Empirical Valence Bond Potential Research Articles

Why Do Empirical Valence Bond Simulations Yield Accurate Arrhenius Plots?

Computer simulations of the temperature dependence of enzyme reactions using the empirical valence bond (EVB) method have proven to give very accurate results in terms of the thermodynamic activation parameters. Here, we analyze the reasons for why such simulations are able to correctly capture activation enthalpies and entropies and how sensitive these quantities are to parametrization of the reactive potential energy function. We examine first the solution reference reaction for the enzyme ketosteroid isomerase, which corresponds to the acetate catalyzed deprotonation of the steroid in water. The experimentally determined activation parameters for this reaction turn out to be remarkably well reproduced by the calculations. By modifying the EVB potential so that the activation and reaction free energies become significantly shifted, we show that the activation entropy is basically invariant to such changes and that ΔS⧧ is instead determined by the specific mixture of the underlying force fields in the transition state region. The coefficients of this mixture do not change appreciably when the EVB potential is modified within reasonable limits, and hence, the estimate of ΔS⧧ becomes very robust. This is further verified by examining a more complex concerted hydride and proton transfer reaction in the enzyme hydroxybutyrate dehydrogenase.

Mixed quantum-classical simulation of the hydride transfer reaction catalyzed by dihydrofolate reductase based on a mapped system-harmonic bath model.

The hydride transfer reaction catalyzed by dihydrofolate reductase is studied using a recently developed mixed quantum-classical method to investigate the nuclear quantum effects on the reaction. Molecular dynamics simulation is first performed based on a two-state empirical valence bond potential to map the atomistic model to an effective double-well potential coupled to a harmonic bath. In the mixed quantum-classical simulation, the hydride degree of freedom is quantized, and the effective harmonic oscillator modes are treated classically. It is shown that the hydride transfer reaction rate using the mapped effective double-well/harmonic-bath model is dominated by the contribution from the ground vibrational state. Further comparison with the adiabatic reaction rate constant based on the Kramers theory confirms that the reaction is primarily vibrationally adiabatic, which agrees well with the high transmission coefficients found in previous theoretical studies. The calculated kinetic isotope effect is also consistent with the experimental and recent theoretical results.

Restrained Proton Indicator in Combined Quantum-Mechanics/Molecular-Mechanics Dynamics Simulations of Proton Transfer through a Carbon Nanotube.

Recently, a collective variable "proton indicator" was purposed for tracking an excess proton solvated in bulk water in molecular dynamics simulations. In this work, we demonstrate the feasibility of utilizing the position of this proton indicator as a reaction coordinate to model an excess proton migrating through a hydrophobic carbon nanotube in combined quantum-mechanics/molecular-mechanics simulations. Our results indicate that applying a harmonic restraint to the proton indicator in the bulk solvent near the nanotube pore entrance leads to the recruitment of water molecules into the pore. This is consistent with an earlier study that employed a multistate empirical valence bond potential and a different representation (center of excess charge) of the proton. We attribute this water recruitment to the delocalized nature of the solvated proton, which prefers to be in high-dielectric bulk solvent. While water recruitment into the pore is considered an artifact in the present simulations (because of the artificially imposed restraint on the proton), if the proton were naturally restrained, it could assist in building water wires prior to proton transfer through the pore. The potential of mean force for a proton translocation through the water-filled pore was computed by umbrella sampling, where the bias potentials were applied to the proton indicator. The free energy curve and barrier heights agree reasonably with those in the literature. The results suggest that the proton indicator can be used as a reaction coordinate in simulations of proton transport in confined environments.

