Kramers’ theory of chemical kinetics: Curvilinear reaction coordinates

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Abstract
Kramers’s theory of chemical kinetics is modified in order to analyze reacting systems in which the path of lowest energy between the reactants and the products is a curve in two dimensions. The potential surface is allowed to be either symmetric or asymmetric with respect to the barrier, and approximate expressions for the rate constant are obtained via both the Smoluchowski and Fokker–Planck equations. Accurate numerical results are computed for a special case and are seen to be in good agreement with the predictions of the theory. The analytical results indicate that the effect of the curved reaction path is to increase the rate constant over its straight-path value when the friction constant β is arbitrarily large. A competing effect arises when the frictional forces are reduced, however, and for sufficiently small β a decrease in the rate constant is noted. Nevertheless, the analyses tend to justify the commonly used notion of a reaction coordinate.