Valence Bond Method Research Articles

4-3 PEFC高分子電解質膜内部のプロトン輸送の分子動力学シミュレーション(セッション4:OS1-1 マルチスケール・シミュレーションとナノ計測)

Proton transfer in polymer electrolyte membrane (PEM) was analyzed by molecular dynamic simulation considering both Vehicle and Grotthus mechanism. The empirical valence bond (EVB) method was used to treat Grotthus mechanism and the intermolecular potential used in this method was determined so that the energy barrier during proton hopping obtained by this potential is consistent with that obtained by Molecular Orbital (MO) calculation. A perfluorosulfonic acid (PFSA) membrane was used as the PEM. The transport phenomena of proton was simulated according to the water content and the detailed mechanism was analyzed paying attention to the nanoscale structure of fluid in the PEM, such as water cluster.

Infrared Spectrum of the Hydrated Proton in Water.

Reactive molecular dynamics simulations have been utilized to calculate the infrared (IR) spectra of acidic HCl solutions of varying concentration with the goal of achieving a better understanding of the spectral features of the hydrated excess protons in bulk water. To incorporate the essential physics of the hydrated proton, we carried out the simulations using the specialized self-consistent iterative multistate empirical valence bond (SCI-MS-EVB) method, which is a form of multiconfigurational (reactive) molecular dynamics. After the pure water absorption background was removed, the calculated difference spectra are in good agreement with prior experimental results. The continuous broad absorption band in the acidic IR spectrum is, for the first time, interpreted based on the concept of a dynamically distorted Eigen cation, H9O4(+), which has been shown to provide the most accurate description for the charge defect character of the hydrated excess proton in liquid water.

Comment on “A stationary-wave model of enzyme catalysis” by Carlo Canepa

Energy barriers for enzyme-catalyzed reactions calculated with quantum mechanics/molecular mechanics (QM/MM) and empirical valence bond (EVB) methods can be in excellent agreement with activation energies derived from experiments, supporting the applicability of transition state theory for enzymic reactions.

On the Electronic Structure of H-Ng-Ng-F (Ng = Ar, Kr, Xe) and the Nonlinear Optical Properties of HXe2F.

The electronic ground state of H-Ng-Ng-F (Ng = Ar, Kr, Xe) has been studied theoretically by employing the ab initio complete active space valence bond (CASVB) and multi-state complete active space perturbation theory (MS-CASPT2) methods. Both levels of theory confirm the diradicaloid character (DC) of the HNg2F ground state, increasing in the order Ar > Kr > Xe. The very significant effect of the first and, even more, the second Xe atom on the (hyper)polarizabilities has been shown and interpreted. Thus, the present results demonstrate a mechanism for producing very large (hyper)polarizabilities.

Atoms in Valence Bond – AiVB. Synopsis and test results

The Atoms in Valence Bond (AiVB) method, a new approach in the Valence Bond, is introduced. This approach combines the ideas behind the early Atoms in Molecules (AIM) developments, e.g. by Moffit [21], to understand a molecular wave function in terms of proper atomic wave functions, with the available framework of the VBSCF [17,18] as implemented in turtle [19]. The fundamental theoretical tools, to explain the AiVB concept, are shown and the initial test results are presented.

Molecular Dynamics Study of Proton Transfer Including Grotthus Mechanism in Polymer Electrolyte Membrane

This study describes the property of proton transfer in Nafion membrane analyzed by molecular dynamics (MD) simulation including both Vehicle and Grotthus mechanism. To treat Grotthus mechanism, Empirical Valence Bond (EVB) method was introduced to MD simulation. The potential energy barrier of proton hopping obtained by EVB method was adjusted to the computational result of Density Functional Theory (DFT). After adjusting EVB potential, it is confirmed that protons hop along the hydrogen bond network consecutively. The parameter for the simulation of Nafion membrane was water contents λ, which is defined as the ratio of water molecules and hydronium ions to sulfo groups, SO3-, obtained byλ=NH2O,H3O+/NSO3-. The changes of transferring properties and structure of molecules with the changes of λ were analyzed by Mean Square Displacement and Radial Distribution Function, respectively.

