Ligand field parameterization

Oelkrug, D. Absorption Spectra and Ligand Field Parameteres of Tetragonal 3 d-Transition Metal Fluorides. Vol. 9, pp. 1-26. 

Two symmetry parameterizations of the angular overlap model of the ligand field. Relation to the crystal field model. C. E. Schaffer, Struct. Bonding (Berlin), 1973,14, 69-110 (33). 

So, ligand-field theory is the name given to crystal-field theory that is freely parameterized. The centrally important point is that ligand-field calculations, whether numerical or merely qualitative, explicitly or implicitly employ a ligand-field Hamiltonian, very much like the crystal-field Hamiltonian, operating upon a basis set of pure d orbitals. Instead of the crystal-field Hamiltonian (Eq. 6.15),... 

Schaffer CE (1968) A Perturbation Representation of Weak Covalent Bonding. 5 68-95 Schaffer CE (1973) Two Symmetry Parameterizations of the Angular-Overlap Model of the Ligand-Field. Relation to the Crystal-Field Model. 14 69-110 Scheldt WR, Lee YJ (1987) Recent Advances in the Stereochemistry of Metallotetrapyrroles. 64 1-70... 

Schaffer, C.E. Two Symmetry Parameterizations of the Angular-Overlap Model of the Ligand-Field. Relation to the Crystal-Field Model. Vol. 14, pp. 69-110. 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

It is highly desirable, of course, that a theory have predictive power as well as the ability to parameterize data. In the context of ligand field theory this means that one hopes that the parameter values obtained for some M—L bond system can at least be used sometimes where this system occurs again and that, more audaciously, there might be some attribute of M and of L that would allow the derivation of the parameter from a knowledge of M and of L. 

It seems that, in its most widely used forms at any rate, the AOM involves such severe approximations and draws on empirical information to such an extent that it cannot be regarded as a proper implementation of quantum mechanics. Nevertheless, as a form of ligand field theory, it possesses distinct advantages and leads to a novel parameterization scheme which promises some degree of transferability of parameters with a metal-ligand bond. This last feature is entirely lacking, at least outside cubic symmetry, in crystal or ordinary ligand field treatments. 

This correlation has been used in the work of Konig and Kremer212-213) who parameterized the experimental susceptibility data by a temperature dependent energy separation e(T) = E(5T2) - E( Ax) determined by the ligand field strength. 

---