Unveiling Curvature Effect on Fe Atom Embedded N‑Doped Carbon Nanotubes for Electrocatalytic Oxygen Reduction Reactions Using Hybrid Quantum-Mechanics/Machine-Learning Potential

The curvature of the catalyst’s surface is a novel dimension of variables that can significantly affect the catalytic activity. Theoretical simulations of the curvature effect on catalytic activity are, however, highly challenging because the catalyst model, being at the mesoscopic scale (nm to μm), is far beyond the current computational power in treating chemical reactions based on first-principles calculations. Here we develop a hybrid QM/ML calculation scheme that combines quantum mechanics (QM) and machine learning (ML) potentials to explore the curvature effect on catalytic activity. With this approach, we are able to establish quantitative curvature–activity relationships in the representative electrocatalytic reactions, namely, oxygen reduction reaction (ORR) on both FeN₄ and Fe₂N₆ moieties embedded in dissimilar carbon substrates (either graphene or carbon nanotubes) with different curvatures (κ) ranging from 0 nm^–1 to 2 nm^–1. The free energy changes of the potential-determining step (ΔG_PDS) decrease linearly with the increase of curvature, and on the Fe₂N₆ it exhibits a steeper slope with dΔG_PDS/dκ = −0.09 eV nm. By analyzing the electronic structures, we find a linear downshift of the energy level of Fe d-orbital as curvature increases, which leads to the change of binding strength of key reaction intermediates, i.e., the enhancement in Fe–OH₂ binding. Our results provide new insights into the design of electrocatalysts by tuning the catalyst’s local curvature.