Abstract
The KID (Koopmans in DFT) protocol usually applies in organic molecules of the closed-shell type. We used the KID procedure on an open-shell Mo-based system for the first time to choose the most suitable density functional to compute global and local reactivity descriptors obtained from the conceptual density-functional theory (DFT). From a set of 18 density functionals, spread from the second until the fourth rung of Jacob’s ladder: BLYP, BP86, B97-D, MN12-L, MN15-L, M06-L, M11-L, CAM-B3LYP, PBE0, B3LYP, N12-SX, M06-2X, MN15, MN12-SX, ωB97X-D, M11, LC-ωHPBE, and APFD, we concluded that CAM-B3LYP provides the best outcome, and in the second place, M06-2X. Because the vertical first ionization potential and vertical first electron affinity in the ground state (gs) are defined as follows I = Egs(N – 1) – Egs(N) and A = Egs(N) – Egs(N + 1), where Egs(N – 1), Egs(N), and Egs(N + 1) correspond to energies of the system bearing N, N + 1, and N – 1 electrons, along with Koopmans’ theorem (KT) given by I ≈ −εHOMO (εHOMO, highest occupied molecular orbital energy) and A ≈ −εLUMO (εLUMO, lowest unoccupied molecular orbital energy), the deviation from the KT was performed by the use of the index, such that JI = |Egs(N – 1) – Egs(N) + εHOMO| and JA = |Egs(N) – Egs(N + 1) + εLUMO|, which are absolute deviations from the perspective of I and A, respectively. Furthermore, the εSOMO (SOMO: singly-occupied molecular orbital energy) leads us to another index given by |ΔSL| = |εSOMO – εLUMO|. Therefore, JHL and |ΔSL| are indexes defined to evaluate the quality of the KT when employed within the context of quantum chemical calculations based on DFT and not the Hartree–Fock theory. We propose the index that could be more suitable to choose the most proper density functional because the JHL and |ΔSL| are independent indexes.
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