Empirical Valence Bond Method Research Articles

Importance of hydrophobic traps for proton diffusion in lyotropic liquid crystals.

The diffusion of protons in self-assembled systems is potentially important for the design of efficient proton exchange membranes. In this work, we study proton dynamics in a low-water content, lamellar phase of a sodium-carboxylate gemini surfactant/water system using computer simulations. The hopping of protons via the Grotthuss mechanism is explicitly allowed through the multi-state empirical valence bond method. We find that the hydronium ion is trapped on the hydrophobic side of the surfactant-water interface, and proton diffusion then proceeds by hopping between surface sites. The importance of hydrophobic traps is surprising because one would expect the hydronium ions to be trapped at the charged headgroups. The physics illustrated in this system should be relevant to the proton dynamics in other amphiphilic membrane systems, whenever there exist exposed hydrophobic surface regions.

Effects of Water Structure on Proton Transport in Nafion Thin Films with Molecular Dynamics Simulations

Proton transport properties in Nafion thin films have been investigated using molecular dynamics simulations to characterize the nanoscopic flow phenomena in the electrode of polymer electrolyte fuel cell. Protons transfer in the ionomer by a combination of the Vehicle mechanism and the Grotthuss mechanism. In this study, the Grotthuss mechanism is described using the anharmonic two-state empirical valence bond method to evaluate quantitative proton transport within the framework of classical molecular dynamics simulations. The electrode consists of platinum-supported carbon and ionomers, and it is well known that the wettability of supported carbon depends on materials and operating environment. Our results suggested that the wettability affects morphology of the ionomer and proton transport.

Empirical Valence Bond Theory Studies of the CH4 + Cl → CH3 + HCl Reaction

We report a theoretical investigation of the CH4 + Cl hydrogen abstraction reaction in the framework of empirical valence bond (EVB) theory. The main purpose of this study is to benchmark the EVB method against previous experimental and theoretical work. Analytical potential energy surfaces for the reaction have been developed on which quasi-classical trajectory calculations were carried out. The surfaces agree well with ab initio calculations at stationary points along the reaction path and dynamically relevant regions outside the reaction path. The analysis of dynamical data obtained using the EVB method, such as vibrational, rotational, and angular distribution functions, shows that this method compares well to both experimental measurements and higher-level theoretical calculations, with the additional benefit of low computational cost.

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.

A modified two-state empirical valence bond model for proton transport in aqueous solutions.

A detailed analysis of the proton solvation structure and transport properties in aqueous solutions is performed using classical molecular dynamics simulations. A refined two-state empirical valence bond (aTS-EVB) method, which is based on the EVB model of Walbran and Kornyshev and the anharmonic water force field, is developed in order to describe efficiently excess proton transport via the Grotthuss mechanism. The new aTS-EVB model clearly satisfies the requirement for simpler and faster calculation, because of the simplicity of the two-state EVB algorithm, while providing a better description of diffusive dynamics of the excess proton and water in comparison with the previous two-state EVB models, which significantly improves agreement with the available experimental data. The results of activation energies for the excess proton and water calculated between 300 and 340 K (the temperature range used in this study) are also found to be in good agreement with the corresponding experimental data.

Qgui: A high-throughput interface for automated setup and analysis of free energy calculations and empirical valence bond simulations in biological systems

Structural information and activity data has increased rapidly for many protein targets during the last decades. In this paper, we present a high-throughput interface (Qgui) for automated free energy and empirical valence bond (EVB) calculations that use molecular dynamics (MD) simulations for conformational sampling. Applications to ligand binding using both the linear interaction energy (LIE) method and the free energy perturbation (FEP) technique are given using the estrogen receptor (ERα) as a model system. Examples of free energy profiles obtained using the EVB method for the rate-limiting step of the enzymatic reaction catalyzed by trypsin are also shown. In addition, we present calculation of high-precision Arrhenius plots to obtain the thermodynamic activation enthalpy and entropy with Qgui from running a large number of EVB simulations.

