Site-Dependent Free Energy Barrier for Proton Reduction on MoS₂ Edges

We calculated the adiabatic free energy surface of the proton reduction reaction on catalytically active MoS 2 edge atoms by combining density functional theory with the Anderson–Newns model, which accounts for solvent fluctuation and charge transfer in the context of Marcus theory. This framework combines three different contributions to the associated reaction energetics and kinetics, namely, the relevant electronic orbitals of the substrate, the possibility of surface relaxation upon adsorption, and the impact of solvation. Under the assumption of fixed edge geometry throughout the reaction, we calculate the free energy barriers on edge S and Mo sites to be 0.65 and 0 eV, respectively. However, if we consider surface relaxation, the barrier on the edge S site is reduced by more than half to 0.31 eV. On edge Mo sites, the d z 2 orbital is responsible not only for the strength of binding but also for the barrierless reaction. On edge S sites, the bound hydrogen atom always retains some finite positive charge, which indicates that it remains partially solvated even after surface binding. In this case, it is crucial to account for the solvation energy in addition to the gas-phase adsorption energy when assessing hydrogen catalysis.