Microscopic quantum mechanical Marcus theory for chemical reactions and its relationship to the Butler-Volmer equation used in redox flow battery analysis

Abstract

The vanadium redox flow battery has been intensively examined since the 1970s. What is missing is a connection between the current-overpotential Butler-Volmer equation, which provides an extremely helpful starting point for analytical and numerical studies, and microscopic quantum mechanical behavior at the atomic level. Such a connection will allow further advancements beyond the macroscopic, though very useful and insightful, modeling already done in the literature. Here we show rigorously the connection between the Butler-Volmer transfer coefficients, and the Marcus Gibbs free energy quantum mechanical parameters, and develop the equation directly in terms of the quantum mechanical parameters.