Reaction-path interpolation models for variational transition state theory

We present interpolation formulas for estimating parameters in the reaction-path Hamiltonian from known data in three vicinities-reactants, saddle point, and products. Whereas conventional transition state theory calculations are usually based on a quadratic expansion of the potential energy surface at the saddle point, the present approach attempts to estimate the variational transition state theory rate constant by also using selected cubic and quartic force constants of the saddle point or by using quadratic force constants determined over a small range of the reaction path, not necessarily including the variational transition state. The method is illustrated and the formulas are tested for four collinear classical reactions.