Valence Bond Approach Research Articles

Q-RepEx: A Python pipeline to increase the sampling of empirical valence bond simulations

The exploration of chemical systems occurs on complex energy landscapes. Comprehensively sampling rugged energy landscapes with many local minima is a common problem for molecular dynamics simulations. These multiple local minima trap the dynamic system, preventing efficient sampling. This is a particular challenge for large biochemical systems with many degrees of freedom. Replica exchange molecular dynamics (REMD) is an approach that accelerates the exploration of the conformational space of a system, and thus can be used to enhance the sampling of complex biomolecular processes. In parallel, the empirical valence bond (EVB) approach is a powerful approach for modeling chemical reactivity in biomolecular systems. Here, we present an open-source Python-based tool that interfaces with the Q simulation package, and increases the sampling efficiency of the EVB free energy perturbation/umbrella sampling approach by means of REMD. This approach, Q-RepEx, both decreases the computational cost of the associated REMD-EVB simulations, and opens the door to more efficient studies of biochemical reactivity in systems with significant conformational fluctuations along the chemical reaction coordinate.

Exploiting the quantum mechanically derived force field for functional materials simulations

The computational design of functional materials relies heavily on large-scale atomistic simulations. Such simulations are often problematic for conventional classical force fields, which require tedious and time-consuming parameterization of interaction parameters. The problem can be solved using a quantum mechanically derived force field (QMDFF)—a system-specific force field derived directly from the first-principles calculations. We present a computational approach for atomistic simulations of complex molecular systems, which include the treatment of chemical reactions with the empirical valence bond approach. The accuracy of the QMDFF is verified by comparison with the experimental properties of liquid solvents. We illustrate the capabilities of our methodology to simulate functional materials in several case studies: chemical degradation of material in organic light-emitting diode (OLED), polymer chain packing, material morphology of organometallic photoresists. The presented methodology is fast, accurate, and highly automated, which allows its application in diverse areas of materials science.

Histidine protonation states are key in the LigI catalytic reaction mechanism.

Lignin is one of the world's most abundant organic polymers, and 2-pyrone-4,6-dicarboxylate lactonase (LigI) catalyzes the hydrolysis of 2-pyrone-4,6-dicarboxylate (PDC) in the degradation of lignin. The pH has profound effects on enzyme catalysis and therefore we studied this in the context of LigI. We found that changes of the pH mostly affects surface residues, while the residues at the active site are more subject to changes of the surrounding microenvironment. In accordance with this, a high pH facilitates the deprotonation of the substrate. Detailed free energy calculations by the empirical valence bond (EVB) approach revealed that the overall hydrolysis reaction is more likely when the three active site histidines (His31, His33 and His180) are protonated at the ɛ site, however, protonation at the δ site may be favored during specific steps of the reaction. Our studies have uncovered the determinant role of the protonation state of the active site residues His31, His33 and His180 in the hydrolysis of PDC.

Valence bond approach and Verma bases

The unitary group approach (UGA) to the many-fermion problem is based on the Gel’fand–Tsetlin (G–T) representation theory of the unitary or general linear groups. It exploits the group chain $$\mathrm {U}(n) \supset \mathrm {U}(n-1) \supset \cdots \supset \mathrm {U}(2) \supset \mathrm {U}(1)$$ and the associated G–T triangular tableau labeling basis vectors of the relevant irreducible representations (irreps). The general G–T formalism can be drastically simplified in the many-electron case enabling an efficient exploitation in either configuration interaction (CI) or coupled cluster approaches to the molecular electronic structure. However, while the reliance on the G–T chain provides an excellent general formalism from the mathematical point of view, it has no specific physical significance and dictates a fixed Yamanouchi–Kotani coupling scheme, which in turn leads to a rather arbitrary linear combination of distinct components of the same multiplet with a given orbital occupancy. While this is of a minor importance in molecular orbital based CI approaches, it is very inconvenient when relying on the valence bond (VB) scheme, since the G–T states do not correspond to canonical Rumer structures. While this shortcoming can be avoided by relying on the Clifford algebra UGA formalism, which enables an exploitation of a more or less arbitrary coupling scheme, it is worthwhile to point out the suitability of the so-called Verma basis sets for the VB-type approaches.

