Empirical Valence-Bond Models for Reactive Potential Energy Surfaces Using Distributed Gaussians

Toward transferable empirical valence bonds: Making classical force fields reactive

The empirical valence bond technique allows classical force fields to model reactive processes. However, parametrization from experimental data or quantum mechanical calculations is required for each reaction present in the simulation. We show that the parameters present in the empirical valence bond method can be predicted using a neural network model and the SMILES strings describing a reaction. This removes the need for quantum calculations in the parametrization of the empirical valence bond technique. In doing so, we have taken the first steps toward defining a new procedure for enabling reactive atomistic simulations. This procedure would allow researchers to use existing classical force fields for reactive simulations, without performing additional quantum mechanical calculations.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Multidimensional H-atom tunneling in the catecholate monoanion

We present the catecholate monoanion as a new model system for the study of multidimensional tunneling. It has a symmetrical O-H double-well structure, and the H atom motion between the two wells is coupled to both low and high frequency modes with different strengths. With a view to studying mode-specific tunneling in the catecholate monoanion, we have developed a full (33) dimensional potential energy surface in transition state (TS) normal modes using a Distributed Gaussian Empirical Valence Bond (DGEVB) based approach. We have computed eigenstates in different subspaces using both unrelaxed and relaxed potentials based on the DGEVB model. With unrelaxed potentials, we present results up to 7D subspaces that include the imaginary frequency mode and six modes coupled to it. With relaxed potentials, we focus on the two most important coupling modes. The structures of the ground and vibrationally excited eigenstates are discussed for both approaches and mode-specific tunneling splitting and their trends are presented.

Physics-based, neural network force fields for reactive molecular dynamics: Investigation of carbene formation from [EMIM+][OAc-]

Reactive molecular dynamics simulations enable a detailed understanding of solvent effects on chemical reaction mechanisms and reaction rates. While classical molecular dynamics using reactive force fields allows significantly longer simulation time scales and larger system sizes compared with ab initio molecular dynamics, constructing reactive force fields is a difficult and complex task. In this work, we describe a general approach following the empirical valence bond framework for constructing ab initio reactive force fields for condensed phase simulations by combining physics-based methods with neural networks (PB/NNs). The physics-based terms ensure the correct asymptotic behavior of electrostatic, polarization, and dispersion interactions and are compatible with existing solvent force fields. NNs are utilized for a versatile description of short-range orbital interactions within the transition state region and accurate rendering of vibrational motion of the reacting complex. We demonstrate our methodology for a simple deprotonation reaction of the 1-ethyl-3-methylimidazolium cation with acetate to form 1-ethyl-3-methylimidazol-2-ylidene and acetic acid. Our PB/NN force field exhibits ∼1 kJ mol^-1 mean absolute error accuracy within the transition state region for the gas-phase complex. To characterize the solvent modulation of the reaction profile, we compute potentials of mean force for the gas-phase reaction as well as the reaction within a four-ion cluster and benchmark against ab initio molecular dynamics simulations. We find that the surrounding ionic environment significantly destabilizes the formation of the carbene product, and we show that this effect is accurately captured by the reactive force field. By construction, the PB/NN potential may be directly employed for simulations of other solvents/chemical environments without additional parameterization.

Reactive Molecular Dynamics at Constant Pressure via Nonreactive Force Fields: Extending the Empirical Valence Bond Method to the Isothermal-Isobaric Ensemble

The Empirical Valence Bond (EVB) method offers a suitable framework to obtain reactive potentials through the coupling of nonreactive force fields. In this formalism, most of the implemented coupling terms are built using functional forms that depend on spatial coordinates, while parameters are fitted against reference data to model the change of chemistry between the participating nonreactive states. In this work, we demonstrate that the use of such coupling terms precludes the computation of the stress tensor for condensed phase systems and prevents the possibility to carry out EVB molecular dynamics in the isothermal-isobaric (NPT) ensemble. Alternatively, we make use of coupling terms that depend on the energy gaps, defined as the energy differences between the participating nonreactive force fields, and derive a general expression for the EVB stress tensor suitable for computation. Implementation of this new methodology is tested for a model of a single reactive malonaldehyde solvated in nonreactive water. Mass densities and probability distributions for the values of the energy gaps computed in the NPT ensemble reveal a negligible role of the reactive potential in the limit of low concentrated solutions, thus corroborating for the first time the validity of approximations based on the canonical NVT ensemble, customarily adopted for EVB simulations. The presented formalism also aims to contribute to future implementations and extensions of the EVB method to research the limit of highly concentrated solutions.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.

