine (AQM) dataset, an extensive quantum-mechanical (QM) dataset that contains the structural and electronic information of 59,783 low-and high-energy conformers of 1,653 molecules with a total number of atoms ranging from 2 to 92 (mean: 50.9), and containing up to 54 (mean: 28.2) non-hydrogen atoms. To gain insights into the solvent effects as well as collective dispersion interactions for drug-like molecules, we have performed QM calculations supplemented with a treatment of many-body dispersion (MBD) interactions of structures and properties in the gas phase and implicit water. Thus, AQM contains over 40 global and local physicochemical properties (including ground-state and response properties) per conformer computed at the tightly converged PBE0+MBD level of theory for gas-phase molecules, whereas PBE0+MBD with the modified Poisson-Boltzmann (MPB) model of water was used for solvated molecules. By addressing both molecule-solvent and dispersion interactions, AQM dataset can serve as a challenging benchmark for state-of-the-art machine learning methods for property modeling and de novo generation of large (solvated) molecules with pharmaceutical and biological relevance.

Two-Channel Model for Electron Transfer in a Dye-Catalyst-Dye Supramolecular Complex for Photocatalytic Water Splitting

To improve the performance of dye-sensitized photoelectrochemical cell (DS-PEC) devices for splitting water, the tailoring of the photocatalytic four-photon water oxidation half-reaction represents a principle challenge of fundamental significance. In this study, a Ru-based water oxidation catalyst (WOC) covalently bound to two 2,6-diethoxy-1,4,5,8-diimide-naphthalene (NDI) dye functionalities provides comparable driving forces and channels for electron transfer. Constrained ab initio molecular dynamics simulations are performed to investigate the photocatalytic cycle of this two-channel model for photocatalytic water splitting. The introduction of a second light-harvesting dye in the Ru-based dye-WOC-dye supramolecular complex enables two separate parallel electron-transfer channels, leading to a five-step catalytic cycle with three intermediates and two doubly oxidized states. The total spin S=1 is conserved during the catalytic process and the system with opposite spin on the oxidized NDI proceeds from the Ru=O intermediate to the final Ru-O2 intermediate with a triplet molecular 3 O2 ligand that is eventually released into the environment. The in-depth insight into the proposed photocatalytic cycle of the two-channel model provides a strategy for the development of novel high-efficiency supramolecular complexes for DS-PEC devices with buildup and conservation of spin multiplicity along the reaction coordinate as a design principle.

Tuning the Proton-Coupled Electron-Transfer Rate by Ligand Modification in Catalyst-Dye Supramolecular Complexes for Photocatalytic Water Splitting

In view of the considerably high activation energy barrier of the O-O bond formation photocatalytic step in water oxidation, it is essential to understand if and how nonadiabatic factors can accelerate the proton-coupled electron transfer (PCET) rate in this process to find rational design strategies facilitating this step. Herein, constrained ab initio molecular dynamics simulations are performed to investigate this rate-limiting step in a series of catalyst-dye supramolecular complexes functionalized with different alkyl groups on the catalyst component. These structural modifications lead to tunable thermodynamic driving forces, PCET rates, and vibronic coupling with specific resonant torsional modes. These results reveal that such resonant coupling between electronic and nuclear motions contributes to crossing catalytic barriers in PCET reactions by enabling semiclassical coherent conversion of a reactant into a product. Our results provide insight on how to engineer efficient catalyst-dye supramolecular complexes by functionalization with steric substituents for high-performance dye-sensitized photoelectrochemical cells.

