Effective quantum reorganization energy for electron transfer

Abstract

The Marcus theory expression for the rate of non-adiabatic electron transfer is widely used across a range of physical conditions. Although Marcus theory defines the reorganization energy classically, here we show that the reorganization parameter governing the activation barrier for normal-region electron transfer is most generally a quantum mechanical object that depends on the electronic coupling, coinciding with the Marcus picture only in the limit of vanishing electronic coupling. This result unifies the physical description of electron-transfer activation barriers across the adiabatic and non-adiabatic regimes and formally predicts that Marcus-like rate expressions remain accurate beyond their traditional non-adiabatic domain of validity. These insights allow us to derive a closed-form expression for the curvature of the current-overpotential relation for electron-transfer-limited reactions at the electrochemical interface, now formally applicable to both inner-sphere and outer-sphere processes.