Rigoberto Hernandez

Ab initio calculation of anharmonic constants for a transition state, with application to semiclassical transition state tunneling probabilities

“Good” (i.e. conserved) action variables exist in the vicinity of a saddle point (i.e. transition state) of a potential energy surface in complete analogy to those related to a minimum on the surface. Transition state theory tunneling (or transmission) probabilities can be expressed semiclassically in terms of these “good” action variables, including the effects of non-separable coupling of all degrees of freedom with each other. This paper shows how ab initio quantum chemistry methods recently developed for calculating anharmonic constants about a potential minimum (i.e. for ordinary vibrational energy levels) can be readily adapted to obtain those related to a transition state, thus providing a rigorous and practical way to apply this non-separable transition state theory. Application is made to the transition state for he reaction D2CO→D2 + CO.

Semiclassical transition state theory. A new perspective

Abstract The semiclassical transition state theory (SCTST) introduced by Miller, Hernandez, Handy, Jayatilaka and Willetts requires the inversion of an (effectively integrable ) Hamiltonian with respect to the action of the reactive coordinate. It is shown that the inversion may be avoided in computing the thermal rate constant; the resulting expression also provides an appealing link to conventional transition state theory. This reformulation of the SCTST rate is illustrated by application to the bimolecular reaction, H + H 2 →H 2 + H, and to the unimolecular dissociation, D 2 CO→D 2 + CO.

A transition state theory‐based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde

A statistical distribution of state‐specific unimolecular decay rates is derived (within the framework of random matrix theory) that is determined completely by the transition state properties of the potential energy surface. It includes the standard χ‐square distributions as a special case. Model calculations are presented to show the extent to which it can differ from the χ‐square distribution, and specific application is made to the state‐specific unimolecular decay rate data for D2CO→D2+CO.

On the accuracy limits of orbital expansion methods: Explicit effects of k-functions on atomic and molecular energies

For selected first- and second-row atoms, correlation-optimized Gaussian k functions have been determined and used in the construction of septuple-ζ basis sets for the correlation-consistent cc-pVXZ and aug-cc-pVXZ series. Restricted Hartree–Fock (RHF) and second-order Moller–Plesset (MP2) total and pair energies were computed for H, N, O, F, S, H2, N2, HF, H2O, and (H2O)2 to demonstrate the consistency of the new septuple-ζ basis sets as extensions of the established (aug)-cc-pVXZ series. The pV7Z and aug-pV7Z sets were then employed in numerous extrapolation schemes on the test species to probe the accuracy limits of the conventional MP2 method vis-a-vis explicitly correlated (MP2-R12/A) benchmarks. For (singlet, triplet) pairs, (X+12)−n functional forms with n=(3, 5) proved best for extrapolations. The (mean abs. relative error, std. dev.) among the 73 singlet pair energies in the dataset is (1.96%, 0.54%) and (1.72%, 0.51%) for explicit computations with the pV7Z and aug-pV7Z basis sets, respectively,...

Quantum time correlation functions and classical coherence

Abstract Quantum time correlation functions for electronically adiabatic and nonadiabatic processes have recently been evaluated directly using the semiclassical initial value representation [J. Cao and G.A. Voth, J. Chem. Phys. 104 (1996) 271]. In this paper, the approach to the classical limit of this theory is analyzed and the nature of coherence in such limits is explored.

Transition State in a Noisy Environment

Transition state theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a time-dependent dividing surface free of such recrossings in the presence of noise. The no-recrossing limit of transition state theory thus becomes generally available for the description of reactions in a fluctuating environment.

Cumulative reaction probabilities for H+H2→H2+H from a knowledge of the anharmonic force field

Abstract In an earlier publication, the authors showed how knowledge of a quartic force field expanded about a transition state can be used to obtain transition state theory tunneling probabilities. Thus coupling between the reaction mode and other modes is included in this second-order perturbation theory approach. Here we study the very anharmonic reaction H+H 2 →H 2 +H and show that even in this extreme case, there is reasonable agreement between the cumulative reaction probabilities calculated by this semiclassical approach, and full quantum calculations.

A random matrix/transition state theory for the probability distribution of state‐specific unimolecular decay rates: Generalization to include total angular momentum conservation and other dynamical symmetries

A previously developed random matrix/transition state theory (RM/TST) model for the probability distribution of state‐specific unimolecular decay rates has been generalized to incorporate total angular momentum conservation and other dynamical symmetries. The model is made into a predictive theory by using a semiclassical method to determine the transmission probabilities of a nonseparable rovibrational Hamiltonian at the transition state. The overall theory gives a good description of the state‐specific rates for the D2CO→D2+CO unimolecular decay; in particular, it describes the dependence of the distribution of rates on total angular momentum J. Comparison of the experimental values with results of the RM/TST theory suggests that there is mixing among the rovibrational states.

Stochastic transition states: Reaction geometry amidst noise

Classical transition state theory (TST) is the cornerstone of reaction-rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space, such that it is crossed once and only once by each transition path.

A combined use of perturbation theory and diagonalization: Application to bound energy levels and semiclassical rate theory

A new method, mixed diagonalization, is introduced in which an effective Hamiltonian operator acting on a reduced dimensional space is constructed using the similarity transformations of canonical Van Vleck perturbation theory (CVPT). This construction requires the characterization of modes into two categories, global and local, which in the bound vibrational problem are tantamount to the large and small amplitude vibrations, respectively. The local modes in the Hamiltonian are projected out by CVPT, and the resulting Hamiltonian operator acts only on the space of global modes. The method affords the treatment of energy levels of bound systems in which some vibrational assignments are possible. In addition, it systematically provides a reduced dimensional Hamiltonian which is more amenable to exact numerical solution than the original full‐dimensional Hamiltonian. In recent work, a semiclassical transition state theory (SCTST) rate expression has been written in terms of a Hamiltonian operator parameteriz...