Comments on limited use of Smoluchowski equation in kinetic analysis of electron-transfer processes

The rate of barrier crossing in a cusped potential serves as a model for electron transfer processes in the presence of dissipation. The spatial diffusion limit for the rate constant is known for thus case in the strong damping limit when the Smoluchowski equation is valid. The paper discusses comparison of different approximation schemes in derivation of a one dimensional Smoluchowski equation for a linear kinetic model derived by a non-Markovian dynamics. Differences in calculated short- and long-time limit properties of the systems resulting from various method of elimination of fast variables question validity of use of Smoluchowski equation in the kinetic rate approach. To calculate the rate, the standard definition in the integrated form of the correlation function is used and the results are shown to be consistent with the predictions of numerical analysis presented in literature. (author)