Molecular Dynamics Simulation of Proton Transport in Polymer Electrolyte Membrane.

We have performed a detailed analysis of proton solvation and transport properties in hydrated Nafion using molecular dynamics simulation. The revised empirical valence bond (EVB) method was developed in order to treat the excess proton transport through the Grotthuss mechanism. The new EVB model predicts a significantly enhanced transport in comparison with previous hopping models as well as the classical hydronium diffusion, which largely improves the agreement with the available experimental data. Our results suggest that a proton hopping mechanism has a small effect on the proton dissociation from the first solvation shell of sulfonate groups, namely that protons are not enhanced to separate from the sulfonate groups by the hopping mechanisms. From diffusion comparison between the Grotthuss and vehicular mechanism, the Grotthuss mechanism dominates the proton diffusion at the studied hydration levels including a hydration level of 3. It was also found that the vehicular mechanism dominates the electroosmotic transport of water molecules at the studied hydration levels.

Molecular dynamics studies on the structures of polymer electrolyte membranes and diffusion mechanism of protons and small molecules

We performed a series of molecular dynamics (MD) simulations on Nafion® membranes containing various quantities of H2O and CH3OH. The simulations afforded diverse nanoscale phase-separated structures, such as clusters, channels, and cluster–channels. The calculated cluster–channel structure qualitatively agrees with the experimental results of X-ray diffraction studies. We also investigated the diffusion mechanisms for H2O, protons, CH3OH, H2, and O2 in these membranes. To reproduce the hopping transfer of protons, we employed a semi-classical MD approach using the empirical valence bond method. The estimated diffusion coefficients of H2O and proton in the membranes significantly depended on the H2O content, and these values showed qualitatively good agreement with the experimental results. The diffusion coefficient of proton in H2O-rich membranes was much larger than that of H2O, and the proton mainly formed H5O2+ complex. Furthermore, the simulation results indicate that the majority of CH3OH permeates through the H2O clusters, and the majority of H2 and O2 permeates through the hydrophobic region of the membrane.

An Improved EVB Model for Proton Transport in Polymer Electrolyte Membrane

The heart of Polymer electrolyte fuel cells (PEFCs) is polymer electrolyte membrane (PEM) that separated the reactant gases and conducts protons. In the nanoscopic structure of the membrane, ion clusters are formed by water molecules gathered vicinity of sulfonate groups which are hydrophilic parts of Nafion membrane, and proton transport (PT) are largely attributed to the nanoscopic structure of polymer membranes and water aggregations. Thus, many macroscopic simulations that are based on continuum theory have found it difficult to discuss the relation between the structural and dynamical properties of protons within the membrane in previous experimental studies. It is critical to understand the PT mechanisms through polymer membrane and clarify an important link between the membrane nanostructure and the PT properties. In the bulk aqueous solution, it is observed that proton mobility is roughly 5 times higher than other cations such as K+ which have an ionic radius similar to the hydronium ions. This property of PT is attributed to a combination of proton hopping, known as the Grotthuss mechanism, and vehicular mechanism where protons diffuse in solution as a hydrated form (e.g. hydronium ions). Many research efforts have been focused on understanding the PT mechanism using theoretical basis for the proton hopping models such as the empirical valence bond (EVB) approaches which allow PT phenomena to be simulated accurately in MD simulations. In Nafion membranes, it is considered that proton hopping transport still takes place although the water dynamic property in the bulk aqueous solution is inhibited by a lack of bulklike water structure at low water contents. Although the PT properties including hopping mechanism in hydrated polymer membrane have been studied using the original two-state EVB method by Walbran et al., the diffusion of water was found to be significantly higher than that of protons as well as that of real water in their model. In this study, a revised EVB model has been developed based on the previous study of the two-state EVB model, the impact of the proton hopping mechanism on the structure and dynamics properties of protons in hydrated Nafion membrane has been investigated at different hydration levels. The new EVB model in bulk water predicts a significantly enhanced transport in comparison with previous hopping models, which largely improves the agreement with the available experimental data. We have determined the diffusion coefficients of protons and water molecules in hydrated Nafion membrane as a function of hydration level, and the results are in good agreement with experimental data for the studied hydration levels. Proton hopping mechanism is found to become more significant at higher hydration levels. The influence of the sulfonate groups on the PT properties have also been investigated in this study. Our simulation results provide insight into quantitative information about PT properties in atomic level.

