Scaling relations and catalytic descriptor for the nitrogen reduction on single-atom catalysts

Single-atom catalysis is a rapidly advancing frontier in catalysis research, with the electrochemical synthesis of NH₃ from N₂ representing a key transformation. In this study, we conducted a computational investigation of a series of single-atom catalysts (SACs), each composed of a single metal atom anchored on nitrogen-doped graphene, to enhance understanding of their complex chemistry in the nitrogen reduction reaction. The results indicate that the most likely pathway depends on the nature of the metal atom and can differ from the classical pathways found on extended catalytic surfaces. Besides electrochemical intermediates, the formation of molecular adducts such as *N₂ and *NH₃ cannot be neglected. Interestingly, it is possible to correlate the stability of reaction intermediates via scaling relations with a simple yet practical descriptor, depending on the stability of two species only, *NNH and *NH₂. This descriptor enables us to rationalize the volcano-shaped dependence of the nitrogen reduction reaction's rate-limiting step and may serve as a useful proxy for screening large catalyst databases, providing qualitative and semi-quantitative insights for more advanced refinement. Last, we show that the *N₂ and *NH₃ chemical adsorbates must be explicitly considered in order to reliably predict the catalyst behavior.