Crystal field parameters simple overlap model

The point-charge electrostatic model is useful in illustrating how symmetry influences the signs of the crystal field parameters B. However, it does not usually result in accurate determinations of their magnitude and therefore other methods have been developed that lead to a better estimation. One such approach is based on the angular overlap model AOM developed and expanded to the/elements by Jprgensen [45]. Another approach is the simple overlap model SOM, proposed by Malta [46]. 

The Angular Overlap Model is a ligand field model which uses parameters20 (A = a, n, 6...) for expressing the orbital energies. For d orbitals X can be only a, n and <5, but it is customary to use as parameters e = e a - ej and e = e - ej. In octahedral complexes a simple correlation exists between these parameters and the usual crystal field parameters21 ... 

The angular overlap model is a relatively crude method which appears to yield results at least as good as those afforded by the crystal field model. As with all simple empirical models, the AOM depends on many approximations and assumptions which cannot be expected to be even approximately correct. Thus, for example, the parameter a is assumed to depend only on the identity of the metal and the ligand, and on the internuclear distance it is independent of the stoichiometry or stereochemistry. The theoretical basis for assuming the proportionality of the AOM matrix elements to overlap integrals is closely related to the Wolfs-berg-Helmholz approximation for the off-diagonal matrix elements of the one-electron operator ... 

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