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

Classical molecular dynamics simulations are reported for the deazetisation and ring opening of meso-2,3-difluoro-2,3-dimethyldiazocyclopropane in three solvents: CHCl3, CHFClBr and CH3CH(OH)CF3 (TFIPA). The achiral reactant leads to enantiomeric allene products, and the question addressed in the study is whether either of the chiral, enantiomerically pure solvents can induce significant enantiomeric excess in the products. The direct dynamics calculations use an empirical valence bond potential for the solute, with empirical parameters optimised against M06-2X/cc-pVTZ density functional results. The results reveal that the exothermic N2 loss and ring opening promote transient strong solvent-solute interactions within the first ∼100 fs of the reaction. Because of the bifurcating reaction path, these interactions occur at time when the "decision" about which enantiomer of the product to form has yet to be made (at least for many of the trajectories). Hence, it is possible in principle that the solvent could exert a larger-than-normal influence on the course of the reaction. In fact, the results reveal no such effect for CHFClBr but do predict that TFIPA should induce 15.2 ± 2.1% enantiomeric excess. This is roughly an order of magnitude larger than solvent-induced enantiomeric excesses found experimentally in reactions where the conversion of reactant(s) to enantiomeric products occur over separate transition states.

Molecular dynamics of excited state intramolecular proton transfer: 3-hydroxyflavone in solution

The ultrafast enol-keto photoisomerization in the lowest singlet excited state of 3-hydroxyflavone is investigated using classical molecular dynamics in conjunction with empirical valence bond (EVB) potentials for the description of intramolecular interactions, and a molecular mechanics and variable partial charge model, dependent on transferring proton position, for the description of solute-solvent interactions. A parallel multi-level genetic program was used to accurately fit the EVB potential energy surfaces to high level ab initio data. We have studied the excited state intramolecular proton transfer (ESIPT) reaction in three different solvent environments: methylcyclohexane, acetonitrile, and methanol. The effects of the environment on the proton transfer time and the underlying mechanisms responsible for the varied time scales of the ESIPT reaction rates are analyzed. We find that simulations with our EVB potential energy surfaces accurately reproduce experimentally determined reaction rates, fluorescence spectra, and vibrational frequency spectra in all three solvents. Furthermore, we find that the ultrafast ESIPT process results from a combination of ballistic transfer, and intramolecular vibrational redistribution, which leads to the excitation of a set of low frequency promoting vibrational modes. From this set of promoting modes, we find that an O-O in plane bend and a C-H out of plane bend are present in all three solvents, indicating that they are fundamental to the ultrafast proton transfer. Analysis of the slow proton transfer trajectories reveals a solvent mediated proton transfer mechanism, which is diffusion limited.

Paradynamics: An Effective and Reliable Model for Ab Initio QM/MM Free-Energy Calculations and Related Tasks

Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

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.

Computational Approach for Ranking Mutant Enzymes According to Catalytic Reaction Rates

A computationally efficient approach for ranking mutant enzymes according to the catalytic reaction rates is presented. This procedure requires the generation and equilibration of the mutant structures, followed by the calculation of partial free energy curves using an empirical valence bond potential in conjunction with biased molecular dynamics simulations and umbrella integration. The individual steps are automated and optimized for computational efficiency. This approach is used to rank a series of 15 dihydrofolate reductase mutants according to the hydride transfer reaction rate. The agreement between the calculated and experimental changes in the free energy barrier upon mutation is encouraging. The computational approach predicts the correct direction of the change in free energy barrier for all mutants, and the correlation coefficient between the calculated and experimental data is 0.82. This general approach for ranking protein designs has implications for protein engineering and drug design.

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.

Towards Accurate Ab Initio QM/MM Calculations of Free-Energy Profiles of Enzymatic Reactions

Reliable studies of enzymatic reactions by combined quantum mechanical/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a large amount of computer time to evaluate the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. This work presents major progress toward the evaluation of ab initio QM/MM free-energy surfaces and activation free energies of reactions in enzymes and in solutions. This is done by exploiting our previous idea of using the empirical valence bond (EVB) method as a reference potential and then using the linear response approximation (LRA) approach to evaluate the free energies of transfer from the EVB to the QM/MM surfaces in the reactant and product state. However, the new crucial step involves the use of a constraint at the transition state that fixes the system at a given value of the reaction coordinate and allows us to use the LRA at the transition state. The advance offered by the present approach is particularly significant because it evaluates the free energy associated with both the substrate and the solvent motions. This evaluation appeared to be a relatively simple task once one uses a classical reference potential. The main problem has been using the reference potential for the evaluation of the free-energy contributions associated with the solute motions where the difference between the reference EVB potential and the QM/MM potential can be large. The present refinement finally allows us to overcome the problems with the solute fluctuations and therefore to obtain, for the first time, a free-energy barrier that reflects the solute entropy properly. Thus, we present a way to evaluate the complete QM/MM activation free energy with an equal footing treatment of the solute and the solvent. This provides a general consistent and effective strategy for evaluating the QM/MM activation free energies in proteins and in solution. Our advance allows one to explore consistently various mechanistic and catalytic proposals while using ab initio (ai) QM/MM approaches.

