Data-driven structural angle mining elucidates hidden design rules for hydrogen evolution single-atom...

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 identifies 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.