Spin-Selective Orbital Filling Regulates Hydrogen Adsorption on Two-Dimensional Half-Metals.

The d-band center theory has long provided a useful framework for understanding hydrogen adsorption in HER electrocatalysis, yet its predictive capability becomes limited in half-metallic systems where spin asymmetry dominates the electronic structure. In such systems, hydrogen adsorption is expected to depend on spin-resolved dz2 orbital filling (n) rather than spin-averaged electronic states. Here, we show that n quantitatively correlates with the hydrogen adsorption Gibbs free energy (ΔG) in two-dimensional half-metal catalysts, as exemplified by transition-metal-doped FeP4 and TMX2 (TM = Cr, Mn, Ti, and V; X = S, Se, and I) monolayers. We demonstrate that hydrogen adsorption is governed by spin-selective orbital interactions: unfilled dz2 states in the metallic spin channel enhance H binding, whereas those in the insulating spin channel weaken adsorption. This competition leads to an optimal adsorption regime when n approaches 0.5, due to cooperative contributions from the two spin channels. These results clarify spin-dependent orbital contributions and reveal a clear correlation between catalytic activity and spin-polarized electronic structure. Spin-resolved dz2 orbital filling thus emerges as a useful design descriptor for HER electrocatalysts based on two-dimensional half-metallic materials.