Effect of molecular size on the electrocatalytic activity of M-N4-C catalysts for ORR, OER, and HER

Abstract

The M-N₄-C catalysts have attracted significant attention in electrocatalysis due to their atomic-level utilization efficiency, high electrocatalytic activity, stability, and the use of earth-abundant metals. However, the actual size of synthesized M-N₄-C catalysts is not uniform, making it challenging to elucidate the true structure and understand the intrinsic activity origin of M-N₄-C catalysts. To address this challenge, this study employs density functional theory (DFT) to comprehensively investigate the electrocatalytic ORR/OER/HER performance of M–N₄ structures (nC@MN₄, M = Fe, Co, Ni, Cu) embedded in carbon substrates with varying sizes (8.7 Å to 26.2 Å). Formation energy calculations reveal a “M”-shaped fluctuation in the stability of nC@MN₄ configurations as molecular size changes. By analyzing the electronic and geometric structure parameters, such as metal center charge, spin population, fundamental gap, and average M–N bond length across different molecular sizes of nC@MN₄, we observed significant size effects for nC@FeN₄ and nC@CoN₄ structures. For both *H and *OOH adsorption free energies, the magnitude of change with molecular size variation follows the order: nC@FeN₄ < nC@CoN₄ < nC@NiN₄ < nC@CuN₄. We also found that the ORR overpotential of FeN₄ fluctuates between 0.53 V and 1.42 V with changes in molecular size, offering a new perspective to understand discrepancies between theoretical calculations and experimental results. Finally, we observed that the fundamental gap is a strong predictor of performance for nC@FeN₄, and charge is a reliable predictor for nC@CoN₄. However, structural parameters exhibit weaker predictive ability for nC@NiN₄ and nC@CuN₄. In summary, this work reveals the size effect in carbon-based single-atom catalysts, providing critical insights into the true activity origin of MN₄ catalysts, and offering a deeper perspective for the development of high-performance MN₄ catalysts.