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 the 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.