Resonance state approach to quantum mechanical variational transition state theory

The thermal rate coefficients for the title reactions with zero total angular momentum are calculated by an ℒ 2 basis-set evaluation of the flux autocorrelation function. We use three dividing surfaces, each one separating one arrangement from the other two. The rate coefficients for O+HD↔OD+H or OH+D are converged to within 1.2% over the temperature range 300–1000 K and to within 2.4% at 200 K. The rate coefficients for the reactions H+OD↔D+OH are converged to within 22% at 1000 K and upper bounds to these rate coefficients are given for the temperature range 200–800 K. Flux autocorrelation functions and rate coefficients are calculated for different positions of the dividing surface to show that the computed rate coefficient is stable with respect to varying this position. Rate coefficients are also calculated by a variational version of quantum mechanical transition state theory and the results are compared to the accurate rate coefficients obtained from flux autocorrelation function theory.

The elementary vapor-phase reaction between Cl atoms and HCHO has been studied by ab initio methods. Calculations at the MP2, MP3, MP4(SDTQ), CCSD, CCSD(T), and MRD-CI levels of theory show that the reaction is characterized by a low electronic barrier; excluding the effects of spin-orbit splitting in Cl, our best estimate at the MRD-CI/aug-cc-pVTZ//RHF-RCCSD(T)/aug-cc-pVTZ level of theory predicts a Born-Oppenheimer barrier height of 0.7 kJ mol-1. The energies of the lowest six electronic states as resulting from MRD-CI calculations are presented at discrete points along the reaction path, and two avoided crossings are found in the transition state region. The spin-orbit splitting in Cl is also calculated along the reaction path; it is not negligible in the transition state region and is found to increase the barrier by only 1.4 kJ mol-1 at the RCCSD(T)/aug-cc-pVTZ transition state geometry. The minimum energy path of the reaction connects an energetically weakly stabilized adduct on the flat potential surface on the reactant side and an energetically strongly stabilized postreaction adduct. The reaction rate coefficient and the kinetic isotope effects were calculated using improved canonical variational theory with small curvature tunneling (ICVT/SCT), and the results were compared to experimental data. The experimental reaction rate coefficient is reproduced within its uncertainty limits by variational transition state theory with interpolated single-point energy corrections (ISPE) at the MP4(SDTQ) level of theory and by conventional transition state theory with interpolated optimized energies (IOE) at the MRD-CI//RCCSD(T) level of theory and interpolated optimized geometries at the RCCSD(T) level of theory on an MP2/aug-cc-pVTZ potential energy surface when employing scaled vibrational frequencies.

Variational transition state theory is a powerful tool for tackling the problem of activated barrier crossing in condensed phases, enabling the exact reduction of infinite-dimensional problems to much more tractable few-dimensional problems. Variational transition state theory may be used to go beyond Kramers’ theory and consider the effects of memory friction and solute nonlinearities on the rate of barrier crossing. In addition, since variational transition state theory is a Hamiltonian based formalism, it is not tied to the limitations of generalized Langevin equation dynamics; thus it can be used to treat nonlinear solute-solvent interactions. Other recent advances include the development of new formalisms for improved optimization of the transition state dividing surface, the incorporation of intramolecular solute modes, and the development of centroid-based quantum transition state theory analogs.

The variational transition state theory (VTST) of chemical reaction rates has been further developed and two previously developed and one new version have been illustrated and tested by various applications to collinear and three-dimensional reactions of the type A + BC ..-->.. AB + C. The first two versions considered are canonical variational theory (CVT), which is based on curves of free energy of activation as functions of location of the VTST dividing surface, and microcanonical variational theory (..mu..VT), which is based on minimizing the reactive flux through the VTST dividing surface at each total energy. CVT is simpler but ..mu..VT is more accurate. The new theory, improved canonical variational theory (ICVT), is almost as simple as CVT but almost as accurate as ..mu..VT. This has been demonstrated by applications to H, O, F, Cl, and I reacting with H/sub 2/, H reacting with F/sub 2/ and Cl/sub 2/, and various isotopic analogs and model systems. It was also demonstrated that VTST leads to very good agreement with accurate quantal results for several collinear reactions. Another project used VTST to explore the systematics of kinetic isotope effects for three-dimensional reactions. The predictions sometimes differ considerably from those of the conventional theory.

