Inter-Site Coupling and Nonlinear Density–Activity Relationship in M–N–C Single-Atom Catalysts

Abstract

Metal-nitrogen-carbon (M-N-C) single-atom catalysts (SACs) exhibit outstanding catalytic performance in overall water splitting reactions. Currently, enhancing metal loading density is a promising strategy to improve catalytic efficiency; however, the intrinsic relationship between loading density-stability-catalytic activity remains unclear. In this study, we employed density functional theory (DFT) calculations to systematically explore the structure-performance relationships of MN4 catalysts across nine metal loading densities by linking inter-site distance with loading levels. Analysis of 234 MN4-X structures shows that structural stability initially increases significantly with decreasing loading density and then plateaus. Furthermore, modulating loading density tunes the adsorption strength of key intermediates, thereby altering reaction barriers. Specifically, IrN4 achieves optimal catalytic performance at loading densities of 0.040 at% and 0.014 at%, with ηHER = –0.30 V and ηOER = 0.40 V, respectively. This behavior is governed by orbital hybridization between intermediates and metal sites, alongside d-band center variations in the potential-determining step. Under high loading density, the MN4 moieties exhibit overlapping electronic structures (multi-site crossover state), whereas they gradually become isolated single-atom sites as loading decreases. The loading–activity relationship is non-monotonic, emphasizing the need for optimal density to maximize performance. This work highlights the critical role of metal loading density and provides a theoretical foundation for designing high-performance single-atom catalysts.