Tackling Solvent Effects by Coupling Electronic and Molecular Density Functional Theory

Solvation effects can have a tremendous influence on chemical reactions. However, precise quantum chemistry calculations are most often done either in vacuum neglecting the role of the solvent or using continuum solvent model ignoring its molecular nature. We propose a new method coupling a quantum description of the solute using electronic density functional theory with a classical grand-canonical treatment of the solvent using molecular density functional theory. Unlike a previous work, both densities are minimized self-consistently, accounting for mutual polarization of the molecular solvent and the solute. The electrostatic interaction is accounted using the full electron density of the solute rather than fitted point charges. The introduced methodology represents a good compromise between the two main strategies to tackle solvation effects in quantum calculation. It is computationally more effective than a direct quantum mechanics/molecular mechanics coupling, requiring the exploration of many solvent configurations. Compared to continuum methods, it retains the full molecular-level description of the solvent. We validate this new framework onto two usual benchmark systems: a water solvated in water and the symmetrical nucleophilic substitution between chloromethane and chloride in water. The prediction for the free energy profiles are not yet fully quantitative compared to experimental data, but the most important features are qualitatively recovered. The method provides a detailed molecular picture of the evolution of the solvent structure along the reaction pathway.

Proton Acceptor near the Active Site Lowers Dramatically the O-O Bond Formation Energy Barrier in Photocatalytic Water Splitting

The O-O bond formation process via water nucleophilic attack represents a thermodynamic and kinetic bottleneck in photocatalytic water oxidation because of the considerably high activation free energy barrier. It is therefore of fundamental significance and yet challenging to find strategies to facilitate this reaction. The microscopic details of the photocatalytic water oxidation step involving the O-O bond formation in a catalyst-dye supramolecular complex are here elucidated by density functional theory-based Car-Parrinello molecular dynamics simulations in the presence of an extra proton acceptor. Introducing a proton acceptor group (OH-) in the hydration shell near the catalytic active site accelerates the rate-limiting O-O bond formation by inducing a cooperative event proceeding via a concerted proton-coupled electron-transfer mechanism and thus significantly lowering the activation free energy barrier. The in-depth insight provides a strategy for facilitating the photocatalytic water oxidation and for improving the efficiency of dye-sensitized photoelectrochemical cells.

Energetic Effects of a Closed System Approach Including Explicit Proton and Electron Acceptors as Demonstrated by a Mononuclear Ruthenium Water Oxidation Catalyst

When considering water oxidation catalysis theoretically, accounting for the transfer of protons and electrons from one catalytic intermediate to the next remains challenging: correction factors are usually employed to approximate the energetics of electron and proton transfer. Here these energetics were investigated using a closed system approach, which places the catalytic intermediate in a simulation box including proton and electron acceptors, as well as explicit solvent. As a proof of principle, the first two catalytic steps of the mononuclear ruthenium-based water oxidation catalyst [Ru(cy)(bpy)(H2O)]2+ were examined using Car-Parrinello Molecular Dynamics. This investigation shows that this approach offers added insight, not only into the free energy profile between two stable intermediates, but also into how the solvent environment impacts this dynamic evolution.

Efficient synthesis of organic thioacetates in water

Thioacetates as precursors of thiols are interesting starting points for synthesizing other organosulfur compounds. Herein, we propose a simple, efficient and fast method to obtain organic thioacetates using water as a solvent. Taking into account the great attention that has been paid toward environmentally friendly synthetic procedures in the past decades, we prove the role and the strength of the thioacetate anion as a nucleophile for nucleophilic displacement reactions in an aqueous medium. The reactions were carried out under pH control, to prevent the decomposition of the mesylate starting materials, using potassium carbonate as a safe and mild base. A simple work up allows products to be obtained with excellent yield and acceptable purity.

An interacting quantum atom study of model SN 2 reactions (X- ···CH3 X, X = F, Cl, Br, and I)

The quantum chemical topology method has been used to analyze the energetic profiles in the X-  + CH3 X → XCH3  + X- SN 2 reactions, with X = F, Cl, Br, and I. The evolution of the electron density properties at the BCPs along the reaction coordinate has been analysed. The interacting quantum atoms (IQA) method has been used to evaluate the intra-atomic and interatomic energy variations along the reaction path. The different energetic terms have been examined by the relative energy gradient method and the ANANKE program, which enables automatic and unbiased IQA analysis. Four of the six most important IQA energy contributions were needed to reproduce the reaction barrier common to all reactions. The four reactions considered share many common characteristics but when X = F a number of particularities occur. © 2017 Wiley Periodicals, Inc.