Empirical Valence Bond Simulations of Organophosphate Hydrolysis: Theory and Practice.

Recent years have seen an explosion of interest in understanding the mechanisms of phosphate ester hydrolysis in biological systems, using a range of computational approaches, each with different advantages and limitations. In this contribution, we present the empirical valence bond (EVB) approach as a powerful tool for modeling biochemical reactivity, using the example of organophosphate hydrolysis by diisopropyl fluorophosphatase as our model reaction. We walk the reader through the protocol for setting up and performing EVB simulations, as well as key technical considerations that need to be taken into account. Finally, we provide examples of the applications of the EVB approach to understanding different experimental observables.

Why does the Y326I mutant of monoamine oxidase B decompose an endogenous amphetamine at a slower rate than the wild type enzyme? Reaction step elucidated by multiscale molecular simulations.

This work investigates the Y326I point mutation effect on the kinetics of oxidative deamination of phenylethylamine (PEA) catalyzed by the monoamine oxidase B (MAO B) enzyme. PEA is a neuromodulator capable of affecting the plasticity of the brain and is responsible for the mood enhancing effect caused by physical exercise. Due to a similar functionality, PEA is often regarded as an endogenous amphetamine. The rate limiting step of the deamination was simulated at the multiscale level, employing the Empirical Valence Bond approach for the quantum treatment of the involved valence states, whereas the environment (solvated protein) was represented with a classical force field. A comparison of the reaction free energy profiles delivered by simulation of the reaction in the wild type MAO B and its Y326I mutant yields an increase in the barrier by 1.06 kcal mol-1 upon mutation, corresponding to a roughly 6-fold decrease in the reaction rate. This is in excellent agreement with the experimental kinetic studies. Inspection of simulation trajectories reveals possible sources of the point mutation effect, namely vanishing favorable electrostatic interactions between PEA and a Tyr326 side chain and an increased amount of water molecules at the active site due to the replacement of tyrosine by a less spacious isoleucine residue, thereby increasing the dielectric shielding of the catalytic environment provided by the enzyme.

SN2 Reaction Rate Enhancement by β-Cyclodextrin at the Liquid/Liquid Interface

An inverse phase transfer catalyst typically enhances the rate of biphasic reaction by bringing the water-insoluble reactant from the organic to the aqueous phase. We use the empirical valence bond (EVB) approach to obtain reaction free energy profiles for a model SN2 reaction inside the β-cyclodextrin (β-CD) cavity at the water/1-bromooctane interface and in bulk water to show that a significant rate enhancement is taking place at the liquid/liquid interface rather than in the bulk. By examining several solvent–solute structural and energetic properties, we demonstrate that the rate enhancement when the reaction takes place inside the cavity at the interface is primarily due to limited accessibility of interfacial water molecules, which results in destabilization of the reactants. Greater accessibility of water molecules when the catalyst is in the bulk stabilizes the reactants and does not lead to rate enhancement despite the significant hydrophobicity of the cavity’s interior.

Merging Empirical Valence Bond Theory with Quantum Chemistry to Model Proton Transfer Processes in Water

Proton transfer processes in water are of fundamental importance for, among others, electrochemical proton discharge. Empirical valence bond (EVB) approaches were shown in the past to be a versatile tool for modeling complex phenomena such as proton discharge at metal electrodes. By replacing empirical fitting procedures with on-the-fly quantum chemistry (QC) calculations, we arrive at a transferable and systematically tunable description of proton transfer in water with EVB.

Theory and Applications of the Empirical Valence Bond Approach: From Physical Chemistry to Chemical Biology

Theory and Applications of the Empirical Valence Bond Approach: From Physical Chemistry to Chemical Biology

On the performance of generalized valence bond theory in predicting magnetic exchange coupling constant in organic diradicals: A comparison with Hartree-Fock theory

We have investigated four different already synthesized meta- and para-connected diradicals to get their magnetic exchange coupling constants (J) through generalized valence bond (GVB) approach and also with Hartree-Fock (HF) theory with a view to establish the superiority of GVB method over HF theory for the prediction of J. In doing so, at first optimization of these molecules are done at B3LYP level of density functional theory using the 6-31++g(d) basis set. With these optimized geometries, J values are computed at GVB method along with TZV basis set and these values are compared with those of the J values obtained using HF/TZV level of theory. Nonetheless, J values found in both the theoretical processes are also compared with the experimental findings. Thus, the supremacy of the wavefunction based GVB method in predicting J is established in comparison with the HF method.

