Calculation of Reaction Rate Constants in the Canonical and Microcanonical Ensemble

Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical periodic orbits on the upside-down potential energy surface, so-called instantons, and the computation of second order quantum corrections. The calculation of these corrections usually involves a matrix diagonalization. In this paper we present an alternative approach, which requires to solve only linear systems of equations involving sparse matrices. Furthermore, the proposed method provides a reliable and numerically stable way to obtain stability parameters in multidimensional systems, which are of particular interest in the context of microcanonical instanton theory.