Grand Canonical Rate Theory for Electrochemical and Electrocatalytic Systems I: General Formulation and Proton-coupled Electron Transfer Reactions

Electrochemical interfaces present a serious challenge for atomistic modelling. Electrochemical thermodynamics are naturally addressed within the grand canonical ensemble (GCE) but the lack of a fixed potential rate theory impedes fundamental understanding and computation of electrochemical rate constants. Herein, a generally valid electrochemical rate theory is developed by extending equilibrium canonical rate theory to the GCE. The extension provides a rigorous framework for addressing classical reactions, nuclear tunneling and other quantum effects, non-adiabaticity etc. from a single unified theoretical framework. The rate expressions can be parametrized directly with self-consistent GCE-DFT methods. These features enable a well-defined first principles route to addressing reaction barriers and prefactors (proton-coupled) electron transfer reactions at fixed potentials. Specific rate equations are derived for adiabatic classical transition state theory and adiabatic GCE empirical valence bond (GCE-EVB) theory resulting in a Marcus-like expression within GCE. From GCE-EVB general free energy relations for electrochemical systems are derived. The GCE-EVB theory is demonstrated by predicting the PCET rates and transition state geometries for the adiabatic Au-catalyzed acidic Volmer reaction using (constrained) GCE-DFT. The work herein provides the theoretical basis and practical computational approaches to electrochemical rates with numerous applications in physical and computational electrochemistry. (C) 2020 The Electrochemical Society (ECS). Published on behalf of ECS by IOP Publishing Limited.