Calculation of Reaction Rate Constants in the Canonical and Microcanonical Ensemble

TL;DR

This paper introduces a new computational method for calculating reaction rate constants using instanton theory, emphasizing linear system solutions over matrix diagonalization, enhancing stability and applicability to multidimensional systems.

Contribution

It presents an alternative approach to compute quantum corrections in instanton theory using linear systems, improving numerical stability especially in multidimensional systems.

Findings

The method avoids matrix diagonalization, simplifying calculations.

It provides stable and reliable stability parameters for multidimensional systems.

Applicable to both canonical and microcanonical ensemble calculations.

Abstract

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.