In the present work, we use Variational Transition State Theory (VTST) to develop a practical method for transition state ensemble optimization by looking for an optimal hyperplanar dividing surface in a space of meaningful trial collective variables. These might be interatomic distances, angles, electrostatic potentials, etc. Restrained molecular dynamics simulations are used to obtain on-the-fly estimates of ensemble averages that guide the variations of the hyperplane maximizing the transmission coefficient. A central result of our work is an expression that quantitatively estimates the importance of the coordinates used for the localization of the transition state ensemble. Starting from an arbitrarily large set of trial coordinates, one can distinguish those that are indeed essential for the advance of the reaction. This facilitates the use of VTST as a practical theory to study reaction mechanisms of complex processes. The technique was applied to the reaction catalyzed by an isochorismate pyruvate lyase. This reaction involves two simultaneous chemical steps and has a shallow transition state region, making it challenging to define a good reaction coordinate. Nevertheless, the hyperplanar transition state optimized in the space of 18 geometrical coordinates provides a transmission coefficient of 0.8 and a committor histogram well-peaked about 0.5, proving the strength of the method. We have also tested the approach with the study of the NaCl dissociation in aqueous solution, a stringest test for a method based on transition state theory. We were able to find essential degrees of freedom consistent with the previous studies and to improve the transmission coefficient with respect to the value obtained using solely the NaCl distance as the reaction coordinate.

We have carried out ab initio calculations for the reaction OH+CH4→H2O+CH3 using second-order Mo/ller–Plesset perturbation theory, employing a very large basis set and scaling all correlation energy for the final energy calculation, but optimizing the equilibrium and transition state structures without scaling (MP-SAC2//MP2). We found that inclusion of correlation energy has an important effect on the geometry, barrier height, and vibrational frequencies of the transition state. The final calculated values for the forward and reverse classical barrier heights are 7.4 and 20.6 kcal/mol, respectively. We have used these with interpolated canonical variational transition state theory and the centrifugal-dominant small-curvature tunneling approximation, including information at the reactants, products, transition state, and two other points along the minimum energy path, to predict the rate constants for the above reaction in the temperature range from 223 to 2400 K. The calculated rate constants agree well with experiment over a wide temperature range.

The reaction of disilane with atomic hydrogen has been studied. This reaction involves both substitution and abstraction. Calculations show that the hydrogen abstraction is the strongest competing channel. The canonical variational transition state theory with a small curvature tunneling correction (SCT) has been used for the kinetic calculation. The theoretical results are in good agreement with the available experimental data. Comparing the reactions of atomic hydrogen with disilane and silane, it can be seen that the reactivity of the Si-H bond is higher in Si 2 H 6 than that in SiH 4 .

In transition state (TS) region almost all systems (reactions) have weak van der waals complex structures. When these systems include heavy atom transfer, the forming quantum tunneling effects are suppressed. At TS region these reactions, especially including insertion minimum energy wells, demonstrate to rapidly the formation of product molecules at low temperature region. This study has focused on H+LiF system, one of systems that have this feature. In this system, since unstable H--F--Li complex quasibound states have the barriers in the TS, it is important to investigate and understand to depending on specific quantum states of the initial and the product molecule for this reaction. The results in collision energy range of 0-0.8 eV were obtained and corrected by using Reel Wave Packet (RWP) methods. Integral reaction cross sections as a function of collision energy were calculated via simple J-shifting (SJS) and reaction rate constants were examined in temperature range of 100-1000 0 K.

