Approach to Evaluating Reorganization Energies of Interfacial Electrochemical Reactions

Reaction rate coefficients for electron-transfer processes at the electrode-electrolyte interface are commonly estimated by using the Butler-Volmer equation, but their values are inaccurate beyond a few tenths of volts of overpotential. The Marcus-Hush-Chidsey (MHC) formalism yields correct asymptotic behavior of the rate coefficients vs applied overpotential but has complex dependencies on the redox system's intrinsic parameters, which can be difficult to model or measure. In this work, we bridge the two kinetics formalisms to estimate the reorganization energy, one of the important parameters for the MHC formalism, and investigate its dependence on other intrinsic parameters such as activation barriers, electronic coupling strength, and the density of states of the electrode surface. We examine the sensitivity of the reorganization energy to these parameters, establish some general relationships for accurately predicting rate coefficients using the MHC formalism over a wide range of applied overpotentials, and compare this approach to calculating MHC rate constants with other empirical approaches for the mechanisms of CO₂ reduction on different metal electrode surfaces.