Symmetry of the ligand environment

As noted earlier, A depends on the symmetry of the ligands surrounding a transition metal ion. The relationships expressed in eqs (2.7), (2.8) and (2.9) for crystal field splittings in octahedral, tetrahedral, body-centred cubic and dodecahedral coordinations are summarized in eq. (2.26) 

---

Although the physical basis of the crystal field model is seen to be unsound, the fact remains that, in summarizing the importance of the symmetry of the ligand environment, it qualitatively reproduces many of the features of the magnetic and spectral properties of transition metal complexes. This early qualitative success established its nomenclature in the fields of these properties. While we shall have little more to say about crystal field theory as such, much of the rest of this article will be couched in the language of the crystal field model, and for that reason some little trouble has been taken to outline its development. 

The polymerization on purely n-allyl complexes of transition metals is of the greatest interest for checking these predictions. Allyl itself is a good low molecular weight model for the end unit of the growing polymer chain. In this connection it may be expected that the symmetry of the ligand environment of the transition metal actually remains invariable during polymerization. This fact, in turn, ensures the retention and constancy of the spin state of the central atom. 

The above general form of the crystal field potential becomes even more restricted when the actual symmetry of the ligand environment is considered. Each symmetry operation R, of the symmetry point group G must leave the potential invariant, i.e. 

It is important that the acceleration of the H-D exchange, observed experimentally on the replacement of the PtCl/ or Pt(H20)4 catalysts by PtClaCH O), could not be related to any calculated quantum-chemical parameters. It was therefore postulated that an optimum combination of the donor-acceptor and dative mechanisms of the transfer of electron density is essential for the effective alkane-platinum(II) complex interaction. Since the contribution of the former inaeases and that of the latter diminishes with the increase of the positive charge on the complex, the optimum combination can be achieved for the complex with zero charge. Somewhat earlier, the presence of a catalytic activity maximum for the complex PtCl2(H20)2 was attributed to the influence of the symmetry of the ligand environment [32]. On the basis of the hypothesis that the formation of a bond with the activated alkane takes place mainly on interaction with the drf AO of the complex, the rates of reaction were correlated with the contribution by this orbital to the LUMO of the platinum(II) complex. Symmetry considerations led to the conclusion that, for n = 0 and n = 4, the LUMO of the complex is formed solely by the AO and cannot contain an admixture of the dfl state. As a consequence of the decrease of symmetry for n =1, 2, 3, such an admixture exists but the n = 2 complex occupies a special place (thus the... 

The above discussion has emphasized that the splitting of the energies of the d-orbitals is dominated by the effects of the formal octahedral or tetrahedral symmetry of the ligand donor atom environment. This dominance is also present for coordination stereochemistries approximating to these symmetries. However, the effects of departure from these cubic symmetries are not negligible, and may be dominant for stereochemistries which do not even approximate to one of the cubic ones, e.g. a square-planar coordination geometry. 

Once the terms for the firee ion have been worked out and put in order of energy, it is necessary to see how the environment of the ligands affects them. This depends on the symmetry of the coordination environment. For a metal in an octahedral array of six identical ligands, the d orbitals split into a lower set of three with symmetry t2g and an upper set of two with symmetry Cg. Environments of lower symmetry lead to different splitting patterns (Figure 9.14). 

Optical activity in metal complexes may also arise either if one of the ligands bound to the metal in the first co-ordination sphere is itself optically active or if the complex as a whole lacks a centre of inversion and a plane of symmetry. Thus all octahedral cts-complexes of the tris-or bis-chelate type have two isomeric forms related by a mirror plane, the d- and /-forms. These species have circular dichroism spectra of identical intensities but opposite in sign. The bands in the circular dichroism spectrum are, of course, modified if ligand exchange occurs but they are also exceedingly sensitive to the environment beyond the first co-ordination sphere. This effect has been used to obtain association constants for ion-pair formation. There also exists the possibility that, if such compounds display anti-tumour activity, only one of the mirror isomers will be effective. 

When a lanthanide ion is placed in a ligand environment with symmetry lower than spherical, the energies of its partly filled 4f orbitals are split by the electrostatic field of the ligand. The result is a splitting of the 2/ + 1 degeneracy of the free ion states (see Figure 1.2). 

---