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Spin-Resolved Nonlocal Second-Order Fukui Index for Open-Shell Systems from Delocalization Index Response
1Group of Modeling of Chemical Systems Using Quantum Calculations, Applied Chemistry Laboratory (LCA), University M. Khider of Biskra, Biskra 07000, Algeria.
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This work presents the first analytical derivation of the spin-resolved nonlocal Second-Order Fukui Index (SOFI) for open-shell molecular systems. The approach is based on the linear response of interatomic delocalization indices (δAB), providing a direct connection between frontier molecular orbital characteristics and real-space electron-sharing redistribution. The methodology is applied to substituted phenoxyl radicals to quantify how electron-donating (EDG) and electron-withdrawing (EWG) groups modulate α- and β-spin channels. The results provide a detailed map of spin-dependent electronic redistribution upon electron addition or removal. Spin-resolved SOFI indices are shown to be effective nonlocal descriptors for rationalizing radical reactivity. This study establishes a theoretical framework for the quantitative investigation of open-shell systems and the influence of substituents on spin-dependent electronic structure.
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