Abstract

We give an analytical method for finding the exact solution for the problem of electronic relaxation in solution, modelled by a particle diffusing under the influence of parabolic potential in the presence of a sink of rectangular shape. The Smoluchowski equation is used to model the diffusive motion. We have derived an analytical formula for the average rate constant in closed form. Solving Smoluchowski equation analytically with a sink of arbitrary width has been an unsolved problem and is important as a realistic model for non-radiative electronic relaxation of a molecule in solution.

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