The properties of ion-water clusters. II. Solvation structures of Na+, Cl−, and H+ clusters as a function of temperature

Ion-water-cluster properties are investigated both through the multistate empirical valence bond potential and a polarizable model. Equilibrium properties of the ion-water clusters H+(H2O)100, Na+(H2O)100, Na+(H2O)20, and Cl-(H2O)17 in the temperature region 100-450 K are explored using a hybrid parallel basin-hopping and tempering algorithm. The effect of the solid-liquid phase transition in both caloric curves and structural distribution functions is investigated. It is found that sodium and chloride ions largely reside on the surface of water clusters below the cluster melting temperature but are solvated into the interior of the cluster above the melting temperature, while the solvated proton was found to have significant propensity to reside on or near the surface in both the liquid- and solid-state clusters.

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.

Molecular Dynamics of Excited State Intramolecular Proton Transfer: 2-(2‘-Hydroxyphenyl)-4-methyloxazole in Gas Phase, Solution, and Protein Environments

The ultrafast enol−keto photoisomerization in the lowest singlet excited state of 2-(2‘-hydroxyphenyl)-4-methyloxazole (HPMO) is investigated using classical molecular dynamics in conjunction with an empirical valence bond potential. This process is studied in four different environments: the gas phase, dimethyl sulfoxide, water, and human serum albumin protein. The effects of the environment on the proton transfer time and the promoting-mode motions are analyzed. The ring−ring in-plane bending of HPMO is identified as the dominant low-frequency vibrational mode that decreases the proton donor−acceptor distance to facilitate proton transfer. The mean proton transfer times are 100−200 fs in all of the environments. The population decay of the enol tautomer in the S1 state is significantly slower for the reaction in water than in DMSO and protein. The slower population decay in water is found to arise from configurations with intermolecular hydrogen bonds between HPMO and water molecules, leading to a disr...

A theoretical study of cis–trans isomerization in HONO using an empirical valence bond potential

The empirical valence bond (EVB) approach proposed by Chang and Miller [J. Phys. Chem. 94, 5884 (1990)] for constructing global potential energy surfaces has the potential for treating large molecular systems. In this work, we slightly modify the expression of Chang and Miller by adding a damping function along the reaction coordinate to ensure the proper asymptotic behavior of the potential. We apply the EVB method to describe the cis–trans isomerization in HONO, and compute the isomerization rates in the low-energy tunneling regime by employing the semiclassical method that treats tunneling within classical trajectory calculations.

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.

Hybrid approach for the dynamical simulation of proton and hydride transfer in solution and proteins

A hybrid approach for simulating proton and hydride transfer reactions in solution and proteins is described. The electronic quantum effects are incorporated with an empirical valence bond potential. The nuclear quantum effects are included with a mixed quantum‐classical molecular dynamics method in which the transferring hydrogen nuclei are represented by multidimensional vibrational wavefunctions. The free energy profiles are obtained as functions of a collective reaction coordinate, and a mapping or umbrella potential is utilized to drive the reaction over the barrier for infrequent events. The vibrationally adiabatic nuclear quantum effects are incorporated into the free energy profiles. The dynamics are described with the molecular dynamics with quantum transitions (MDQT) surface hopping method, which incorporates vibrationally non-adiabatic effects. The MDQT method is combined with a reactive flux approach to calculate the transmission coefficient and to investigate the real-time dynamics of reactive trajectories. Nuclear quantum effects such as zero point energy, hydrogen tunnelling and non-adiabatic transitions, as well as the dynamics of the solvent and protein environment, are included during the generation of the free energy profiles and dynamical trajectories. This methodology provides detailed mechanistic information at the molecular level and allows the calculation of rates and kinetic isotope effects. The feasibility of this approach is illustrated through an application to hydride transfer in the enzyme liver alcohol dehydrogenase. This approach may be extended for use with mixed quantum mechanical‐molecular mechanical potentials and alternative mixed quantum‐classical molecular dynamics methods. It has also been generalized for multiple proton and protoncoupled electron transfer reactions.

