Path integral representation of the reaction rate constant in quantum mechanical transition state theory

Feynman’s path integral representation of the Boltzmann operator e−βH is used to express the rate constant of a recently formulated quantum mechanical version of transition state theory. By evaluating the path integral in two separate stages, one is able to interpret the result as a generalization of a model suggested several years ago by Johnston and Rapp for handling the nonseparable aspect of tunneling in transition state theory. A Fourier series expansion of the path integral is also developed, and this approach has promise for direct numerical evaluation of the quantum rate expression.