Hengyue Xu
Curvature is an essential geometric motif in biological redox centers, yet its catalytic role in heterogeneous systems remains largely unexplored. Here we establish curvature engineering as a general strategy to modulate the activity of MN 4 single-atom catalysts (SACs) for the hydrogen evolution reaction (HER). Inspired by concave and convex porphyrinic motifs in metalloenzymes, we construct a systematic curvature continuum by embedding MN 4 sites into carbon supports spanning concave, flat, and convex curvature. Density functional theory reveals that each metal exhibits a distinct curvature optimum, where curvature-induced electronic relaxation precisely balances intrinsic metal–hydrogen affinity, yielding a nearly thermoneutral hydrogen adsorption free energy (Δ G H* ). Machine-learning analysis, benchmarked by cross-validated XGBoost models, identifies the melting point, curvature, group, and atomic radius as key descriptors that cooperate with the curvature to tune adsorbate energetics. Correlation analysis further confirms that curvature functions not as a singular descriptor but as a geometrically programmable field that couples with the host electronic structure. Together, these results introduce a generalizable design concept, nanoscale curvature modulation of the SAC electronic structure, and establish curvature as a predictive and transferable design axis for next-generation electrocatalysts.