Assessing the Role of Composition and Size Effects in the Hydrogen Evolution Reaction on Ni_<i>m</i>Pd_{<i>n</i>–<i>m</i>} Clusters (<i>n</i> = 13 and 27)

The low-cost generation of green hydrogen (H₂) via water electrolysis depends on advances in catalysts for the hydrogen evolution reaction (HER). Although palladium and nickel nanoparticles have demonstrated potential catalytic performance, the exact interplay between particle size and composition in their binary forms remains an unresolved issue. Here, we explore Ni _<i>m</i> Pd _{<i>n</i>-<i>m</i>} nanoclusters consisting of 13 and 27 atoms to improve our atomistic understanding of the fundamental mechanisms of HER at a nanoscale regime. We used the putative global minimum structure of the bare clusters and employed data mining techniques to generate and select preferential hydrogen adsorption structures. The electronic and geometrical properties are predicted using a cost-effective calculation protocol, based on density functional theory calculations with the PBE functional including van der Waals corrections. The computational hydrogen electrode (CHE) model was employed to calculate Gibbs free energies. We found that atomic H adsorbs on bridge and hollow sites in the 13-atom clusters and only on hollow sites in the 27-atom clusters. The effects of size and composition on the adsorption energies are also calculated, and their relation to the bulk values is presented. Our results on the Gibbs free energy for the HER reaction suggest that, at the subnanometer scale, the most promising catalysts are obtained when earth-abundant nickel clusters are doped with a small percentage of palladium, which has potential application for cost reduction. For instance, Ni₁₀Pd₃ shows a Δ<i>G</i> of -0.35 eV, while Ni₁₃ and Pd₁₃ unary counterparts present -0.51 and -0.47 eV, respectively. An analysis of electron density reveals that within these Ni _<i>m</i> Pd _{<i>n</i>-<i>m</i>} nanoclusters, a substantial charge transfer from the cluster to the hydrogen atom is correlated with lower values of Δ<i>G</i>. This observation implies that charge transfer is a significant factor in the HER.