Optimization and benchmarking of a perturbative Metropolis Monte Carlo quantum mechanics/molecular mechanics program

In this work, we present an optimized perturbative quantum mechanics/molecular mechanics (QM/MM) method for use in Metropolis Monte Carlo simulations. The model adopted is particularly tailored for the simulation of molecular systems in solution but can be readily extended to other applications, such as catalysis in enzymatic environments. The electrostatic coupling between the QM and MM systems is simplified by applying perturbation theory to estimate the energy changes caused by a movement in the MM system. This approximation, together with the effective use of GPU acceleration, leads to a negligible added computational cost for the sampling of the environment. Benchmark calculations are carried out to evaluate the impact of the approximations applied and the overall computational performance.

Microsolvation effects on the reactivity of oxy-nucleophiles: the case of gas-phase SN2 reactions of YO-(CH3OH) n=1,2 towards CH3Cl

The modified G4(MP2) method was applied to explore microsolvation effects on the reactivity of four solvated normal oxy-nucleophiles YO^-(CH₃OH) _n=1,2 (Y = CH₃, C₂H₅, FC₂H₄, ClC₂H₄), and five α-oxy-nucleophiles YO^-(CH₃OH) _n=1,2 (Y = HO, CH₃O, F, Cl, Br), in gas-phase S_N2 reactions towards the substrate CH₃Cl. Based on a Brønsted-type plot, our calculations reveal that the overall activation barriers of five microsolvated α-oxy-nucleophiles are obviously smaller than the prediction from the correlation line constructed by four normal microsolvated ones to different degrees, and clearly demonstrate the existence of an α-effect in the presence of one or two methanol molecule(s). Moreover, it was found that the α-effect of the mono-methanol microsolvated α-nucleophile is stronger than that of the monohydrated α-nucleophile. However, the α-effect of YO^-(CH₃OH)₂ becomes weaker for Y = HO and CH₃O, whereas it becomes stronger for Y = F, Cl, Br than that of YO^-(H₂O)₂, which can be explained by analyses of the activation strain model in the two cases. It was also found that the rationale about the low ionization energy of α-nucleophile inducing the α-effect was not widely significant. Graphical abstract Variation of alpha-effect in the gas-phase S_N2 reaction with the microsolvation.

Introducing a closed system approach for the investigation of chemical steps involving proton and electron transfer; as illustrated by a copper-based water oxidation catalyst

We present an ab initio molecular dynamics approach to characterize proton-coupled electron transfer catalytic steps and identify the preferred reaction mechanism.

Aqueous solutions: state of the art in ab initio molecular dynamics

The simulation of liquids by ab initio molecular dynamics (AIMD) has been a subject of intense activity over the last two decades. The significant increase in computational resources as well as the development of new and efficient algorithms has elevated this method to the status of a standard quantum mechanical tool that is used by both experimentalists and theoreticians. As AIMD computes the electronic structure from first principles, it is free of ad hoc parametrizations and has thus been applied to a large variety of physical and chemical problems. In particular, AIMD has provided microscopic insight into the structural and dynamical properties of aqueous solutions which are often challenging to probe experimentally. In this review, after a brief theoretical description of the Born-Oppenheimer and Car-Parrinello molecular dynamics formalisms, we show how AIMD has enhanced our understanding of the properties of liquid water and its constituent ions: the proton and the hydroxide ion. Thereafter, a broad overview of the application of AIMD to other aqueous systems, such as solvated organic molecules and inorganic ions, is presented. We also briefly describe the latest theoretical developments made in AIMD, such as methods for enhanced sampling and the inclusion of nuclear quantum effects.

Acidity constants of lumiflavin from first principles molecular dynamics simulations

DFT-based molecular dynamics simulations predict the acidity of lumiflavin in different redox states.

