Sulfur-deficient edges as active sites for hydrogen evolution on MoS₂

A grand-canonical approach is employed to calculate the voltage-dependent activation energy and estimate the kinetics of the hydrogen evolution reaction (HER) on intrinsic sites of MoS₂, including edges of varying S-coverage as well as S-vacancies on the basal plane. Certain edge configurations are found to be vastly more active than others, namely S-deficient edges on the Mo-termination where, in the fully S-depleted case, HER can proceed with activation energy below 0.5 eV at an electrode potential of 0 V vs. SHE. There is a clear distinction between the performance of Mo-rich and S-rich adsorption sites, as HER at the latter sites is characterized by large (generally above 1.5 eV) Heyrovsky and Tafel energy barriers despite near-thermoneutral hydrogen adsorption energy. Thus, exposing Mo-atoms on the edges to which hydrogen can directly bind is crucial for efficient hydrogen evolution. While S-vacancies on the basal plane do expose Mo-rich sites, the energy barriers are still significant due to high coordination of the Mo atoms. Kinetic modelling based on the voltage-dependent reaction energetics gives a theoretical overpotential of 0.25 V and 1.09 V for the Mo-edge with no S atoms and the weakly sulfur-deficient (2% S-vacancies) basal plane, respectively, with Volmer-Heyrovsky being the dominant pathway. These values coincide well with reported experimentally measured values of the overpotential for the edges and basal plane. For the partly Mo-exposed edges, the calculated overpotential is 0.6-0.7 V while edges with only S-sites give overpotential exceeding that of the basal plane. These results show that the overpotential systematically decreases with increased sulfur-deficiency and reduced Mo-coordination. The fundamental difference between Mo- and S-rich sites suggests that catalyst design of transition metal dichalcogenides should be focused on facilitating and modifying the metal sites, rather than activating the chalcogen sites.