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Canonical instanton theory is a widespread approach to describe the dynamicsof chemical reactions in low temperature environments when tunneling effectsbecome dominant. It is a semiclassical theory which requires locating classicalperiodic orbits on the upside-down potential energy surface, so-calledinstantons, and the computation of second order quantum corrections. Thecalculation of these corrections usually involves a matrix diagonalization. Inthis paper we present an alternative approach, which requires to solve onlylinear systems of equations involving sparse matrices. Furthermore, theproposed method provides a reliable and numerically stable way to obtainstability parameters in multidimensional systems, which are of particularinterest in the context of microcanonical instanton theory.

Calculation of Reaction Rate Constants in the Canonical and Microcanonical Ensemble