Tests of an adaptive QM/MM calculation on free energy profiles of chemical reactions in solution

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

RECENT DEVELOPMENT IN THE STUDY OF SN2 REACTIONS AT HETEROATOMS AND ION PAIR SYSTEMS

Present review outlines the experimental and theoretical studies on the SN 2 reactions at heteroatoms ( N , O and S ) and ion pair systems in recent years, especially introduce research carried out at our group in detail. The similarities and differences between SN 2 at heteroatoms and at carbon are discussed. Some new structure–energy relationships were proposed. The accuracy of various theoretical schemes for calculating potential energy surfaces has been assessed.

Binding affinity of a small molecule to an amorphous polymer in a solvent. Part 1: free energy of binding to a binding site

Crystallization is commonly used in a separation and purification process in the production of a wide range of materials in various industries. In industry, crystallization usually starts with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood; however, we hypothesize that there might be a possible correlation between binding affinity to a surface and enhancement of nucleation. Recent studies show that amorphous polymers can be used to control crystallization, selectively produce pharmaceutical polymorphs, and discover novel pharmaceutical polymorphs. To investigate the possible correlation between the binding affinity of one molecule to key binding sites (local binding) and heterogeneous nucleation activity as well as the possibility of using this binding affinity to help guide the selection of polymers that promote heterogeneous nucleation, we computed the free energy of binding of aspirin to four nonporous cross-linked polymers in an ethanol-water 38 v% mixture. These cross-linked polymers are poly(4-acryloylmorpholine) (PAM), poly(2-carboxyethyl acrylate) (PCEA), poly(4-hydroxylbutyl acrylate) (PHBA), and polystyrene (PS); all of them were cross-linked with divinylbenzene (DVB). These systems were used because their heterogeneous nucleation activities are available in literature, and the ranking is PAM > PCEA > PHBA ≈ PS. We generated three independent surfaces for each polymer and computed the free energy of binding of aspirin to the best binding site that we found on each surface. The average free energies of binding to the best sites of PAM, PCEA, PHBA, and PS are -20.4 ± 1.0, -16.7 ± 1.0, -14.4 ± 1.1, and -13.6 ± 1.1 kcal/mol, respectively. We found that the trend of the magnitudes of the average free energies of binding to the best sites is PAM > PCEA > PHBA ≈ PS. This trend is very similar to that of heterogeneous nucleation activity. Our results suggest the importance of the free energy of binding to key sites (local binding) and the possibility of using this quantity to help guide the selection of polymers that promote heterogeneous nucleation.

Free energy of binding of a small molecule to an amorphous polymer in a solvent

Crystallization is a commonly used purification process in industrial practice. It usually begins with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood, but we hypothesize that a possible correlation between binding affinity to a surface and nucleation enhancement might exist. Amorphous polymers have been used in controlling crystallization. However, to our knowledge, no attempt has been made to calculate the free energy of binding of a small molecule to an amorphous polymer in a solvent, and to characterize the binding sites/conformations of this system at a molecular level. We developed a two-step approach, first using Adsorption Locator to identify probable binding sites and molecular dynamics to screen for the best binding sites and then using the Blue-Moon Ensemble method to compute the free energy of binding. A system of ethylene glycol, polyvinyl alcohol (PVA), and heavy water (D(2)O) was used for validation, since experimental data exists on a related system. Looking at four independently constructed surfaces, we found that ethylene glycol binds to an indentation on the surface or in a hole beneath the surface. We focused on the indentation binding sites because they are easily accessible and do not have large free energy barriers. The closest system for which experimental data on binding energetics exists is ethylene glycol on PVA in aqueous solutions/gels, and the magnitudes of the free energy of binding to the three best indentation binding sites are close to the experimental value, 0.4-3.7 kcal/mol higher. Our approach offers a way to compute the free energy of binding and characterize the binding sites/conformations, and is general enough to apply to other small molecule/amorphous polymer/solvent systems.

