Theory of Electronic relaxation in solution: Exact solution in case of parabolic potential with a sink of finite width

TL;DR

This paper presents an exact analytical solution for electronic relaxation in solution modeled by diffusive motion in a parabolic potential with a finite-width sink, improving understanding of non-radiative molecular relaxation.

Contribution

It introduces a novel method to obtain exact solutions for electronic relaxation with a finite-width sink, specifically providing the first analytical solution for the parabolic potential case.

Findings

Exact solution for parabolic potential with finite-width sink

Enhanced model accuracy over previous approaches

Analytical Green's function in Laplace domain

Abstract

We give a general method for finding the exact solution for the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under a potential in the presence of a sink of finite width. The solution requires the knowledge of the Green's function in Laplace domain in the absence of any sink. We find the exact solution for the case of parabolic potential. This model has considerable improvement over the existing models for understanding non-radiative electonic relaxation of a molecule in solution, in fact this is the first model where a simple analytical solution is possible in the case of a sink of finite width.