Unveiling Coordination Effects for Hydrogen Evolution Reaction Using an Interpretable Machine Learning Model

In this work, we combined density functional theory (DFT) and an interpretable machine learning (ML) model to accelerate the discovery of hydrogen evolution reaction (HER) catalysts based on transition metal (TM)-doped graphene. We compute hydrogen adsorption energies ( ${\text{Δ}E}_H^{\ast }$ ) for 140 single-atom configurations spanning 28 TMs and five local coordination motifs (TM-N₀, TM-N₁, TM-N₂, TM-N₃, and TM-N₄). Machine learning (ML) models trained on the DFT dataset identify XGBoost as the best predictor of ${\text{Δ}E}_H^{\ast }$ , while SHapley Additive exPlanations (SHAP) quantify descriptor importance and reveal key structure-property trends governing hydrogen binding. Activity is assessed by mapping ${\text{Δ}E}_H^{\ast }$ onto volcano relationships and exchange current density trends, which highlight coordination-dependent performance across the catalyst space. Notably, Cu and Ag in the C₃N₁ environment and La in the C₀N₄ environment emerge as the most promising candidates, exhibiting near-optimal hydrogen adsorption relative to the screened dataset. Overall, this work establishes an interpretable, data-driven framework for rational design of graphene-supported single-atom HER catalysts and provides a coordination guidelines for prioritizing experimental targets.