Long Range Electron Transfer Reactions: An Analytically Solvable Model

TL;DR

This paper introduces an analytical approach to model long-range electron transfer reactions in solution, using diffusive motion and delta function couplings, providing a solvable framework for complex potential interactions.

Contribution

It presents a novel analytical method for solving long-range electron transfer problems with multiple potentials coupled via delta functions, based on the Laplace transform of Green's functions.

Findings

Provides explicit solutions for electron transfer rates

Offers a framework for analyzing multi-potential systems

Enhances understanding of diffusive electron transfer mechanisms

Abstract

We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of many potentials which are involved (donor - bridge - acceptor) in the process. The coupling between these 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.