Machine learning-assisted exploration of the interfacial valence electron fitting rule for MBene-based single-atom catalysts†

Single-atom catalysts (SACs) have garnered significant interest due to their exceptional catalytic activity and selectivity when incorporated into two-dimensional materials. However, the d-band center theory for SACs still exhibits discrepancies in describing the adsorption energies of reaction intermediates. This study integrates machine learning (ML) with density functional theory to introduce a valence electron fitting descriptor for elucidating the adsorption mechanisms of intermediates on MBene-based SACs. By combining DFT calculations with ML-driven feature analysis, an M-condition valence-electron fitting rule (VeFO/VFOH) between the valence electron count of the anchored metal (V_TM) and that of the adsorbed intermediates (V_O/OH) was identified: M < 5: V_O + V_TM = 11, V_OH + V_TM = 11; M = 5: V_O + V_TM = 12, V_OH + V_TM = 11; M > 5: V_O + V_TM = 12, V_OH + V_TM = 12. This descriptor provides a unified framework for predicting intermediate adsorption behavior across different MBene substrates. Electronic-structure analysis indicates that adsorption is driven by electron-sharing through orbital hybridization, and that optimal orbital resonance positions, pronounced overlap-peak intensities, and moderate charge-transfer magnitudes collectively underpin strong adsorption. Well-fitted multidimensional SISSO adsorption energy descriptors probe the d-electron number of TM and M as the main manifestation of the structure's adsorption capacity, and the structure's ability to adsorb O/OH decreases/increases with increasing d-electron number. The dimensional augmentation of the descriptors enhances the goodness-of-fit (R_O3² = 0.86 and R_OH3² = 0.89) and, concurrently, confirms the validity of the M-conditional valence-electron fitting rule for d-orbital hybridization filling angles. This study reveals the M-conditional valence-electron fitting rule governing adsorption intermediates on TM–M₂B₂O₂ materials, thereby rectifying the poor goodness-of-fit exhibited by the conventional d-band center model for adsorption energies (R_O² = 0.02 and R_OH² = 0.25). These insights furnish guidance for the rational design of OER catalysts centered on the OH → O intermediate and establish a novel theoretical framework and design paradigm for understanding and predicting how adsorption energies of reaction intermediates—and their rate-determining conversion steps—vary across different catalytic substrates.