Semiclassical Green's functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit

TL;DR

This paper develops a semiclassical instanton approach to calculate electron-transfer rates in nonadiabatic systems, extending Marcus theory to include anharmonic environments and nuclear tunnelling effects.

Contribution

It introduces a new instanton formulation based on semiclassical Green's functions for nonadiabatic electron transfer, avoiding traditional approximations.

Findings

Derives a physically transparent instanton rate expression.

Extends Marcus theory to anharmonic and tunnelling regimes.

Provides a basis for numerical evaluation in future work.

Abstract

We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi's golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In the following paper, we discuss numerical evaluation of the formulae.