Grand canonical rate theory for electrochemical and electrocatalytic systems I: General formulation and proton-coupled electron transfer reactions

A generally valid rate theory at fixed potentials is developed to treat electrochemical and electrocatalytic potential-dependent electron, proton, and proton-coupled electron reactions. Both classical and quantum reactions in adiabatic and non-adiabatic limits are treated. The applicability and new information obtained from the theory is demonstrated for the gold catalyzed acidic Volmer reaction.