A comparison of approaches to estimate the resonance energy

We discuss Ab Initio approaches to calculate the energy lowering (stabilisation) due to aromaticity. We compare the valence bond method and the block-localised wave function approaches to calculate the resonance energy. We conclude that the valence bond approach employs a Pauling–Wheland resonance energy and that the block-localised approach employs a delocalisation criterion. The latter is shown to be more basis set dependent in a series of illustrative calculations.

Generalized X-Pol Theory and Charge Delocalization States.

The mixed molecular orbital and valence bond (MOVB) method has been used to generalize the explicit polarization (X-Pol) potential to incorporate charge delocalization resonance effects in the framework of valence bond theory. In the original X-Pol method, a macromolecular system is partitioned into individual fragments or blocks, and the molecular orbitals of the system are strictly localized within each block. Consequently, these block-localized molecular orbitals (BLMOs) are nonorthogonal across different blocks. In the generalized X-Pol (GX-Pol) theory, we construct charge delocalization VB states by expanding the localization space from monomer blocks into pairwise delocalized blocks. Thus, the expansion of the basis space leads to charge delocalization between monomer pairs, and a series of pairwise delocalization states can be constructed. In general, L-body delocalized states can be analogously defined by grouping L monomer blocks into one. The Hartree product wave function for each state can be fully antisymmetrized, which introduces explicitly exchange repulsion among all blocks. The GX-Pol wave function is a linear combination of all L-body charge transfer (valence bond) states, which incorporates charge delocalization and their resonance as well as static correlation effects. The GX-Pol method provides a general and rigorous theory to incorporate charge delocalization explicitly into these fragment-based electronic structural methods for macromolecular systems.

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.

VB/MM Protein Landscapes: A Study of the SN2 Reaction in Haloalkane Dehalogenase

QM/MM methods are widely used for studies of reaction mechanisms in water and protein environments. Recently, we have developed the VB/MM method in which the QM part is implemented by the ab initio valence bond (VB) method. Here, we report on further improvement of the VB/MM method which makes it possible to use the method for reactivity studies in systems where the QM and MM parts are connected by covalent bonds followed by first ab initio VB study of reactivity in proteins. We implemented a simple link atom scheme to treat the boundary interactions. We tested the performance of the link atom treatment in combination with the VB/MM method on an S(N)2 reaction and found it to be sufficiently accurate. We then used the VB/MM method to study the S(N)2 reaction in haloalkane dehalogenase (DhlA). We show that the predicted reaction barrier heights are in good agreement with estimated experimental values, thereby validating the method. Finally, we analyze the reaction energetics in terms of contributions of the VB configurations and conclude that such analysis is instrumental in pinpointing the essential features of the catalytic mechanism.

Determinant of Cation Blocking Behavior in Aquaporin-1

The most extensively studied member of the aquaporin family, wildtype (WT) aquaporin-1 (AQP1), has been shown to effectively block cations from permeation across the cell membrane, thus maintaining the osmotic pressure of the cell. Recent experiments have suggested the essential role that the Selectivity Filter (SF) region of the channel plays in blocking cation flux. In the present study, the potential of mean forces for permeation of sodium cation (Na+), potassium cation (K+), and classical hydronium cation (H3O+) (without the possibility of Grotthuss proton shuttling) are characterized for a series of AQP1 mutants. The free energy barriers for conducting hydrated excess protons (H+), which diffuse via the Grotthuss mechanism, are characterized as well, by utilizing the multi-state empirical valence bond (MS-EVB) method. The maximum cation conductance is calculated using the Poisson-Nerst-Planck theory. The present study reveals the key role of the SF domain in cation gating and provides insight into the subtle mechanism of proton permeation mutants of the AQP1 channel.