Validating computer simulations of enantioselective catalysis; reproducing the large steric and entropic contributions in Candida Antarctica lipase B

The prospect for computer-aided refinement of stereoselective enzymes is further validated by simulating the ester hydrolysis by the wild-type and mutants of CalB, focusing on the challenge of dealing with strong steric effects and entropic contributions. This was done using the empirical valence bond (EVB) method in a quantitative screening of the enantioselectivity, considering both k(cat) and k(cat)/K(M) of the R and S stereoisomers. Although the simulations require very extensive sampling for convergence they give encouraging results and major validation, indicating that our approach offers a powerful tool for computer-aided design of enantioselective enzymes. This is particularly true in cases with large changes in steric effects where alternative approaches may have difficulties in capturing the interplay between steric clashes with the reacting substrate and protein flexibility.

Molecular Dynamics Simulations of Proton Transport in 3M and Nafion Perfluorosulfonic Acid Membranes

Proton transfer and local structures in 3M (EW 825) and Nafion (EW 890) membranes are investigated in this study by both standard nonreactive molecular dynamics and the self-consistent iterative multistate empirical valence bond method, which is capable of simulating multiple reactive protons and accounting for the Grotthuss mechanism of proton transport. The Nafion and 3M systems have the same backbone, so we can isolate and compare the effect of the different side chains by calculating the radial distribution functions (RDFs), self-diffusion constants, and other properties for three hydration levels at 5, 9, and 14 at 300 and 353 K. The conformations of the 3M and Nafion side chains are also compared. We found that even though many results are similar for both F3C and SPC/Fw water models, certain trends such as the sulfonate clustering can depend on the water model selected. The relationship between the different RDFs for the sulfonate, water, and hydronium is discussed. The self-diffusion constants of water for both membranes are found to be close with respect to each water model selected, even though the experimental values for 3M at 300 K are higher. The calculated self-diffusion constants of the excess protons are found to be higher for 3M than Nafion for hydration levels 9 and 14 at 300 K but statistically the same at 353 K.

Quantum Chemistry as a Tool in Asymmetric Biocatalysis: Limonene Epoxide Hydrolase Test Case

Cluster model: Large active-site models (see figure) are used to investigate the selectivity of limonene epoxide hydrolase, both the wild type and mutants optimized through directed evolution. Good agreement is found between theory and the experimental data, thus demonstrating that the quantum chemical cluster approach can be a powerful tool in the field of asymmetric biocatalysis.

Optimization of reorganization energy drives evolution of the designed Kemp eliminase KE07

Understanding enzymatic evolution is essential to engineer enzymes with improved activities or to generate enzymes with tailor-made activities. The computationally designed Kemp eliminase KE07 carries out an unnatural reaction by converting of 5-nitrobenzisoxazole to cyanophenol, but its catalytic efficiency is significantly lower than those of natural enzymes. Three series of designed Kemp eliminases (KE07, KE70, KE59) were shown to be evolvable with considerable improvement in catalytic efficiency. Here we use the KE07 enzyme as a model system to reveal those forces, which govern enzymatic evolution and elucidate the key factors for improving activity. We applied the Empirical Valence Bond (EVB) method to construct the free energy pathway of the reaction in the original KE07 design and the evolved R7 1/3H variant. We analyzed catalytic effect of residues and demonstrated that not all mutations in evolution are favorable for activity. In contrast to the small decrease in the activation barrier, in vitro evolution significantly reduced the reorganization energy. We developed an algorithm to evaluate group contributions to the reorganization energy and used this approach to screen for KE07 variants with potential for improvement. We aimed to identify those mutations that facilitate enzymatic evolution, but might not directly increase catalytic efficiency. Computational results in accord with experimental data show that all mutations, which appear during in vitro evolution were either neutral or favorable for the reorganization energy. These results underscore that distant mutations can also play role in optimizing efficiency via their contribution to the reorganization energy. Exploiting this principle could be a promising strategy for computer-aided enzyme design. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.

