Data-Driven Structural Angle Mining Elucidates Hidden Design Rules for Hydrogen Evolution Single-Atom Electrocatalysts

Abstract

Structural distortions in modified two-dimensional transition metal dichalcogenides (MX2) influence electrocatalytic activity, yet quantitative and predictive structure-property relationships remain underdeveloped. To bridge this gap, we perform data-driven structural angle mining across hundreds of thousands of single-atom doped configurations (TM1@MX2) and establish geometrically defined angular descriptors. These descriptors exhibit high predictive accuracy for hydrogen evolution electrocatalysis. Crucially, our analysis reveals that catalytic activity correlates more strongly with long-range angular parameters describing peripheral geometric effects than with the local coordination environment. Guided by these descriptors, we identify specific angular signatures as quantitative predictors for high-performance catalysts: an outer-shell S-centered angle indicates optimal hydrogen evolution reaction (HER) activity for Ir1@MoS2 (S-vacancy), while a distinct Mo-centered angle identified V1@MoS2 (Mo-vacancy) as a promising earth-abundant candidate. Experimental verification confirms these predictions: synthesized Ir1@MoS2, with an ultralow loading of 0.1 wt%, achieves performance comparable to commercial Pt/C on a mass-activity basis, while V1@MoS2 enhances HER performance relative to pristine MoS2. The framework also shows strong computational correlations with oxygen evolution activity, though experimental validation for OER remains an important direction for future investigation. The angular descriptor framework introduced here provides a geometrically intuitive and electronically grounded strategy for the rational design and accelerated discovery of advanced energy materials.