Extending non-adiabatic rate theory to strong electronic couplings in the Marcus inverted regime

TL;DR

This paper introduces the Optimal Golden Rule (OGR) theory, a modified rate theory for electron transfer that remains accurate at strong electronic couplings, extending the applicability of traditional non-adiabatic rate models.

Contribution

The paper develops a new OGR theory that accurately predicts electron transfer rates in the Marcus inverted regime at large couplings, integrating with existing quantum and anharmonic models.

Findings

OGR correctly predicts rate turnover at large couplings

The theory performs well against exact quantum dynamics simulations

Application to a photosensitizer shows strong coupling inhibits charge recombination

Abstract

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's Golden rule, which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory, however in short range electron/energy transfer reactions this coupling can become very large, and therefore Fermi's Golden Rule fails to make even qualitatively accurate rate predictions. In this paper I present a simple modified Golden Rule theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. The theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating Golden Rule rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore the Optimal Golden Rule (OGR) theory can also combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus-Levich-Jortner theory, offering clear physical insight into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a BODIPY-Anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of four. Overall OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insight into a range of non-adiabatic processes.