Comparison of quantum and semiclassical variational transition state models for the HO2→H+O2 microcanonical rate constant

Abstract

Comparisons, for J=0, are made between HO2→H+O2 reaction path anharmonic energy levels, variational transition states, and unimolecular rate constants determined by three different semiclassical models and a quantum mechanical model. The semiclassical models are based on the reaction path Hamiltonian. However, to determine anharmonic energy levels, the harmonic potential of this Hamiltonian is replaced by the actual anharmonic DMBE IV potential for the HO2 system. Two of the semiclassical models use Einstein–Brillouin–Keller (EBK) quantization to determine energy levels for motion orthogonal to the reaction path; i.e., one model neglects anharmonic coupling between modes, while the other retains all the coupling. The third semiclassical model is based on a quartic expansion of the potential and second-order perturbation theory to determine the energy levels. A comparison of the results of these three semiclassical models shows that anharmonic coupling between modes orthogonal to the reaction path is unimportant for HO2 dissociation. The separable EBK model gives a RRKM rate constant versus energy in very good agreement with that obtained from a quantum mechanical calculation which retains full coupling between modes in determining the reaction path energy levels. If anharmonicity is treated, the reaction path Hamiltonian and its vibrator transition state give accurate RRKM rate constants for HO2 dissociation. Rate constants calculated with the flexible transition states model are in very good agreement with those of the semiclassical and quantum vibrator transition state models, if the O2 stretch conserved mode is treated as an anharmonic oscillator in the flexible model. However, in contrast to the vibrator transition state models, ‘‘steps’’ are not observed in the rate constants for the flexible model, since the transitional mode is treated classically. Harmonic and anharmonic rate constants are compared for both the vibrator and flexible transition state models.