Cumulative reaction probability from Siegert eigenvalues: Model studies

Abstract

A simple approach to cumulative reaction probability, N(E), calculation is described and tested using one-dimensional symmetric and nonsymmetric Eckart potential barriers. This approach combines semiclassical transition state theory formulated by Miller [Faraday Discuss. Chem. Soc. 62, 40 (1977)] and reviewed recently by Seideman and Miller [J. Chem. Phys. 95, 1768 (1991)] and the complex coordinate method for calculations of Siegert eigenvalues. Siegert eigenvalues calculated numerically and analytically are found in excellent agreement with each other. It is demonstrated that corresponding eigenfunctions are localized in the potential barrier region and can be counted by their nodes. Perfect agreement between semiclassical N(E) dependence and exact quantum mechanical results was found in a broad energy range.