A possible valence-bond approach to symmetry-adapted perturbation theory

The multi-configurational ansatz of valence-bond theory may serve as basis for calculating intermolecular interaction energies in a non-orthogonal basis. We look in the present contribution at the possibility to obtain the 1st-order electrostatic interactions from breathing-orbital valence-bond densities, and the 2nd-order dispersion energy from dipole-dipole interactions. The discussion is based on numerical results for the interaction of two N2O molecules.

Comparing hydroxide and hydronium at the instantaneous air-water interface using polarizable multi-state empirical valence bond models

A new molecular model for the hydroxide anion was developed and its propensity for the air-water interface was compared with that of the hydronium ion. The multi-state empirical valence bond approach with polarizable potentials was used for both of these, allowing them to share their charge with adjacent water molecules. The hydroxide anion appeared to have a lower propensity for the air-water interface than that of hydronium when comparing its potential of mean force with respect to the Gibbs dividing surface. However, upon further inspection it was found that the hydroxide and hydronium ions had similar free energies at the instantaneous air-water interface. The reason for this discrepancy is that the hydroxide anion has a greater free energy when it was partially solvated. Or in other words, when the hydroxide anion is one molecular layer from the instantaneous air-water interface, but potentially still near the Gibbs dividing surface, it is less stable than the hydronium in a similar configuration. This shows that using the instantaneous interface can provide additional important insights.

Combining rival π‐space descriptions of O3 and of SO2

Two rival solutions have emerged from applications of spin‐coupled (SC) theory, also known as the full‐generalized valence bond (full‐GVB) approach, to the π system of O3. The lowest solution (SCd) corresponds to significant diradical character but there is a second solution (SCc) which lies fairly close in energy. Combining these two descriptions, it turns out that both of them make significant contributions, with neither being dominant. The situation is entirely different for SO2, with the SCc description being overwhelmingly dominant over SCd. It can be concluded from an examination of various combinations of rival π‐space descriptions for both molecules that neither of the SCc nor SCd solutions provides a very satisfactory description on its own of the π system in O3, but that SO2 is already fairly well described by SCc before the explicit incorporation of any SCd character. © 2016 Wiley Periodicals, Inc.

Molecular Dynamics Study of Proton Transport in Modeled Water Cluster Structure of Polymer Electrolyte Membrane

The polymer electrolyte membrane (PEM) is one of the principal components for polymer electrolyte fuel cells. 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, 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 within a molecular dynamics (MD) framework. In PEM, 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 bulk-like water structure due to the phase separation in PEM. Since the phase separation is considered one of the primary factors affecting its performance, the morphological properties of PEM have been studied experimentally and been characterized by proposing the cluster models (e.g., the cylinder model, the lamellar model, and the cluster-rod model) which reasonably fit the experimental scattering spectra. However, a detailed relationship between the morphological features and PT is still under debate. In this study, atomistic MD simulations have been performed to study the effects of water cluster structure on PT properties. The systems were built to closely approximate the proposed hydrophilic cluster structures (the cylinder model and the lamellar model) that are the most major morphological models of Nafion. The PT properties were estimated in terms of diffusion coefficient and proton pathway using a modified EVB model developed based on the previous study of the two-state EVB model by Walbran et al. The diffusion coefficients in each dimension were calculated and correlated with the cluster size as well as the type of cluster models. It was found that proton diffusion is strongly affected by the cluster model and its size, which can be associated with the proton pathway in each cluster model. The influence of the sulfonate groups on the PT properties were also investigated. Our simulation results provide insight into quantitative information about PT properties in atomic level.

Nature of the chemical bond and origin of the inverted dipole moment in boron fluoride: a generalized valence bond approach.