Proton Conduction in Exchange Membranes across Multiple Length Scales

Concerns over global climate change associated with fossil-fuel consumption continue to drive the development of electrochemical alternatives for energy technology. Proton exchange fuel cells are a particularly promising technology for stationary power generation, mobile electronics, and hybrid engines in automobiles. For these devices to work efficiently, direct electrical contacts between the anode and cathode must be avoided; hence, the separator material must be electronically insulating but highly proton conductive. As a result, researchers have examined a variety of polymer electrolyte materials for use as membranes in these systems. In the optimization of the membrane, researchers are seeking high proton conductivity, low electronic conduction, and mechanical stability with the inclusion of water in the polymer matrix. A considerable number of potential polymer backbone and side chain combinations have been synthesized to meet these requirements, and computational studies can assist in the challenge of designing the next generation of technologically relevant membranes. Such studies can also be integrated in a feedback loop with experiment to improve fuel cell performance. However, to accurately simulate the currently favored class of membranes, perfluorosulfonic acid containing moieties, several difficulties must be addressed including a proper treatment of the proton-hopping mechanism through the membrane and the formation of nanophase-separated water networks. We discuss our recent efforts to address these difficulties using methods that push the limits of computer simulation and expand on previous theoretical developments. We describe recent advances in the multistate empirical valence bond (MS-EVB) method that can probe proton diffusion at the nanometer-length scale and accurately model the so-called Grotthuss shuttling mechanism for proton diffusion in water. Using both classical molecular dynamics and coarse-grained descriptions that replace atomistic representations with collective coordinates, we investigated the proton conductivity of polymer membrane structure as a function of hydration level. Nanometer-sized water channels form torturous pathways that are traversed by the charges during fuel cell operation. Using a combination of coarse-grained membrane structure and novel multiscale methods, we demonstrate emerging approaches to treat proton motion at the mesoscale in these complex materials.

Proton Transport Pathways in [NiFe]-Hydrogenase

Hydrogenases reversibly catalyze the production of molecular hydrogen. Current interest in these enzymes is focused on understanding the catalysis, since this may prove useful for hydrogen-based fuel cell and photosynthetic hydrogen production cell technologies. A key step in the hydrogenase catalytic cycle and the focus of this work is proton transport (PT) to and from the active site. The PT mechanism of the enzyme is studied using reactive molecular dynamics simulations of the full protein and the excess proton transfers via the multistate empirical valence bond (MS-EVB) method. Pathways connecting the bulk and the active site are located that suggest possible participation by several protonatable residues. PT free energy surfaces are calculated to differentiate the pathways.

Towards Quantitative Computer‐Aided Studies of Enzymatic Enantioselectivity: The Case of Candida antarctica Lipase A

The prospect for consistent computer-aided refinement of stereoselective enzymes is explored by simulating the hydrolysis of enantiomers of an α-substituted ester by wild-type and mutant Candida antarctica lipase A, using several strategies. In particular, we focused on the use of the empirical valence bond (EVB) method in a quantitative screening for enantioselectivity, and evaluate both k(cat) and k(cat)/K(M) of the R and S stereoisomers. We found that an extensive sampling is essential for obtaining converging results. This requirement points towards possible problems with approaches that use a limited conformational sampling. However, performing the proper sampling appears to give encouraging results and to offer a powerful tool for the computer-aided design of enantioselective enzymes. We also explore faster strategies for identifying mutations that will help in augmenting directed-evolution experiments, but these approaches require further refinement.