Artificial reaction coordinate "tunneling" in free-energy calculations: the catalytic reaction of RNase H

We describe a method for the systematic improvement of reaction coordinates in quantum mechanical/molecular mechanical (QM/MM) calculations of reaction free-energy profiles. In umbrella-sampling free-energy calculations, a biasing potential acting on a chosen reaction coordinate is used to sample the system in reactant, product, and transition states. Sharp, nearly discontinuous changes along the resulting reaction path are used to identify coordinates that are relevant for the reaction but not properly sampled. These degrees of freedom are then included in an extended reaction coordinate. The general formalism is illustrated for the catalytic cleavage of the RNA backbone of an RNA/DNA hybrid duplex by the RNase H enzyme of Bacillus halodurans. We find that in the initial attack of the phosphate diester by water, the oxygen-phosphorus distances alone are not sufficient as reaction coordinates, resulting in substantial hysteresis in the proton degrees of freedom and a barrier that is too low (approximately 10 kcal/mol). If the proton degrees of freedom are included in an extended reaction coordinate, we obtain a barrier of 21.6 kcal/mol consistent with the experimental rates. As the barrier is approached, the attacking water molecule transfers one of its protons to the O1P oxygen of the phosphate group. At the barrier top, the resulting hydroxide ion forms a penta-coordinated phosphate intermediate. The method used to identify important degrees of freedom, and the procedure to optimize the reaction coordinate are general and should be useful both in classical and in QM/MM free-energy calculations.

To address accuracy and precision using methods from analytical chemistry and computational physics

In this work the pesticides were determined by liquid chromatography-mass spectrometry (LC-MS). In present study the occurrence of imidacloprid in 343 samples of oranges, tangerines, date plum, and watermelons from Valencian Community (Spain) has been investigated. The nine additional pesticides were chosen as they have been recommended for orchard treatment together with imidacloprid. The Mulliken population analysis has been applied to present the charge distribution in imidacloprid. Partitioned energy terms and the virial ratios have been calculated for certain molecules entering in interaction. A new technique based on the comparison of the decomposed total energy terms at various configurations is demonstrated in this work. The interaction ability could be established correctly in the studied case. An attempt is also made in this work to address accuracy and precision. These quantities are well-known in experimental measurements. In case precise theoretical description is achieved for the contributing monomers and also for the interacting complex structure some properties of this latter system can be predicted to quite a good accuracy. Based on simple hypothetical considerations we estimate the impact of applying computations on reducing the amount of analytical work.

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.

Duocarmycins binding to DNA investigated by molecular simulation

Duocarmycins are a potent class of antitumor agents, whose activity arises through their covalent binding to adenine nucleobases of DNA.(1-3) Here, we perform molecular dynamics (MD) and hybrid Car-Parinello QM/MM simulations to investigate aspects of duocarmycin binding to the d(pGpApCpTpApApTpTpGpApC) oligonucleotide. We focus on the derivatives (+)-duocarmycin SA (DSA) and (+)-duocarmycin SI (DSI), for which structural information of the covalent complex with the oligonucleotide is available, as well as on the related, but less reactive, NBOC-duocarmycin SA (NBOC-DSA), interacting with the same oligonucleotide. Comparison is made with adenine alkylation reaction in water performed by the smallest of these compounds (NBOC-DSA). The MD calculations suggest that, in noncovalent complexes, (i) drug binding causes a partial dehydration of the minor groove, without inducing a significant conformational changes, and (ii) DSA and DSI occupy a more favorable position for nucleophilic attack than NBOC-DSA, consistently with the lower reactivity of the latter. The QM/MM calculations, which are used to investigate the first step of the alkylation reaction, turn out to provide strongly underestimated free energy barriers. Within these approximations, our calculations suggest that an important ingredient for the experimentally observed DNA catalytic power is the polarization of the drug by the biomolecular scaffold.

