Efficient and low-cost electrocatalysts are crucial for sustainable hydrogen production via water splitting. Here, 33 single-atom catalysts (SACs) supported on C24N24 were systematically investigated using first-principles calculations. Structural, thermal, and electrochemical stability analyses indicate that only In-, Si-, Ge-, and Bi-C24N24 are stable under operating conditions. Hydrogen adsorption free energy calculations reveal that Ge-C24N24 exhibits the most optimal ΔGH* for acidic HER (-0.14 eV), followed by In-C24N24 (-0.38 eV). In alkaline media, Ge-C24N24 also shows the most favorable thermodynamic profile (0.21 eV). However, explicit kinetic analysis of the water dissociation step demonstrates high activation barriers (>1.83 eV) for all candidates, indicating sluggish alkaline HER kinetics. Machine-learning analysis based on the SISSO algorithm identifies metal charge, electronegativity, metal-nitrogen distance, valence electron count, electron affinity, and first ionization energy as key descriptors governing HER activity trends. Overall, Ge-C24N24 emerges as a promising SAC for acidic HER, while the large water dissociation barriers highlight the intrinsic kinetic limitations of C24N24-supported SACs for alkaline HER. These findings provide mechanistic insights and theoretical guidance for rational catalyst design.
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