First-principles and machine learning study of the NRR in curvature-tuned TM-doped CNTs

Although significant progress has been made in enhancing the catalytic performance of single-atom transition metal catalysts (SACs) through structural and morphological engineering, the critical role of substrate curvature remains underexplored, particularly in the context of the nitrogen reduction reaction (NRR). In this study, we systematically investigate the electrocatalytic NRR performance of single-atom transition metal-doped carbon nanotubes (TM-N₃CNTs) with varying curvatures using first-principles calculations combined with machine learning. We comprehensively analyze the thermodynamic and kinetic competition between the adsorption of single, double, and triple nitrogen molecules, key reaction intermediates (*NNH) and hydrogen atoms. The subsequent electrocatalytic nitrogen reduction reaction (eNRR) was also thoroughly explored. Taking the W-N₃CNT structure as an example, lower curvatures promote delocalized electron distributions, stronger W-N (*NNH) bonding, and reduced overpotentials, while high-curvature systems demonstrate higher activity during the initial reaction stages. By employing the sure independence screening and sparsifying operator (SISSO) algorithm, we performed machine learning to model the reaction ratio of *NNH and *H atoms, as well as Δ<i>G</i>(*NNH), identifying physically meaningful descriptors. These findings elucidate the intrinsic relationship between curvature and catalytic performance from a multi-scale perspective, providing theoretical insights and optimization strategies for the curvature-based design of single-atom transition metal catalysts.