Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Analysis of the H + D2 reaction mechanism through consideration of the intrinsic reactant polarisation

The effect of reactant polarisation on the dynamics of the title reaction at collision energies up to 1.6 eV is analysed in depth. The analysis takes advantage of two novel theoretical concepts: intrinsic reaction properties and stereodynamical portraits. Exact quantum methods are used to determine the polarisation moments that quantify the intrinsic reactant polarisation at various levels of detail, including or not product state and/or scattering angle resolution. The data is then examined with the aid of stereodynamical portraits, which facilitate the rationalisation of the stereochemical effects that are relevant for the reaction dynamics. This allows for detailed characterisations of the so-called direct and delayed reaction mechanisms.     

A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.     

Novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: free energy calculation for the Beckmann rearrangement promoted by proton transfers in the supercritical water

The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3 kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7 kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the C?H Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Wild-type and molten globular chorismate mutase achieve comparable catalytic rates using very different enthalpy/entropy compensations

The origin of the catalytic power of enzymes with a meta-stable native state,e.g.molten globular state,is an unsolved challenging issue in biochemistry.To help understand the possible differences between this special class of enzymes and the typical ones,we report here computer simulations of the catalysis of both the well-folded wild-type and the molten globular mutant of chorismate mutase.Using the ab initio quantum mechanical/molecular mechanical minimum free-energy path method,we determined the height of reaction barriers that are in good agreement with experimental measurements.Enzyme-substrate interactions were analyzed in detail to identify factors contributing to catalysis.Computed angular order parameters of backbone N–H bonds and side-chain methyl groups suggested site-specific,non-uniform rigidity changes of the enzymes during catalysis.The change of conformational entropy from the ground state to the transition state revealed distinctly contrasting entropy/enthalpy compensations in the dimeric wild-type enzyme and its molten globular monomeric variant.A unique catalytic strategy was suggested for enzymes that are natively molten globules:some may possess large conformational flexibility to provide strong electrostatic interactions to stabilize the transition state of the substrate and compensate for the entropy loss in the transition state.The equilibrium conformational dynamics in the reactant state were analyzed to quantify their contributions to the structural transitions enzymes needed to reach the transition states.The results suggest that large-scale conformational dynamics make important catalytic contributions to sampling conformational regions in favor of binding the transition state of substrate.     

Practical approximation to reaction probabilities from selected initial quantum states

A method for the economical of reasonable approximations to the probability of reaction from specified internal states of reactants is proposed for elementary exchange reactions. It requires the solution of the close coupling equations in the reactant channel only and the imposition of boundary conditions on a hypersurface at the transition state. A numerical comparison with the complete quantum calculation for the planar H + H₂ reaction is presented and the agreement is shown to be good.     

A combined theoretical and experimental approach to the unimolecular loss of molecular hydrogen from protonated formaldehyde: Determination of the average internal energy of metastable [CH2OH]+ ions

Ab initio quantum chemical calculations (MP2/4–31G**) were performed for the dihydrogen elimination reaction from protonated formaldehyde. The energy difference between reactants and products and the activation energies were found to be in good agreement with the corresponding experimental quantities. Theoretical rate vs. energy curves were computed for a series of isotopic variants of the reaction using the Rice–Ramsperger–Kassel–Marcus (RRKM) method. The vibrational frequencies used in these calculations were taken from the 4–31G** geometry-optimized transition state and reactant structures. Quantum mechanical tunnelling was introduced to explain the existence of metastable CH₂OH ions, and a negative kinetic shift of about 0.1 eV was found. The intramolecular kinetic isotope effect for loss of HH/HD and DH/DD was calculated and compared with the experimental data. The result is consistent with the assumption that the average internal energy of metastable [CH₂OH]⁺ ions is very close to the critical energy for H₂ loss.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.     

A quantum theory of chemical processes and reaction rates based on diabatic electronic functions coupled in an external field

The method discussed in this work provides a theoretical framework where simple chemical reactions resemble any other standard quantum process, i.e., a transition in quantum state mediated by the electromagnetic field. In our approach, quantum states are represented as a superposition of electronic diabatic basis functions, whose amplitudes can be modulated by the field and by the external control of nuclear configurations. Using a one-dimensional three-state model system, we show how chemical structure and dynamics can be represented in terms of these control parameters, and propose an algorithm to compute the reaction probabilities. Our analysis of effective energy barriers generalizes previous ideas on structural similarity between reactant, and product, and transition states using the geometry of conventional reaction paths. In the present context, exceptions to empirical rules such as the Hammond postulate appear as effects induced by the environment that supplies the external field acting on the quantum system.     

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.     

Atomistic evidence of how force dynamically regulates thiol/disulfide exchange

The intricate coupling of mechanical force and chemical reactivity has been increasingly revealed in recent years by force spectroscopy experiments on the thiol/disulfide exchange reaction. We here aimed at elucidating the underlying dynamic effects of force on the reaction center for the case of disulfide bond reduction by dithiothreitol at forces of 200-2000 pN, by combining transition path sampling and quantum/classical mechanical simulations. Reaction rates and their dependence on force as quantified by Δx(r), the distance between reactant and transition state, are in good agreement with experiments but indicate a shift of the transition state structure at high forces. Indeed, while an associate S(N)2 mechanism prevails, force causes a move of the transition state to a longer length of the cleaving bond and a shorter length of the forming disulfide bond. Our results highlight the distribution of force into various degrees of freedom, which implies that care must be taken when correlating Δx(r) with a single order parameter of the reaction.     

