A reaction path-Liouville approach to the rate constant for polyatomic chemical reactions

An approximate, computationally feasible expression for the rate constant is derived in terms of a generalized formulation of the reaction path Hamiltonian, plus a distributed gaussian expansion scheme to the solution of the Liouville equation for the phase space distribution function. This scheme is shown to yield a rigorous upper bound to the exact classical rate constant, which is in turn lower than, or at most equal to, that given by transition state theory. The method is tested with the Muller-Brown model system, giving rise to fairly accurate results.