0301 水分子ネットワーク構造におけるプロトン輸送特性の解明(OS3-1 ナノスケールの熱流動現象,オーガナイズドセッション)

In this paper, we present molecular dynamics study of the fast proton transport in water confined between hydroxylated silica surfaces. Empirical valence bond (EVB) method was introduced to our MD simulation system for reproducing Grotthuss mechanism (proton hopping). We evaluated the enhancement of Grotthuss mechanism by counting the number of hopping events in confined and bulk water. The number in confined water increases by 4-6 times compared to bulk value, suggesting the enhancement of proton transport. Furthermore, the activation energy of Grotthuss mechanism was calculated from Arrhenius plot for the number of hopping events. As a result, the activation energy decreases from 4.5 kcal/mol in bulk water to 3.4 kcal/mol in confined water, which leads to the fast proton motion.

T0501-2-2 分子動力学法を用いた高分子電解質膜内のプロトン輸送特性の解析([T0501-2]マイクロ・ナノスケールの熱流体現象(2))

This study describes the property of proton transfer in Nafion membrane analyzed by molecular dynamics (MD) simulation including both Vehicle and Grotthus mechanism. To treat Grotthus mechanism, Empirical Valence Bond(EVE) method was introduced to MD simulation. The potential energy barrier of proton hopping obtained by EVB method was adjusted to the computational result of Density Functional Theory (DFT). After adjusting EVB potential, it is confirmed that protons hop along the hydrogen bond network consecutively. The parameter for the simulation of Nafion membrane was water contents λ, which is defined as the ratio of water molecules and hydronium ions to sulfo groups, SO_<3^->, obtained by λ=N_<H2O,H3O+>/N_<SO3->. The changes of transferring properties and structure of molecules with the changes of λ were analyzed by Mean Square Displacement and Radial Distribution Function, respectively.

Hybrid Quantum/Classical Molecular Dynamics Simulations of the Proton Transfer Reactions Catalyzed by Ketosteroid Isomerase: Analysis of Hydrogen Bonding, Conformational Motions, and Electrostatics

Hybrid quantum/classical molecular dynamics simulations of the two proton transfer reactions catalyzed by ketosteroid isomerase are presented. The potential energy surfaces for the proton transfer reactions are described with the empirical valence bond method. Nuclear quantum effects of the transferring hydrogen increase the rates by a factor of approximately 8, and dynamical barrier recrossings decrease the rates by a factor of 3-4. For both proton transfer reactions, the donor-acceptor distance decreases substantially at the transition state. The carboxylate group of the Asp38 side chain, which serves as the proton acceptor and donor in the first and second steps, respectively, rotates significantly between the two proton transfer reactions. The hydrogen-bonding interactions within the active site are consistent with the hydrogen bonding of both Asp99 and Tyr14 to the substrate. The simulations suggest that a hydrogen bond between Asp99 and the substrate is present from the beginning of the first proton transfer step, whereas the hydrogen bond between Tyr14 and the substrate is virtually absent in the first part of this step but forms nearly concurrently with the formation of the transition state. Both hydrogen bonds are present throughout the second proton transfer step until partial dissociation of the product. The hydrogen bond between Tyr14 and Tyr55 is present throughout both proton transfer steps. The active site residues are more mobile during the first step than during the second step. The van der Waals interaction energy between the substrate and the enzyme remains virtually constant along the reaction pathway, but the electrostatic interaction energy is significantly stronger for the dienolate intermediate than for the reactant and product. Mobile loop regions distal to the active site exhibit significant structural rearrangements and, in some cases, qualitative changes in the electrostatic potential during the catalytic reaction. These results suggest that relatively small conformational changes of the enzyme active site and substrate strengthen the hydrogen bonds that stabilize the intermediate, thereby facilitating the proton transfer reactions. Moreover, the conformational and electrostatic changes associated with these reactions are not limited to the active site but rather extend throughout the entire enzyme.