The state-to-state-to-state model for direct chemical reactions: application to D+H2-->HD+H

A simple theoretical model is developed to predict the state-to-state dynamics of direct chemical reactions. Motivated by traditional ideas from transition state theory, expressions are derived for the reactive S matrix that may be computed using the local transition state dynamics. The key approximation involves the use of quantum bottleneck states to represent the near separable dynamics taking place near the transition state. Explicit expressions for the S matrix are obtained using a Franck-Condon treatment for the inelastic coupling between internal states of the collision complex. It is demonstrated that the energetic thresholds for various initial reagent states of the D+H(2) reaction can be understood in terms of our theory. Specifically, the helicity of the reagent states are found to correlate directly to the symmetry of the quantum bottleneck states, which thus possess very different thresholds. Furthermore, the rotational product state distributions for D+H(2) are found to be associated with interfering pathways through the quantum bottleneck states.     

Catalytic mechanism and product specificity of the histone lysine methyltransferase SET7/9: an ab initio QM/MM-FE study with multiple initial structures

Histone lysine methylation is emerging as an important mechanism to regulate chromatin structure and gene activity. To provide theoretical understanding of its reaction mechanism and product specificity, ab initio quantum mechanical/molecular mechanical free energy (QM/MM-FE) calculations and molecular dynamics simulations have been carried out to investigate the histone lysine methyltransferase SET7/9. It is found that the methyl-transfer reaction catalyzed by SET7/9 is a typical in-line S(N)2 nucleophilic substitution reaction with a transition state of 70% dissociative character. The calculated average free energy barrier at the MP2(6-31+G) QM/MM level is 20.4 +/- 1.1 kcal/mol, consistent with the activation barrier of 20.9 kcal/mol estimated from the experimental reaction rate. The barrier fluctuation has a strong correlation with the nucleophilic attack distance and angle in the reactant complex. The calculation results show that the product specificity of SET7/9 as a monomethyltransferase is achieved by disrupting the formation of near-attack conformations for the dimethylation reaction.     

某些电荷转移反应中线性反应坐标确定的反应途径的非唯一性

在电子转移半经典模型的基础上,对氟代苯并菲组成的盘状液晶体系的电荷转移反应进行了研究,其反应动力学参数在量子化学B3LYP/6-31G(d,p)水平进行计算.研究中发现在反应物和产物的构型确定后,用线性反应坐标构造的反应途径和过渡态的构型不是唯一的.其原因是反应物和产物确定后,其独立内坐标的选择并不是唯一的.因此在计算电荷转移速率常数时必须考虑到多个过渡态构型才能得到定性正确的结果.     

The catalytic power of pyruvate decarboxylase. A stochastic model for the molecular evolution of enzymes.

Pyruvate decarboxylase (PDC) catalyzes the decarboxylation of pyruvate anion by a factor of around 10(12), compared with the non-enzymic decarboxylation by thiamine, under standard state conditions of 1 mM pyruvate and thiamine diphosphate (TDP), pH 6.2. Free-energy diagrams constructed on the basis of earlier measurements for the enzymic and non-enzymic reactions give some information on catalysis by PDC. PDC stabilizes the reactant state preceding TDP addition to pyruvate by 76 kJ mol-1 and the transition state for the addition by 83 kJ mol-1. PDC stabilizes the reactant state preceding decarboxylation (presumably alpha-lactyl-TDP) by 27 kJ mol-1 and the transition state for decarboxylation by 68 kJ mol-1. In addition, the free-energy diagrams reveal a leveling of reactant-state free energies in the enzymic reaction compared with the non-enzymic reaction, in that the former are nearly equal to each other. The enzyme-bound transition-state energies are similarly leveled. The energetic leveling of reactant states has been noted by Albery, Knowles and their coworkers in many enzymic reactions and termed 'matched internal thermodynamics.' They showed that the result would arise naturally (and inevitably) in the 'evolution to perfection' of enzymes, when the evolutionary process was treated by a deterministic model. The critical assumption of this model was the validity of a Marcus-type or Br?nsted-type linear free-energy relationship between rate and equilibrium constants for reactions occurring wholly within enzyme complexes. Here a completely stochastic simulation of molecular evolution, with no deterministic assumptions, is shown to reproduce both 'matched internal thermodynamics' and the 'matched internal kinetics' or leveling of transition-state energies noted here. The Albery-Knowles result is thus more general than might have been supposed.     

Smooth solvation method for d-orbital semiempirical calculations of biological reactions. 1. Implementation

The present paper describes the extension of a recently developed smooth conductor-like screening model for solvation to a d-orbital semiempirical framework (MNDO/d-SCOSMO) with analytic gradients that can be used for geometry optimizations, transition state searches, and molecular dynamics simulations. The methodology is tested on the potential energy surfaces for separating ions and the dissociative phosphoryl transfer mechanism of methyl phosphate. The convergence behavior of the smooth COSMO method with respect to discretization level is examined and the numerical stability of the energy and gradient are compared to that from conventional COSMO calculations. The present method is further tested in applications to energy minimum and transition state geometry optimizations of neutral and charged metaphosphates, phosphates, and phosphoranes that are models for stationary points in transphosphorylation reaction pathways of enzymes and ribozymes. The results indicate that the smooth COSMO method greatly enhances the stability of quantum mechanical geometry optimization and transition state search calculations that would routinely fail with conventional solvation methods. The present MNDO/d-SCOSMO method has considerable computational advantages over hybrid quantum mechanical/molecular mechanical methods with explicit solvation, and represents a potentially useful tool in the arsenal of multi-scale quantum models used to study biochemical reactions.     

硅杂环丙烯异构化反应的理论研究

用量子化学理论方法研究了硅杂环丙烯单重态的异构化反应。结果表明:该异构化反应的过渡态为三元环结构,该反应为氢迁移反应;反应的势垒高度为276.67kJ·mol^-^1[MP2/6-31G(d)]。通过内禀反应坐标(IRC)计算,获得了沿反应途径的势能剖面。