Assessing Fluxionality Effects on Small Clusters of High Interest for Hydrogen Evolution Reaction

Structural fluxionality challenges the common practice of predicting electrocatalytic trends from a single optimized geometry. Here, we quantify fluxionality effects on hydrogen evolution reaction descriptors for subnanometer group-10 clusters Ni13, Pd13, and Pt13 using an ensemble-based DFT workflow that samples low-lying metastable backbones and multiple H* adsorption minima within the CHE framework. Metastable motifs substantially broaden the distribution of hydrogen adsorption free energies ΔGH*, showing that a description based solely on the global-minimum structure captures only a portion of the accessible adsorption landscape. Volcano-type analyses show that fluxionality widens the range of accessible adsorption energetics, whereas the thermodynamic ensemble descriptor remains close to the global-minimum value because metastable backbones carry small statistical weights. Site-resolved sampling reveals that Ni13 and Pd13 favor bridge/hollow-like adsorption motifs, whereas Pt13 preferentially stabilizes atop-like H* configurations that reach near-thermoneutral binding within the global-minimum basin. The Ni13 and Pd13 global minima are comparatively rigid and largely preserve their motifs after adsorption, whereas Pt13 undergoes pronounced adsorbate-induced restructuring, enabled by relativistic bonding and enhanced sd hybridization. As a result, HER thermodynamics in Pt13 cannot be assigned to a single structural minimum, emphasizing the limitations of conventional single-structure descriptors and volcano interpretations at the subnanometer scale. Finally, symbolic-regression models provide compact, physically interpretable structure–property relations for each metal (RMSE of 0.066 and 0.064 eV for Ni13 and Pd13, respectively), whereas a single unified model across all TM13 compositions is challenging (RMSE of 0.128 eV), highlighting the system dependence of adsorption energetics in fluxional nanoclusters.