Theory of Proton Discharge on Metal Electrodes: Electronically Adiabatic Model

The first step of the hydrogen evolution reaction, an important reaction for the storage of renewable energy, is the formation of a surface-adsorbed hydrogen atom through proton discharge to the electrode surface, commonly known as the Volmer reaction. Herein a theoretical description of the Volmer reaction is presented. In this formulation, the electronic states are represented in the framework of empirical valence bond theory, and the solvent interactions are treated using a dielectric continuum model in the linear response regime. The nuclear quantum effects of the transferring proton are incorporated by quantization along the proton coordinate. The ground and excited state electron-proton vibronic free energy surfaces are computed as functions of the proton donor-acceptor distance and a collective solvent coordinate. In the fully adiabatic regime, the current densities and Tafel slopes are computed from the ground state vibronic free energy surface. This theory is applied to the proton-coupled electron transfer reaction involving proton discharge from H₃O⁺ in aqueous solution to a gold electrode. This theoretical model opens the door for future studies, including examination of the effects of vibronic nonadiabaticity, electronic friction, and solvent dynamics.