Metadynamics as a tool for exploring free energy landscapes of chemical reactions

The metadynamics or hills method is a relatively new molecular dynamics technique aimed to enhance the sampling of separated regions in phase space and map out the underlying free energy landscape as a function of a small number of order parameters or collective variables. The high efficiency allows for the application of metadynamics in combination with first principles dynamics methods, in particular with Car-Parrinello molecular dynamics, to study processes in which changes in the electronic structure play a dominant role, such as chemical reactions. The option to choose several independent collective variables is important to tackle complex and concerted transformations that lack an obvious a priori choice for a single reaction coordinate. In this Account, we discuss the role of metadynamics in the search of transition states, local minima, reaction paths, free energy profiles, and reaction coordinates among a growing list of alternative methods.

Static and dynamic descriptions of bond breaking/formation: A complementary view?

Ab initio molecular-dynamic simulations using density-functional theory and the recent atom-centered density-matrix propagation (ADMP) method were used to study the bond breaking and formation for a case-study substitution nucleophilic bimolecular reaction, namely, the Walden inversion. Using the atoms-in-molecule approach, we have performed a detailed analysis to investigate intra- and intermolecular charge transfer along the ADMP trajectory. These results were compared to those obtained considering a static approach, such as the intrinsic reaction path. In particular, the topological properties computed along the dynamic trajectory well evidence a stronger electron exchange tending to spontaneously maximize the rising covalent interaction. Furthermore, their analysis suggests that the bond formation mechanism involves a reactive intermediate with a bonding interaction stronger than in the final product.

Evidence for Different Types of Water Participation in the Solvolysis of 1-Adamantyl, tert-Butyl, and Methyl Chlorides from Density Functional Theory Computations

[structure: see text] The activation energy in the gas phase (deltaE(double dagger)) and the free energy of activation (deltaG(double dagger)) in water solution for the hydrolysis of the monohydrates of methyl chloride (MeCl), tert-butyl chloride (t-BuCl), and 1-adamantyl chloride (AdCl) have been computed with the B3LYP/631-G(d) method and the polarizable continuum (PCM) solvation model. There is a fair agreement between the deltaG(double dagger) values computed by us and the experimental data. The mechanistic implications of our computations are in severe contradiction with conventional representations. Thus, the computed nucleophilic solvent assistance (NSA) for the backside attack of a water molecule in the hydrolysis of MeCl is slightly lower than the corresponding NSA for t-BuCl. Hence, the hydrolysis of both MeCl and t-BuCl takes place mainly according to the classical S(N)2 mechanism. The most relevant difference is that deltaG(double dagger) for the frontside attack of water to t-BuCl is disfavored only by ca. 2 kcal/mol with regard to the backside attack but by ca. 23 kcal/mol in the case of MeCl. The higher solvolysis rate in water of t-BuCl in relation to AdCl is not due to steric factors affecting the specific solvation of the corresponding transition states, but to differential bulk solvent effects, which are accounted for by the PCM model.

Carbon nanotube inner phase chemistry: the Cl- exchange SN2 reaction

Density functional calculations have been carried out to investigate the nature of the inner phase of a (6,6) carbon nanotube, using the Cl(-) exchange S(N)2 reaction as an indicator. Inside the carbon nanotube the classical barrier height increases by 6.6 kcal/mol due to the nanotube polarizability. This suggests that the inner phase environment can be considered a form of solid solvation, offering the possibility of obtaining altered guest properties and reactivity through dielectric stabilization.

Blue Moon Sampling, Vectorial Reaction Coordinates, and Unbiased Constrained Dynamics

We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic dynamics which, unlike the usual constrained molecular dynamics, introduces no bias. Finally, we give a new perspective on bias removal by using constrained molecular dynamics.

A Recipe for the Computation of the Free Energy Barrier and the Lowest Free Energy Path of Concerted Reactions

The recently introduced hills method (Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12562) is a powerful tool to compute the multidimensional free energy surface of intrinsically concerted reactions. We have extended this method by focusing our attention on localizing the lowest free energy path that connects the stable reactant and product states. This path represents the most probable reaction mechanism, similar to the zero temperature intrinsic reaction coordinate, but also includes finite temperature effects. The transformation of the multidimensional problem to a one-dimensional reaction coordinate allows for accurate convergence of the free energy profile along the lowest free energy path using standard free energy methods. Here we apply the hills method, our lowest free energy path search algorithm, and umbrella sampling to the prototype S(N)2 reaction. The hills method replaces the in many cases difficult problem of finding a good reaction coordinate with choosing relatively simple collective variables, such as the bond lengths of the broken and formed chemical bonds. The second part of the paper presents a guide to using the hills method, in which we test and fine-tune the method for optimal accuracy and efficiency using the umbrella sampling results as a reference.

