Application of semiclassical methods to reaction rate theory

Abstract

This work is concerned with the development of approximate methods to describe relatively large chemical systems. This effort has been divided into two primary directions: First, we have extended and applied a semiclassical transition state theory (SCTST) originally proposed by Miller to obtain microcanonical and canonical (thermal) rates for chemical reactions described by a nonseparable Hamiltonian, i.e. most reactions. Second, we have developed a method to describe the fluctuations of decay rates of individual energy states from the average RRKM rate in systems where the direct calculation of individual rates would be impossible. Combined with the semiclassical theory this latter effort has provided a direct comparison to the experimental results of Moore and coworkers. In SCTST, the Hamiltonian is expanded about the barrier and the ``good`` action-angle variables are obtained perturbatively; a WKB analysis of the effectively one-dimensional reactive direction then provides the transmission probabilities. The advantages of this local approximate treatment are that it includes tunneling effects and anharmonicity, and it systematically provides a multi-dimensional dividing surface in phase space. The SCTST thermal rate expression has been reformulated providing increased numerical efficiency (as compared to a naive Boltzmann average), an appealing link to conventional transition state theory (involving a ``prereactive`` partition function depending on the action of the reactive mode), and the ability to go beyond the perturbative approximation.