The Reaction Mechanism for the Hydrogen Evolution Reaction on the Basal Plane Sulfur Vacancy Site of MoS_2 Using Grand Canonical Potential Kinetics

Abstract

We develop the grand canonical potential kinetics (GCP-K) formulation based on thermodynamics from quantum mechanics calculations to provide a fundamental basis for understanding heterogeneous electrochemical reactions. Our GCP-K formulation arises naturally from minimizing the free energy using a Legendre transform relating the net charge of the system and the applied voltage. Performing this macroscopic transformation explicitly allows us to make the connection of GCP-K to the traditional Butler–Volmer kinetics. Using this GCP-K based free energy, we show how to predict both the potential and pH dependent chemistry for a specific example, the hydrogen evolution reaction (HER) at a sulfur vacancy on the basal plane of MoS_2. We find that the rate-determining steps in both acidic and basic conditions are the Volmer reaction in which the second hydrogen atom is adsorbed from the solution. Using the GCP-K formulation, we show that the stretched bond distances change continuously as a function of the applied potential. This shows that the main reason for the higher activity in basic conditions is that the transition state is closer to the product, which leads to a more favorable Tafel slope of 60 mV/dec. In contrast if the transition state were closer to the reactant, where the transfer coefficient is less than 0.5 we would obtain a Tafel slope of almost 150 mV/dec. Based on this detailed understanding of the reaction mechanism, we conclude that the second hydrogen at the chalcogenide vacant site is the most active toward the hydrogen evolution reaction. Using this as a descriptor, we compare it to the other 2H group VI metal dichalcogenides and predict that vacancies on MoTe_2 will have the best performance toward HER.