Chlorinated hydrocarbons (CHCs) are the most common contaminant found at hazardous waste sites and are the most prevalent contaminants on U.S. Department of Energy (DOE) weapons production sites. Many of the CHCs are either known or suspected carcinogens and thus pose health risks to the public and/or site workers. Unlike simple hydrocarbons, CHCs are resistant to biodegradation, but can degrade by abiotic processes such as hydrolysis, nucleophilic substitution, and dehydrochlorination. Unfortunately, few studies of the reactions of chlorinated hydrocarbons have been reported in literature, and disagreement still exists about the mechanisms and rates of many of the key reactions. In this work, we modeled the reactions involved in the degradation of CHCs in the groundwater. The goals of the research proposed are: • development of a computational approach that will allow reaction pathways and rate constants to be accurately calculated • development of more approximate approaches, evaluated against the more accurate approach, which will lay the groundwork for exploratory studies of more complex CHCs • application of these approaches to study the degradation pathways of CHCs in aqueous liquids • application of the more approximate approaches to study the mechanism of forming complex CHC polychlorinated benzene compounds and dioxins. We examined elementary reactions involved in the aqueous-phase chemistry of chlorinated methanes and ethylenes in an attempt to obtain a detailed understanding of the abiotic processes involved in the degradation of this important class of contaminants. We began by studying the reactions of CHnCl(4-n) and C2HnCl(4-n) with OH¯, as these are thought to be the dominant processes involved in the degradation of these chlorinated species. We used state-of-the-art theoretical techniques to model the elementary reactions of CHCs important in the groundwater. We employed high-accuracy electronic structure methods (e.g., perturbation theory and coupled cluster methods with correlation-consistent basis sets) to determine the energies of the various stable species, intermediates, and transition states involved in the elementary reactions of CHCs. Effects of solvation on the reaction energetics were studied by including small numbers of solvent molecules (microsolvation). Our own N-layered molecular orbital + molecular mechanics (ONIOM) method was used because it allows the number of solvent molecules to be increased, and hybrid quantum mechanical/molecular mechanics (QM/MM) methods and continuum solvation models were used to estimate the effects of bulk solvation. Rate constants for the gas-phase, microsolvated, and bulk-phase reactions were computed using variational transition state theory (VTST).

We test several approximate theories of thermal rate constants against accurate quantal equilibrium rate constants for collinear bimolecular reactions governed by given potential energy surfaces. The systems considered are F+H2 and F+D2 for the Muckerman potential energy surface no. 5 at 200–1200 K and H+F2, D+F2, and T+F2 for potential surface II of Jonathan, Okuda, and Timlin at 233–1260 K. For F+H2, conventional transition state theory overestimates the accurate rate constant by factors of 2.9–3.4, with the largest errors at the lowest and highest temperatures. Vibrationally adiabatic transmission coefficients or variational transition state theory decrease the error to factors of 1.2–1.3 at the lowest temperature and to a factor of 3.2 at the highest temperature. The unified statistical model reduces the errors to a factor of 1.1 at the lowest temperature and a factor of 2.7 at the highest temperature. For F+D2 the trends are similar but the errors in all the methods are smaller at all temperatures. For H+F2 conventional transition state theory underestimates the rate constants by a factor of 0.56 at the lowest temperature with the error decreasing to 2% at the highest temperature. Various formulations of vibrationally adiabatic transmission coefficients, in conjunction with either conventional or variational transition state theory, reduce the error to factors of 0.84–0.96 at the lowest temperature while not destroying the good agreement at the highest temperature. The unified statistical theory seems to overestimate the recrossing correction for this reaction, though only by about 10%. The results are similar for D+F2 and T+F2 except that the low-temperature underestimates of the calculations without tunneling are not as severe. The best theory, improved canonical variational theory with the Marcus–Coltrin path semiclassical adiabatic ground-state transmission coefficient, reproduces the accurate quantal results for H+F2, D+F2, and T+F2 within 5% or better in every case for the whole temperature range.

