Electron-Counting Controls Bifunctional Activity in Single-Atom Catalysts through a Three-Regime Adsorption Mechanism

Developing efficient bifunctional electrocatalysts for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) is crucial for metal-air batteries and regenerative fuel cells. Among the most promising candidates, transition-metal single-atom catalysts (SACs) supported on N-doped graphene offer high atomic utilization and tunable coordination environments, but their rational design remains challenging because their molecule-like electronic states often fall outside conventional descriptor frameworks based on linear scaling relations or d-band concepts. Here, we show that the bifunctional activity of these SACs is governed by an electron-counting rule defined by the total number of metal s and d valence electrons, Nds. By combining subgroup discovery, first-principles calculations, projected-density-of-states and COHP analyses, we uncover a three-regime adsorption mechanism in which intermediate binding is controlled by the interplay among metal-adsorbate hybridization, antibonding-state occupation, and shell saturation. As Nds increases, the adsorption strength first increases, then decreases, and finally partially recovers, leading to a nonmonotonic periodic dependence of the binding energies of *OH, *O, and *OOH, and consequently of bifunctional ORR/OER activity. Guided by this mechanism, we develop physics-informed predictive models that enable high-throughput screening of more than 1000 candidate SACs and identify optimal bifunctional systems. Experimental synthesis and electrochemical characterization of Rh-SAC and Co-SAC systems confirm the predicted trends and their benchmark-level bifunctional performance. These results establish electron counting as a unifying physical principle for oxygen electrocatalysis on single-atom catalysts and provide a general route toward mechanism-driven catalyst discovery.