Reaction mechanism and isotope effects derived from centroid transition state theory in intramolecular proton transfer reactions

In this article the tautomerization reaction of the enol form of malonaldehyde is used to investigate the magnitude and origin of changes in centroid transition state theory proton transfer reaction rate predictions caused by the quantum dispersion of heavy nuclei. Using an empirical valence bond method to construct the potential energy surface, it is found that quantization of the nuclear degrees of freedom of the carbon atoms significantly influences the centroid potential of mean force used to describe the proton transfer reaction. In contrast, an ab initio simulation carried out using a recently developed molecular mechanics based importance sampling method [J. Chem. Phys. 114, 6763 (2001)] in combination with an accurate density functional theory evaluation of the electronic energies shows a substantially smaller influence of the quantum nuclear degrees of freedom of the secondary atoms on the centroid potential of mean force. A detailed analysis of the different influence of quantization of the nuclear degrees of freedom of secondary atoms observed in the ab initio and empirical valence bond centroid potential of mean force was carried out. It is shown that for the empirical valence bond potential, a significant decrease of the centroid potential of mean force arises through the quantum tunneling of carbon atoms in the molecular backbone. Furthermore, it is demonstrated that in molecular mechanics potentials aimed to describe intramolecular proton transfer reactions, the functional form of the potential energy terms coupling the primary and secondary atom motions as the reaction proceeds as well as the mass of the primary particle can significantly influence the centroid transition state theory predictions of secondary kinetic isotope effects. Finally, the dependence of the reaction rate predictions and isotope effects on the choice of reaction coordinate is investigated and the validity of calculating kinetic isotope effects using the centroid transition state theory formalism is discussed.

Hybrid ab Initio Quantum Mechanics/Molecular Mechanics Calculations of Free Energy Surfaces for Enzymatic Reactions: The Nucleophilic Attack in Subtilisin

An effective approach for ab initio calculations of activation free energies of enzymatic reactions is developed and examined. This approach uses an empirical valence bond (EVB) potential surface as a reference potential for evaluating the free energies of a hybrid ab initio quantum mechanics/molecular mechanics (QM(ai)/MM) potential surface. This procedure involves an automated calibration of the EVB potential using gas-phase ab initio calculations. In addition, strategies for treating the contact region of QM and MM atoms as well as enzyme and solvent environments are developed. Two levels of ab initio calculations are used in studying the QM atoms: the HF/4-31G method, which allows calculations on a large number of points while still giving accurate results, and the MP2/6-31+G* approach. The QM(ai)/MM method is implemented and examined by simulating the nucleophilic attack step in the catalytic reaction of subtilisin. It is found that the use of the EVB potential as a reference allows one to obtain th...

An empirical valence bond model for constructing global potential energy surfaces for chemical reactions of polyatomic molecular systems

An empirical valence bond (EVB) model is proposed for constructing reactive potential energy surfaces of polyatomic molecular systems. Specifically, it is shown how the exchange potential V{sub 12}(q) of the EVB model can be chosen so that the EVB potential V(q) {triple bond} 1/2(V{sub 11}(q) + V{sub 22}(q)) - ((1/2(V{sub 11}(q) - V{sub 22}(q))){sup 2} + V{sub 12}(q){sub 2}){sup 1/2} exactly reproduces the transition-state geometry, energy, and force constant matrix obtained by an independent ab initio calculation. (Here q denotes all the 3N-6 nuclear coordinates of the N-atom system, and V{sub 11} and V{sub 22} are empirical diabatic, i.e., nonreactive, potential functions that describe the reactant and product regions of the potential surface, respectively.) Application of the overall prescription to a variety of two-dimensional test potential surfaces shows that this version of the EVB model provides an excellent description of reactive potential surfaces for a wide variety of situations.