Diffusion coefficients for H, D, and T on a Ni(100) surface and in bulk Ni are calculated using variational transition state theory with semiclassical ground-state transmission coefficients using two potential energy surfaces obtained by the embedded atom method (EAM). The original EAM potential reproduces experimental bulk diffusion coefficients, but greatly overestimates the diffusion coefficients for H and D on Ni(100). By refining the empirical potential parameters, a new EAM potential is developed that accurately reproduces both the bulk and surface diffusion coefficients. The variational transition state theory calculations are used to analyze the unusually low (compared to gas phase) H/D kinetic isotope effects for diffusion in bulk and on the Ni(100) surface. For the temperature range for which experiments have been carried out, quantum mechanical tunneling contributes negligibly to the diffusion and, in these cases, the kinetic isotope effect is determined largely by the change in zero-point energy between the reactant equilibrium binding sites and the transition state. A near equality of the reactant and transition state zero-point energies leads to the unusually low kinetic isotope effects. Using the same refined EAM potential energy surface, the energetics of diffusion on the Ni(111) and Ni(110) surfaces are also presented. The barriers for diffusion on these two surfaces are sufficiently low, about 1.0 kcal/mol, that the approximation of uncorrelated hops needed to relate the computed hopping rate to the diffusion coefficient is suspect. Although diffusion coefficients were not computed, based upon an analysis of the zero-point energies at the reactants and saddle points, we predict that the H/D kinetic isotope effects for diffusion on these two surfaces will also be close to unity.

The reaction path, the dynamical properties along the reaction path and CVT rate constants are computed by the ab initio MO method, the reaction path Hamiltonian theory and the variational transition state theory. The results show that the effect of the electron correlation energy on activation barrier is large, the recrossing and tunneling effects exist in the reaction.

The large-curvature ground-state model for the transmission coefficient of generalized transition state theory [presented in a previous paper by B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400(1983)] is tested against accurate quantal calculations of the rate coefficients for collinear reactions with very large inertial effects, namely Cl+HCl→ClH+Cl, Cl+DCl→ClD+Cl, and Cl+MuCl→ClMu+Cl. The tests cover the temperature range 200–2400 K. The accurate rate calculations are based on reaction probabilities obtained by a new numerical method for solving Schrödinger’s equation in Delves’ coordinates. Improved canonical variational transition state theory predicts rate coefficients 5.0–18 times smaller than those predicted by conventional transition state theory for the H transfer; for the D transfer, the ratio is 2.0–3.4; and for Mu it is 22–2.8×107. The large-curvature model predicts transmission coefficients as large as 41, 8, and 206 for the H, D, and Mu-transfer cases at 200 K, decreasing to 1.2, 1.1, and 1.4 at 2400 K. Despite the large effect of variationally optimizing the transition state location and the large size of the tunneling effect and the wide variation of both effects with temperature, improved canonical variational transition state theory with large-curvature ground-state transmission coefficients (ICVT/LCG) is accurate within a factor of 1.7 over a temperature range of a factor of 8, 300–2400 K, for all three reactions. At 200 K, the ICVT/LCG model underestimates the rate coefficients, by factors of 2.3, 1.9, and 1.5 for H, D, and Mu, respectively.

Reactions of β-hydroxypropyl radicals with O2 on the HOC3H6OO• potential energy surfaces: A theoretical study

A variant of the Kac-Zwanzig model is used to test the prediction of transition state theory (TST) and variational transition state theory (VTST). The model describes the evolution of a distinguished particle moving in a double-well external potential and coupled to N free particles through linear springs. While the Kac-Zwanzig model is deterministic, under appropriate choice of the model parameters the evolution of the distinguished particle can be approximated by a two-state Markov chain whose transition rate constants can be computed exactly in suitable limit. Here, these transition rate constants are compared with the predictions of TST and VTST. It is shown that the application of TST with a naive (albeit natural) choice of dividing surface leads to the wrong prediction of the transition rate constants. This is due to crossings of the dividing surface that do not correspond to actual transition events. However, optimizing over the dividing surface within VTST allows one to eliminate completely these spurious crossings, and therefore derive the correct transition rate constants for the model. The reasons why VTST is successful in this model are discussed, which allows one to speculate on the reliability of VTST in more complicated systems.