Stability of graphene-based single-atom catalysts across the first-row transition series: the interplay of coordination, composition, and metal identity.

The rational design of graphene-supported single-atom catalysts (SACs) requires maximizing metal utilization while ensuring structural stability, yet the underlying principles remain fragmented across the literature. Here we present a systematic DFT study of 60 SACs comprising first-row transition metals anchored to mono- and divacancy graphene supports, with and without nitrogen doping, and complemented by Ni(111)-supported metallic systems. By decomposing metal adsorption into deformation and intrinsic binding contributions, we distinguish structural from electronic metrics that contribute to the stability of these systems. Divacancies provide significantly stronger and more flexible coordination environments than monovacancies, and carbon coordination consistently outperforms nitrogen coordination regarding the metal-graphene bond. Across the transition-metal series, stability is primarily governed by the alignment between metal d states and the graphene Fermi level, further modulated by radius-dependent geometric accommodation. For the later transition metals, nitrogen doping weakens binding by partially filling antibonding states. Meanwhile, incorporation on a Ni(111) support enhances metal anchoring in divacancies but weakens it in monovacancies, while preserving the overall trends observed for unsupported systems. Magnetization and charge transfer are strongly correlated with the metal-graphene binding energies. Together, these trends define a categorical framework that intertwines the tendencies of vacancy topology, coordination chemistry, and electronic alignment. This understanding provides crucial insights for engineering robust graphene-based SACs and offers a basis for pre-selecting experimentally viable candidates.