Theory of barrierless electronic relaxation in solution. Delta function sink models

Abstract

We give a general method for finding the exact solution for the problem of electronic relaxation in solution, modelled by a particle undergoing diffusive motion in a potential in the presence of a delta function sink. The diffusive motion is described by the Smoluchowski equation and the sink could be a delta function of arbitrary position and strength. The solution requires the knowledge of the Laplace transform of the Green function for the motion in the absence of the sink. We use the method to find the solutions for two different models. These are: (a) the particle in a box and (b) the particle on a ring model. Explicit expressions are obtained for the rate constants for these two models. We also analyze the short term behaviour of the excited state decay rate and arrive at analytical expressions which are of general validity.