The Angular Overlap Model and Vibronic Coupling in Treating s-p and d-s Mixing – a DFT Study

Abstract

The steric and energetic lone pair effect induced by s-p mixing can be parameterised within the angular overlap model (AOM), as is shown for a series of halide molecules and complexes mainly of the fifth main group (oxidation state +III) with the coordination numbers 3 to 6. The derived effective AOM parameters e sp eff , defined for the average bond lengths of the distorted structures, decrease the softer the considered entity is, and seem to be transferable within groups of chemically related species.We base the analysis on results of DFT calculations, using specifically Kohn-Sham MO diagrams in comparison to corresponding many-electron energies. There is definite experimental evidence for s-p and for d-s mixing as well, as is demonstrated by the DFT analysis of spectral data for some model complexes. The equivalence of the vibronic coupling approach on the MO level with the AOM is emphasized; the advantage of the AOM is, however, that angular and radial (bond length) contributions can be cleanly separated.

A Spectroscopic and Structural Study of M(3d)2+‐Doped β‐Tricalcium Phosphate – the Binding Properties of Ni2+ and Cu2+ in the Pseudo‐Octahedral Ca(5)O6 Host‐Sites

“…We cannot account for the distinct band at 18800 cm –1 , which is possibly caused by a tiny Ni 2+ percentage on one of the other Ca 2+ sites in the β‐TCP structure with considerably larger Ca–O distances than the ones in Ca(5). It is assigned to 3 A 2g → {}^3_bT 1g with an accordingly very small Δ parameter – not unusual for a substitution into voluminous Ca 2+ positions 9; the other two spin‐allowed d–d transitions vanish under the first main band of Ni 2+ in the Ca(5) site (→ {}^3_aT 1g ) and appear only outside the reliably accessible range of measurement < 5000 cm –1 (→ 3 T 2g ), respectively (Figure 1). The yellow hue is due to the colour‐determining minimum in the visible region between 15 and 20000 cm –1 .…”

“…The nephelauxetic ratio β = B / B o that measures the decrease of the interelectronic repulsion in respect to the value of the free ion ( B o = 1040 cm –1 ), is near to 0.9, indicating a rather ionic Ni–O bond (Table 2). This can be led back to the strong contrapolarising power of the small P V atom, to which the ligating oxygen atom is bonded 9. It enhances the oxygen electronegativity and hence the tendency to form ionic bonds (see also other solids with PO 4 3– ‐type ligands in Table 2).…”

“…Even stronger is the polarising strength of protons on oxygen and somewhat less the one of the C IV atom, whereas in NiO the oxygen ligand is more covalent. The variation of the ligand field strength Δ is more complex to interpret because it also strongly depends on the interplay between σ‐ and π‐overlap 9.…”

The Correlation between Structure and Color of Iron Oxide‐type Solids, Sustainable Pigments with Gentle Hues

“…Though the accompanying phenomena, in particular the sometimes striking colour changes, appear as being distinct, the involved bond length changes are only tiny. Thus, for example in the case of octahedral Ni 2+ in various oxidic solids, is found to vary within about 30 % (7.9 (±) 1.3 × 10 3 cm –1 ), while the bond lengths differ by only 2 % (2.06 (±) 0.02 Å) 20. The obvious conclusion is, that the bond distances are not very sensitive in respect to changes, which involve the 3d‐orbitals.…”

“…It seems appropriate to shortly examine here the results of a thorough study, which considered the modification of an octahedral ligand field – exerted on 3d n cations such as Fe 2+ and Fe 3+ via oxidic ligator atoms – and this, if additionally various other cations are bonded to the oxygen ligand 20. The charges and the radii of the latter cations, but also whether they are d 0 ‐ or d 10 ‐configurated for example – these parameters shape the second sphere coordination – may explain the considerable variability of the ligand field parameter Δ (and the bond covalency, accessible via the Racah' parameters B and C, as well).…”