  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.
