Density functional theory calculations have been used to calculate activation barriers for N 2 dissociation on a range of possible active sites on ruthenium (Ru) nanoparticles, including step, edge, and planar sites. Variations in activation barriers are rationalized through a combination of geometric and electronic effects. The lowest-energy barriers are obtained using a favorable five-fold Ru atom surface feature, although surfaces with four-fold Ru atom features are also able to offer appreciably low barriers. The degree of undercoordination of the various sites has been quantified using generalized coordination numbers and is found to largely account for differences in activity between sites with the same geometry. Transition state energies have been converted to rate constants at typical industrial conditions using harmonic transition state theory. It is found that the most active site is the so-called B 5 step site, commonly accepted to be the active site for N 2 dissociation. However, several other step sites also offer competitive reactivity, within an order of magnitude at industrial conditions. Further, several edge sites, which have been previously identified as present on representative nanoparticles, have been found to give appreciably low barriers; the most active edge site is only 20 times less active than the most active step site, lending to the possibility of other sites contributing to the industrial formation of NH 3 . Even the quasi-planar (101̅ 1) site exhibits a modest transition state energy, which may contribute to the formation of NH 3 on large nanoparticles, given its likely very high abundance.

Periodic density functional theory calculations are used to elucidate the mechanism of the hydrogen evolution reaction on the Mo edge of graphene-and Au(111)-supported molybdenum disulfide (MoS 2 ) electrocatalysts. Calculated potential-dependent energy barriers, employing a detailed model of the electrochemical cell, reveal that the Volmer− Heyrovskýmechanism (barrier: 1.3 eV) is favored over the Volmer−Tafel mechanism at potentials close to 0 V vs the standard hydrogen electrode (SHE). In this mechanism, H preferentially adsorbs to a S atom, but the formation of H 2 occurs with H ads on Mo. Therefore, surface diffusion of H ads is required, which contributes to the overall barrier. The Volmer−Heyrovskýbarrier is similar on both supports, which is consistent with experimental rate measurements. However, H ads diffusion is the limiting step in the overall reaction on graphene-supported MoS 2 , whereas on Au-supported MoS 2 , the Volmer and Heyrovskýbarriers both contribute. This differing behavior between supports affects how the reaction rate changes with the potential, showing the importance of considering explicit reaction barriers. Our results provide a thorough understanding of hydrogen evolution kinetics and support-tuning effects, contributing to the optimization of MoS 2 as a catalyst for this key reaction in sustainable energy production.

ΔGHads on the basal plane and edges of MoS2 can be tuned using carbon based supports. The ΔGHads value on the edge relates directly to the degree of charge transfer between MoS2 and support.