Theoretical Assessment of Hydrogen Evolution Reaction Activity on 3d, 4d, and 5d TM13 Transition-Metal Nanoclusters

Abstract Hydrogen evolution on nanocluster catalysts is governed by a balance between stabilizing adsorbed hydrogen and enabling its subsequent removal; however, periodic trends linking cluster electronic structure to hydrogen adsorption thermodynamics remain underexplored. Here, density functional theory calculations quantify how structural and electronic descriptors control hydrogen binding on 13-atom transition-metal clusters. Screening across the 3d (Fe, Co, Ni, Cu), 4d (Ru, Rh, Pd, Ag), and 5d (Os, Ir, Pt, Au) series reveals periodic trends in adsorption-site preference, charge redistribution, and s–d hybridization. The occupied d-state width increases from the 3d to the 4d and 5d clusters within Groups 8 to 10 and correlates with the shift from bridge and hollow coordination to predominantly top binding in the 5d series. Within the computational hydrogen electrode framework, the Gibbs free energy of hydrogen adsorption is negative for all 12 clusters, ranging from −0.061 to −0.925 eV, placing the entire set in the strong-binding regime. Comparison with previously reported values for the corresponding close-packed facets suggests a size effect in which undercoordination and enhanced metal–H hybridization stabilize H* on finite clusters. Thermodynamically, this strong binding implies a tendency toward hydrogen poisoning on reactive 5d metals, whereas Ag13 approaches thermoneutral hydrogen adsorption through adsorption-induced relaxation; Fe13 and Cu13 also emerge as competitive candidates when abundance is considered. These results provide physically grounded design rules for nanocluster electrocatalysts by linking adsorption thermodynamics to electronic descriptors and structural compliance.