Multi-Channel Electron Transfer Reactions: An Analytically Solvable Model

TL;DR

This paper introduces an analytical approach to multi-channel electron transfer reactions in solution, modeling diffusive motion with multiple acceptor potentials coupled via Dirac Delta functions, solved using Laplace transforms of Green's functions.

Contribution

It presents a novel analytical method for solving multi-channel electron transfer reactions with Dirac Delta coupling, expanding understanding of complex diffusive processes.

Findings

Provides an exact analytical solution for multi-channel electron transfer.

Utilizes Laplace transforms of Green's functions for uncoupled potentials.

Enhances theoretical understanding of electron transfer dynamics.

Abstract

We propose an analytical method for understanding the problem of multi-channel electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of one donor and several acceptor potentials. The coupling between the donor potential and acceptor potentials are assumed to be represented by Dirac Delta functions. The diffusive motion in this paper is represented by the Smoluchowski equation. Our solution requires the knowledge of the Laplace transform of the Green's function for the motion in all the uncoupled potentials.