Barrierless electronic relaxation in solution -- two state model with exact analytical solution in time domain

TL;DR

This paper introduces an exact analytical solution for electronic relaxation in solution modeled by a two-state diffusion process with delta-function coupling, providing a novel approach to solve related problems in the time domain.

Contribution

The paper presents the first analytical time-domain solution for a two-state diffusion model with delta-function coupling in electronic relaxation.

Findings

Derived an exact analytical expression for survival probability in time domain

First analytical solution of its kind for this class of problems

Method applicable to other potential models in similar systems

Abstract

We propose an analytical method for solving the problem of electronic relaxation in solution in time domain, modelled by a particle undergoing diffusion under the influence of two coupled potentials. The coupling between the two potentials is assumed to be represented by a Dirac delta function of arbitrary position and strength. Smoluchowskii equation is used model the diffusion motion on both the potentials. We report an analytical expression for survival probability in time domain. This is the first time analytical solution in time domain is derived and this method can be used to solve problems involving other potentials.