A 3D visualization of the substituent effect : A brief analysis of two components of the operational formula of dual descriptor for open-shell systems

A combined QTAIM/IRI topological analysis of the effect of axial/equatorial positions of NH2 and CN substituents in the [(PY5Me2)MoO]+ complex

By means of the Interaction Region Indicator (IRI) and Quantum Theory of Atoms in Molecules (QTAIM), the influence exerted by NH₂ (amino) and CN (cyano) as electron donor and electron acceptor substituent groups, respectively, located at para-positions of axial and equatorial pyridine rings of derivatized complexes coming from the [(PY₅Me₂)MoO]⁺ complex during the hydrogen molecular release in the gas phase was analyzed. In any case, a H-H covalent bond is forming at the transition state, with a strengthening of the electron density of 5.5% when the substituent group involved is NH₂ at the para-position of the axial pyridine ring. However, there was no difference between NH₂ and CN when these substituent groups are located at the para-positions of the equatorial pyridine rings. The topological properties of electron densities from the QTAIM are not perturbed by the electron donor and electron acceptor nature of the substituents, even when these substituent groups are located at the axial or equatorial pyridine rings of the Mo-based complex.

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 = E _gs(N - 1) - E _gs(N) and A = E _gs(N) - E _gs(N + 1), where E _gs(N - 1), E _gs(N), and E _gs(N + 1) correspond to energies of the system bearing N, N + 1, and N - 1 electrons, along with Koopmans' theorem (KT) given by I ≈ -ε_HOMO (ε_HOMO, highest occupied molecular orbital energy) and A ≈ -ε_LUMO (ε_LUMO, lowest unoccupied molecular orbital energy), the deviation from the KT was performed by the use of the index, such that J _I = |E _gs(N - 1) - E _gs(N) + ε_HOMO| and J _A = |E _gs(N) - E _gs(N + 1) + ε_LUMO|, which are absolute deviations from the perspective of I and A, respectively. Furthermore, the ε_SOMO (SOMO: singly-occupied molecular orbital energy) leads us to another index given by |ΔSL| = |ε_SOMO - ε_LUMO|. Therefore, J _HL 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 J _HL and |ΔSL| are independent indexes.