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).

Methane-to-Methanol Oxidation by the Hydrated Iron(IV) Oxo Species in Aqueous Solution: A Combined DFT and Car−Parrinello Molecular Dynamics Study

Previously, we have shown that the ferryl ion ([FeIVO]2+) is easily produced from Fenton's reagent (i.e., a mixture of Fe2+ ions and H2O2 in aqueous solution), using DFT and Car-Parrinello MD calculations. To verify that the ferryl ion can indeed act as the active species in oxidation reactions with Fenton's reagent, we study in the present paper the reactivity of the ferryl ion toward an organic substrate, in particular the oxidation of methane to methanol. In the first part of this paper, we perform static DFT calculations on the reaction of CH4 with the [(H2O)5FeIVO]2+ complex in vacuo that show a strong prevalence of the oxygen-rebound mechanism over the methane coordination mechanism. This is in agreement with the static DFT results for methane oxidation by biocatalysts MMO and P450, but not with those for methane oxidation by bare metal-oxo ions, where the methane coordination mechanism prevails. The highest energy barrier in the oxygen-rebound mechanism is only 3 kcal/mol in vacuo, whereas in the methane coordination mechanism the highest barrier is 23 kcal/mol. Overall the oxidation reaction energy is downhill by 47 kcal/mol. We conclude that the ferryl ion can indeed act as the oxidative intermediate in the Fenton oxidation of organic species. In the second part of this paper, we perform a preliminary assessment of solvent effects on the oxidation by the ferryl ion in aqueous solution using the method of constrained (first principles) molecular dynamics. The free energy barrier of the H-abstraction reaction from methane by the ferryl ion (i.e., the first step in the rebound mechanism) in aqueous solution is, with 22 kcal/mol in solution, significantly higher than in vacuo. Given the fact that methane has a relatively strong C-H bond (ca. 10 kcal/mol stronger than the C-H bonds in the more typical Fenton's reagent substrates), we infer that for many organic substrates oxidation with the ferryl ion as an active intermediate may be a perfectly viable route.

A multilayered approach to approximating solute polarization

A hybrid multilayered "ONIOM"-type approach to solvation is presented in which the basic free energy of hydration is taken from the Poisson Boltzmann method and the contribution to the solute polarization is taken from a quantum mechanical implementation of the Born method. The method has been tested on the 52 neutral molecules used in the AM1-SM2 parameterization, and the polarized continuum method is taken as the standard by which the results are assessed. Regression analysis shows that the method gives a small improvement over the standard Poisson Boltzmann method or a dramatic improvement over the Born method. The system presented here represents one of the more straightforward applications of the multilayered approach to solvation, but other more sophisticated approaches are discussed.

Solvation effects on alternative nucleophilic substitution reaction paths for chloride/allyl chloride and gamma-methylated congeners

An adiabatic connection method, mPW1PW91(0.581)/6-31G(d), was employed in conjunction with the continuum solvation model SM5.42 to study the effects of solvation on the S(N)1, S(N)2, and syn and anti S(N)2' nucleophilic substitution reactions of chloride anion with allyl chloride and its gamma-methylated analogues Z- and E-crotyl chloride and isoprenyl chloride. The impact of equilibrium solvation on the potential energy surfaces of these systems is large and leads to significant changes in both the geometries and the relative energetics of different reaction pathways for different species. The predicted effects of increased solvent dielectric constant are consistent with available experimental data and provide semiquantitative insights into the relative influence of different solvents on particular properties.