Orbital Discreteness Modulates Electron-Counting Adsorption Trends in Atomically Dispersed Catalysts

Abstract Understanding adsorption at atomically dispersed catalytic sites remains a central challenge, as conventional d-band theory fails to describe emerging molecular-like electronic structures in single-atom systems. Here, we identify a unified electronic framework that bridges metallic single-atom alloys and nitrogen-coordinated graphene single-atom catalysts (transition-metal atoms coordinated by four nitrogen atoms in graphene, TM-N4-Gr), connecting band-like and ligand-field-dominated regimes through a common orbital-filling picture. Systematic density functional theory calculations for C, N, and O adsorption show that adsorption-energy minima in both platforms exhibit a common ten-electron-like counting trend across transition-metal dopants. This behavior originates from molecular-orbital-like filling of dopant-adsorbate hybrid states, linking electron-counting behavior in metallic and coordination-stabilized single-atom environments. Crucially, orbital discreteness is identified as an important factor regulating how this electron-counting trend manifests. In TM-N4-Gr systems, localized d states promote more distinct bonding and antibonding states, leading to enhanced sensitivity to electron filling beyond the optimal electron count, whereas metallic hosts induce electronic delocalization that smooths this response. These results establish a unified orbital-filling framework in which adsorption is governed by the interplay between electron counting and orbital discreteness, providing a general physical basis for atomically dispersed catalysis.