Algorithm to evaluate rate constants for polyatomic chemical reactions. I. Theory and computational details

A classical reaction path, Liouville algorithm, as previously developed by the authors, has been reformulated in a more efficient form, based on the time-dependent first integral method from the theory of partial differential equations. Both the theory and computational details are presented. The formulation is based on solving the complete rate constant problem, concerning both the density distribution as well as the reactive flux, by means of solving the classical Liouville equation. The numerical implementation is discussed in detail, including some specifics concerning the reaction path calculation. The formulation is tested with the well-known Müller-Brown bidimensional potential energy surface.