The generalized product function energy partitioning (GPF-EP) method has been applied to investigate the nature of the chemical bond and the origin of the inverted dipole moment of the BF molecule. The calculations were carried out with GPF wave functions treating all of the core electrons as a single Hartree-Fock group and the valence electrons at the generalized valence bond perfect-pairing (GVB-PP) or full GVB levels, with the cc-pVTZ basis set. The results show that the chemical structure of both X (1)Σ(+) and a (3)Π states is composed of a single bond. The lower dissociation energy of the excited state is attributed to a stabilizing intraatomic singlet coupling involving the B 2sp-like lobe orbitals after bond dissociation. An increase of electron density on the B atom caused by the reorientation of the boron 2sp-like lobe orbitals is identified as the main responsible effect for the electric dipole inversion in the ground state of BF. Finally, it is shown that π back-bonding from fluorine to boron plays a minor role in the electron density displacement to the bonding region in both states. Moreover, this effect is associated with changes in the quasi-classical component of the electron density only and does not contribute to covalency in either of the states. Therefore, at least for the case of the BF molecule, the term back-bonding is misleading, since it does not contribute to the bond formation.

A quantitative metric for conjugation in polyene hydrocarbons having a single classical structure.

A quantitative measure of the extent of conjugation is introduced. The number of Dewar resonance structures (DS) in a conjugated hydrocarbon quantitatively determines its extent of conjugation interaction. The greater the degree of conjugation the more stable is the conjugated hydrocarbon. The number of single bonds joining the exo-double bonds of a purely cross-conjugated hydrocarbon is equal to its number of Dewar resonance structures (DS). Polyene cross-conjugated hydrocarbons are minimally conjugated and possess only one classical structure with a succession of fixed single and exo-double bonds. There are three increasing levels of conjugation for systems with a single classical structure according to whether they are cross-conjugated, linear extended two-way conjugated, and ring-enhanced conjugated. Numerous analytical expressions have been derived. Our valence-bond (VB) approach involves studying the interrelationship of several well-known series of conjugated hydrocarbons having only a single classical structure, i.e., the number of Kekulé resonance structures is one (K = 1). This work provides a totally new perspective to the concept of conjugation.

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.

Chemical reaction with two different elementary transition states

The phenomenon of the elementary chemical reaction with two different transition states (TSs) between reactant and product is represented. Different examples of the reaction with two transition states were reported during the last decade. In some cases, one route is dominant, in another cases the energy of the barriers is similar, but the electronic structure of TSs are different. The Valence Bond (VB) approach provides the rationalization for the phenomenon of the chemical reaction with two TSs: the reactant and product pair is based on three dominant VB structures (anchors). The VB approach provides an opportunity to distinguish between different resonance mechanisms – different TSs. The 2D‐domain is based on two minima, the reactant and the product, which are connected by two different TSs and can include the electronic degeneracy. Physical consequences of the chemical reaction with dual reaction routes are discussed. © 2014 Wiley Periodicals, Inc.

A tutorial for understanding chemical reactivity through the valence bond approach

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

Modern valence-bond description of aromatic annulene ions

Spin-coupled theory for ‘N electrons in M orbitals’ active spaces [SC(N,M)], an ab initio valence-bond (VB) approach which uses a compact and easy-to-interpret wave function comparable in quality to a ‘N in M’ complete-activespace self-consistent field [CASSCF(N,M)] construction, is used to obtain modern VB descriptions of the π-electron systems of the most important annulene rings with 4n + 2 π electrons: the cyclopropenium ion, the cyclobutadiene dication and dianion, the cyclopentadienide anion, benzene, the cycloheptatrienyl cation, and the cyclooctatetraene dication and dianion in their highest-symmetry nuclear conformations. The SC wave functions for the cyclopropenium ion, cyclopentadienide anion, cycloheptatrienyl cation, cyclooctatetraene dication and dianion are shown to closely resemble the well-known SC model of the classical example of an aromatic system, benzene. The SC orbitals for the cyclobutadiene dication and dianion are more delocalized and demonstrate the ways in which SC wave functions adjust to electron-deficient and electron-rich environments. The high levels of resonance observed in all annulene ions with 4n + 2 π electrons clearly demonstrate their aromaticity.