KID Procedure Applied on the [(PY₅Me₂)MoO]⁺Complex

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 JHL=JI2+JA2 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 JHLS=JHL2+|ΔSL|2 index that could be more suitable to choose the most proper density functional because the JHL and |ΔSL| are independent indexes.