Quantum dynamics of vibrational excitations and vibrational charge transfer processes in H+ + O2 collisions at collision energy 23 eV

Quantum mechanical study of vibrational state-resolved differential cross sections and transition probabilities for both the elastic/inelastic and the charge transfer processes have been carried out in the H+ + O2 collisions at the experimental collision energy of 23 eV. The quantum dynamics has been performed within the vibrational close-coupling rotational infinite-order sudden approximation framework employing our newly obtained quasi-diabatic potential energy surfaces corresponding to the ground and the first excited electronic states which have been computed using ab initio procedures and Dunning’s correlation consistent-polarized valence triple zeta basis set at the multireference configuration interaction level of accuracy. The present theoretical results for elastic/inelastic processes provide an overall agreement with the available state-selected experimental data, whereas the results for the charge transfer channel show some variance in comparison with those of experiments and are similar to the earlier theoretical results obtained using model effective potential based on projected valence bond method and using semi-empirical diatomics-in-molecules potential. The possible reason for discrepancies and the likely ways to improve the results are discussed in terms of the inclusion of higher excited electronic states into the dynamics calculation.

The Physical Origin of Saytzeff’s Rule

Hyperconjugation, hybridization, or what? The hyperconjugative effects in primary, secondary, and tertiary alkenes were estimated using ab initio valence bond methods to trace the origin of the empirical Saytzeff rule, which states that the formation of the more substituted alkene is preferred. Hyperconjugation between the π bond and the π-donating substituents governs Saytzeff's rule, whereas all other factors support an anti-Saytzeff pathway.

New problems for ab-initio valence bond theory

The ab-initio valence bond method previously developed in our laboratory proved to be particularly useful in the description of electronic structure of molecules and the evaluation of ionization potentials. More recently, the photoelectron spectrum of pyridine has been described by the same method allowing for the assignment of the n+ and π+ bands. From these studies a variational valence bond method of calculating intermolecular forces stemmed, that was applied to the He-He and He-Li systems. Its main feature is the use of a nonorthogonal basis set in order to avoid over-extension basis error. Another application is the theoretical study of the formation of acetylene from two CH fragments which revealed a sudden change in spin coupling in the approach of the two fragments. A more elaborate procedure to obtain a basis set to be used in the description of excited states has been developed and successfully applied to the LiH molecule.

On the adsorption of hydrogen by supported transition-metal catalysts and MgO

Many industrial catalysts consist of fine particles of transition metals bonded to substrates such as silica or alumina. These particles may be as few as 6 to 12 atoms (in fact some sources believe that the essential catalytic unit may be as few as two transition-metal atoms) in number. Such systems may catalyze a wide variety of reactions. The simplest reaction possible is the dissociation of H/sub 2/. In this paper the interaction of hydrogen with supported transition-metal catalysts is examined. Another system which dissociates H/sub 2/ is MgO when properly prepared. The active site for H/sub 2/ dissociation on an MgO surface is also examined and the behavior of MgO with that of a support transition metal for H/sub 2/ dissociation is contrasted. All calculations are performed using a molecular cluster approach. The computational methods employed are the restricted Hartree-Fock method, the unrestricted Hartree-Fock method, and the generalized valence bond method in the perfect pairing limit.

Interaction potentials and dynamics for Li + F collisions

We present diabatic potential curves for 1Σ, states of LiF and integral cross sections for elastic scattering of Li(2S) + F(2P) at thermal collision energies. Potential curves were obtained using atomic pseudopotentials and the extended valence-bond method. Pairs of coupled scattering equations were numerically integrated with a recently developed approach. Comparison of cross sections for homopolar (single channel) and homopolar plus ionic (two coupled channels) interactions provides information on the electron jump mechanism during collision.

Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase SN2 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.