Analysis of Proton and Water Transfer in PFSA Membrane by Molecular Dynamics Simulation

Protons transfer in polyelectrolyte membrane by both Vehicle and Grotthus mechanisms. This study describes the property of proton and water transfer in perfluorosulfonic acid (PFSA) membrane using molecular dynamics (MD) simulation in view of both Vehicle and Grotthus mechanisms. To treat Grotthus mechanism, Empirical Valence Bond (EVB) method was introduced to MD simulation. The potential energy barrier of proton hopping in EVB method was adjusted to the computational result of Density Functional Theory (DFT) to replicate the experimental value of diffusion coefficient of oxonium ions in water. The parameter for the simulation of PFSA membrane was water contents λ, which is defined as the ratio of water molecules and oxonium ions to sulfo groups, SO3-, obtained byλ=NH2O,H3O+/NSO3-. The structure of water and PFSA membrane was analyzed by Radial Distribution Function (RDF) and diffusion coefficient of proton was found out from Mean Square Displacement (MSD).

Development of the New Model for the Proton Hopping by Molecular Dynamics Simulation

The aim of this study is refinement of proton(s) hopping rate by applying new model for Molecular Dynamics (MD) calculation with Empirical Valence Bond (EVB) method. The overview about this new model is an acceptor selection method based on energy prediction instead of the one based on distance. The effect of water molecules outside the Eigen cation was mainly considered in this new model. Then, microenvironment interaction to the formation of the cluster and proton hopping were reasonably expressed as an actual condition. This procedure was applied for proton hopping. The total number of cluster formation and cancel were also analyzed.

Proton Solvation and Transport in Hydrated Nafion

Proton solvation properties and transport mechanisms have been studied in hydrated Nafion using the self-consistent multistate empirical valence bond (SCI-MS-EVB) method that includes the effects excess proton charge defect delocalization and Grotthuss proton hopping. It was found that sulfonate groups influence excess proton solvation, as well as the proton hydration structure, by stabilizing a more Zundel-like (H(5)O(2)(+)) structure in their first solvation shells. Hydrate proton-related hydrogen bond networks were observed to be more stable than networks with water alone. Diffusion rates, Arrhenius activation energies, and transport pathways were calculated and analyzed to characterize the nature of the proton transport. Diffusion rate analysis suggests that a proton-hopping mechanism dominates the proton transport for the studied water loading levels and that there is a clear degree of anticorrelation with the vehicular transport. The activation energy drops quickly with an increasing water content when the water loading level is smaller than ∼10 H(2)O/SO(3)(-), which is consistent with experimental observations. The sulfonate groups were also found to affect the proton hopping directions. The temperature and water content effects on the proton transport pathways were also investigated.

Infrared spectroscopy of small protonated water clusters at room temperature: An effective modes analysis

We perform infrared vibrational analysis on small protonated water clusters H(+)(H(2)O)(n), with n = 2, [ellipsis (horizontal)], 6, at room temperature. The absorption spectra are calculated based on classical trajectories obtained by the multistate empirical valence bond method. The analysis is carried out based on the effective modes analysis, which has been recently developed [Martinez et al., J. Chem. Phys. 125, 144106 (2006)] as generalization of the normal modes analysis. This technique enables us to decompose the full spectrum in maximally localized bands which are obtained by accounting for temperature and anharmonic effects. These effects are especially considered in the determination of the modes coupling. The spectra of the small clusters are interpreted by identifying the behavior of the excess charge, by understanding the role of hydrogen bonds, and by considering the effect of (micro-)solvation. Our results are presented by showing comparisons with other numerical methods and experimental measurements which are available in the literature.