Bridging Kohn - Sham DFT and the Angular Overlap Model. Ligand-Field Parameters and Bond Covalencies in Tetrahedral Complexes

Kohn–Sham density functional theory (DFT), constrained by the average-of-configuration computations, allows the valence shell of regular tetrahedral chlorido complexes of a complete series of 3d transition metal ions to be orbitally compared. The concept of classificational parentage provides a handle on the discussion of the energetic ordering of all the valence orbitals and illuminates an almost identical ordering for all the systems. Only the participation of the metal 4s orbital in bonding causes a few minor fluctuations. The partially filled ‘3d’ molecular orbitals sit in an energy window framed by completely filled ‘ligand orbitals’ on the low-energy side and an empty metal ‘4s’ orbital on the high-energy side. Regular tetrahedral symmetry requires the halides to be linearly ligating and this property is stable within the ‘experimental’ uncertainty for small distortions. By lowering the symmetry towards the planar configuration, keeping the equivalence of the ligands stable, the information content of the computations was doubled and the angular overlap energy parameters referring to the individual ligands obtained. The orbital energies of the partially filled shell depend linearly on the Angular Overlap Model (AOM) parameters eλ, the slope being the sum of the squares of the single-ligand λ angular overlaps (λ = σ and π). Mulliken population analysis shows the contents of the appropriate ligand orbitals in the ‘d’ orbitals to vary in parallel with the molecular orbital AOM energies and to increase pronouncedly with the oxidation number z. Results for tetraoxidoferrate(vi) show a remarkable resemblance with the chloride complexes of even the divalent metal ions. However, although the bonding orbitals are more π-bonding, the totally symmetrical bonding orbitals use M_4s less in the oxido complex. The sensitivity of covalency and spectroscopic energy parameters towards radial distortions are examined and show Werner-type complexes and the high-valent FeO42– to behave somewhat differently.