Coupled Valence-Bond State Molecular Dynamics Description of an Enzyme-Catalyzed Reaction in a Non-Aqueous Organic Solvent

Enzymes are widely used in nonaqueous solvents to catalyze non-natural reactions. While experimental measurements showed that the solvent nature has a strong effect on the reaction kinetics, the molecular details of the catalytic mechanism in nonaqueous solvents have remained largely elusive. Here we study the transesterification reaction catalyzed by the paradigm subtilisin Carlsberg serine protease in an organic apolar solvent. The rate-limiting acylation step involves a proton transfer between active-site residues and the nucleophilic attack of the substrate to form a tetrahedral intermediate. We design the first coupled valence-bond state model that simultaneously describes both reactions in the enzymatic active site. We develop a new systematic procedure to parametrize this model on high-level ab initio QM/MM free energy calculations that account for the molecular details of the active site and for both substrate and protein conformational fluctuations. Our calculations show that the reaction energy barrier changes dramatically with the solvent and protein conformational fluctuations. We find that the mechanism of the tetrahedral intermediate formation during the acylation step is similar to that determined under aqueous conditions, and that the proton transfer and nucleophilic attack reactions occur concertedly. We identify the reaction coordinate to be mostly due to the rearrangement of some residual water molecules close to the active site.

Computational Study of Competition between Direct Abstraction and Addition-Elimination in the Reaction of Cl Atoms with Propene

Quasi-classical trajectory calculations on a newly constructed and full-dimensionality potential energy surface (PES) examine the dynamics of the reaction of Cl atoms with propene. The PES is an empirical valence bond (EVB) fit to high-level ab initio energies and incorporates deep potential energy wells for the 1-chloropropyl and 2-chloropropyl radicals, a direct H atom abstraction route to HCl + allyl radical (CH2CHCH2(•)) products (Δ(r)H(298K)(⊖) = −63.1 kJ mol(-1)), and a pathway connecting these regions. In total, 94 000 successful reactive trajectories were used to compute distributions of angular scattering and HCl vibrational and rotational level populations. These measures of the reaction dynamics agree satisfactorily with available experimental data. The dominant reaction pathway is direct abstraction of a hydrogen atom from the methyl group of propene occurring in under 500 fs. Less than 10% of trajectories follow an addition–elimination route via the two isomeric chloropropyl radicals. Large amplitude motions of the Cl about the propene molecular framework couple the addition intermediates to the direct abstraction pathway. The EVB method provides a good description of the complicated PES for the Cl + propene reaction despite fitting to a limited number of ab initio points, with the further advantage that dynamics specific to certain mechanisms can be studied in isolation by switching off coupling terms in the EVB matrix connecting different regions of the PES.

Prediction of enhanced solvent-induced enantioselectivity for a ring opening with a bifurcating reaction path

A fully atomistic molecular dynamics simulation predicts enhance induction of enantiomeric excess in the products of a reaction with a bifurcating reaction coordinate, when run in a chiral solvent.

Reactive force fields made simple

Combining QMDFF with EVB allows to generate reactive force fields of useful quality for widely varying reactions with minimal effort.

Challenges in computational studies of enzyme structure, function and dynamics

In this review we give an overview of the field of Computational enzymology. We start by describing the birth of the field, with emphasis on the work of the 2013 chemistry Nobel Laureates. We then present key features of the state-of-the-art in the field, showing what theory, accompanied by experiments, has taught us so far about enzymes. We also briefly describe computational methods, such as quantum mechanics-molecular mechanics approaches, reaction coordinate treatment, and free energy simulation approaches. We finalize by discussing open questions and challenges.

Multisurface Adiabatic Reactive Molecular Dynamics

Adiabatic reactive molecular dynamics (ARMD) simulation method is a surface-crossing algorithm for modeling chemical reactions in classical molecular dynamics simulations using empirical force fields. As the ARMD Hamiltonian is time dependent during crossing, it allows only approximate energy conservation. In the current work, the range of applicability of conventional ARMD is explored, and a new multisurface ARMD (MS-ARMD) method is presented, implemented in CHARMM and applied to the vibrationally induced photodissociation of sulfuric acid (H2SO4) in the gas phase. For this, an accurate global potential energy surface (PES) involving 12 H2SO4 and 4 H2O + SO3 force fields fitted to MP2/6-311G++(2d,2p) reference energies is employed. The MS-ARMD simulations conserve total energy and feature both intramolecular H-transfer reactions and water elimination. An analytical treatment of the dynamics in the crossing region finds that conventional ARMD can approximately conserve total energy for limiting cases. In one of them, the reduced mass of the system is large, which often occurs for simulations of solvated biomolecular systems. On the other hand, MS-ARMD is a general approach for modeling chemical reactions including gas-phase, homogeneous, heterogeneous, and enzymatic catalytic reactions while conserving total energy in atomistic simulations.

