Rate constant and transmission coefficient in the diffusion theory of reaction rates

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Abstract
The diffusion theory of reaction rates, originally described by H. A. Kramers, is extended and new results are derived. It is shown that valuable information can be gained by using backward diffusion equations (equations in which the initial values are independent variables), in addition to the Fokker–Planck equation. Three theoretical formulations of the rate constant are described. The first formulation uses transition state theory. The second formulation uses a modification of Kramers’s theory. In the third formulation, the rate constant is defined to be the reciprocal of the mean time to cross a given energy barrier. The three formulations of the rate constant are compared with each other and with Monte Carlo experiments. By using the backward equation, it is possible to calculate the transmission coefficient. The theoretical results are compared with Monte Carlo experiments.

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