Diffusion-reaction approach to electronic relaxation in solution. Exact solution for 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 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's function for the motion in the absence of the sink. We use the method to find the solution of the problem in the case where the diffusive motion is on a parabolic potential. This has been an unsolved problem for some time and is of considerable importance as a model for non-radiative electronic relaxation of a molecule in solution. The solution is analyzed to obtain the viscosity and temperature dependences of the rate constants.