Empirical valence bond models for reactive potential energy surfaces: a parallel multilevel genetic program approach

We describe a new method for constructing empirical valence bond potential energy surfaces using a parallel multilevel genetic program (PMLGP). Genetic programs can be used to perform an efficient search through function space and parameter space to find the best functions and sets of parameters that fit energies obtained by ab initio electronic structure calculations. Building on the traditional genetic program approach, the PMLGP utilizes a hierarchy of genetic programming on two different levels. The lower level genetic programs are used to optimize coevolving populations in parallel while the higher level genetic program (HLGP) is used to optimize the genetic operator probabilities of the lower level genetic programs. The HLGP allows the algorithm to dynamically learn the mutation or combination of mutations that most effectively increase the fitness of the populations, causing a significant increase in the algorithm's accuracy and efficiency. The algorithm's accuracy and efficiency is tested against a standard parallel genetic program with a variety of one-dimensional test cases. Subsequently, the PMLGP is utilized to obtain an accurate empirical valence bond model for proton transfer in 3-hydroxy-gamma-pyrone in gas phase and protic solvent.

Proton Transfer Studied Using a Combined Ab Initio Reactive Potential Energy Surface with Quantum Path Integral Methodology

The rates of intramolecular proton transfer are calculated on a full-dimensional reactive electronic potential energy surface that incorporates high level ab initio calculations along the reaction path and by using classical Transition State theory, Path-Integral Quantum Transition State Theory, and the Quantum Instanton approach. The specific example problem studied is malonaldehyde. Estimates of the kinetic isotope effect using the latter two methods are found to be in reasonable agreement with each other. Improvements and extensions of this practical, yet chemically accurate framework for the calculations of quantized, reactive dynamics are also discussed.

A Non-Orthogonal Block-Localized Effective Hamiltonian Approach for Chemical and Enzymatic Reactions

The effective Hamiltonian-molecular orbital and valence bond (EH-MOVB) method based on non-orthogonal block-localized fragment orbitals has been implemented into the program CHARMM for molecular dynamics simulations of chemical and enzymatic reactions, making use of semiempirical quantum mechanical models. Building upon ab initio MOVB theory, we make use of two parameters in the EH-MOVB method to fit the barrier height and the relative energy between the reactant and product state for a given chemical reaction to be in agreement with experiment or high-level ab initio or density functional results. Consequently, the EH-MOVB method provides a highly accurate and computationally efficient QM/MM model for dynamics simulation of chemical reactions in solution. The EH-MOVB method is illustrated by examination of the potential energy surface of the hydride transfer reaction from trimethylamine to a flavin cofactor model in the gas phase. In the present study, we employed the semiempirical AM1 model, which yields a reaction barrier that is more than 5 kcal/mol too high. We use a parameter calibration procedure for the EH-MOVB method similar to that employed to adjust the results of semiempirical and empirical models. Thus, the relative energy of these two diabatic states can be shifted to reproduce the experimental energy of reaction, and the barrier height is optimized to reproduce the desired (accurate) value by adding a constant to the off-diagonal matrix element. The present EH-MOVB method offers a viable approach to characterizing solvent and protein-reorganization effects in the realm of combined QM/MM simulations.

Block-Localized Density Functional Theory (BLDFT), Diabatic Coupling, and Their Use in Valence Bond Theory for Representing Reactive Potential Energy Surfaces

A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchange-correlation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of H2+ and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of H2+, the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S(N)2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.

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.

Efficient estimators for quantum instanton evaluation of the kinetic isotope effects: Application to the intramolecular hydrogen transfer in pentadiene

The quantum instanton approximation is used to compute kinetic isotope effects for intramolecular hydrogen transfer in cis-1,3-pentadiene. Due to the importance of skeleton motions, this system with 13 atoms is a simple prototype for hydrogen transfer in enzymatic reactions. The calculation is carried out using thermodynamic integration with respect to the mass of the isotopes and a path integral Monte Carlo evaluation of relevant thermodynamic quantities. Efficient "virial" estimators are derived for the logarithmic derivatives of the partition function and the delta-delta correlation functions. These estimators require significantly fewer Monte Carlo samples since their statistical error does not increase with the number of discrete time slices in the path integral. The calculation treats all 39 degrees of freedom quantum mechanically and uses an empirical valence bond potential based on a molecular mechanics force field.

Block-Localized Wavefunction (BLW) Method at the Density Functional Theory (DFT) Level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).

Optimizing the Performance of the Multiconfiguration Molecular Mechanics Method

Multiconfiguration molecular mechanics (MCMM) is a general algorithm for constructing potential energy surfaces for reactive systems (Kim, Y.; Corchado, J. C.; Villà, J.; Xing, J.; Truhlar, D. G. J. Chem. Phys. 2000, 112, 2718). This paper illustrates how the performance of the MCMM method can be improved by adopting improved molecular mechanics parameters. We carry out calculations of reaction rate constants using variational transition state theory with optimized multidimensional tunneling on the MCMM PESs for three hydrogen transfer reactions, and we compare the results to direct dynamics. We find that the MCMM method with as little as one electronic structure Hessian can describe the dynamically important regions of the ground-electronic state PES, including the corner-cutting-tunneling region of the reaction swath, with practical accuracy.