Curvature-induced geometric strain engineering of Ni@S₄CNTs for bifunctional oxygen electrocatalysis

Curvature effects are crucial in regulating catalyst activity, yet their structure-activity relationship remains unclear. Here, spin-polarized density functional theory calculations were performed on a series of Ni@S₄CNTs-(m,0) models with systematically varied nanotube curvature. Increasing curvature induces a gradual transition from sp²-dominated to more sp³-like hybridization in CNTs, mainly manifested as enhanced SNiS angular distortion and increased Ni out-of-plane displacement. Electronic-structure analysis shows that curvature does not monotonically change the net Ni charge but induces charge redistribution around the local NiS₄ coordination unit. Thermodynamic analysis further demonstrates that curvature can precisely tune the catalytic activity of Ni@S₄CNTs, with the most favorable bifunctional thermodynamic performance achieved at Ni@S₄CNTs-(7,0) (η_ORR/OER = 0.33/0.31 V). COHP/ICOHP bonding analysis of the ∗OH and ∗O adsorption states further reveals that curvature does not uniformly regulate the corresponding NiO_ads interactions. In particular, ∗O -related NiO_ads bonding exhibits a substantially stronger curvature dependence than ∗OH-related bonding. Meanwhile, the intrinsic ∗OH / ∗OOH scaling relation remains largely preserved. Curvature therefore primarily changes the relative thermodynamic position of ∗O between ∗OH and ∗OOH, redistributing the free-energy burden between the ∗OH → ∗O and ∗O → ∗OOH steps. This behavior is attributed to the differential binding of catalytic intermediates induced by spin-polarized redistribution of Ni 3d orbitals under curvature. Such orbital differentiation, quantified by Δε_d^orb, elucidates the theoretical mechanism of curvature-regulated oxygen electrocatalysis.