Crystal field parameters angular overlap model

Crystal field splitting parameter, 2, 309 Crystal field theory, 1, 215-221 angular overlap model, 1, 228 calculations, 1, 220 generality, 1,219 low symmetry, 1,220 /-orbital, 1, 231 Crystal hydrates, 2, 305,306 bond distances, 2, 307 Crystals... 

The crystal-field parameters introduced in sect. 4.1 still contain all the structural information about the local environment. Therefore, a direct comparison of crystal-field parameters derived from different hosts, even with the same site symmetry, is not reasonable. In addition, the crystal-field parameters cannot be directly related to the distance and angle variations induced by the high-pressure application. Widely used models which extract the structural information from the crystal-field parameters are the angular-overlap (Jprgensen et al., 1963) and superposition model (Bradbury and Newman, 1967). In the case of f elements, the superposition model has been employed widely for the analysis of crystal-field parameters. 

As a last remark, it should be mentioned that also a few evaluations of the crystal-field parameters of Pr3"1" in LaCH in the scope of the angular overlap model have been made. Urland et al. (1985) andUrland (1989) used the angular overlap model to calculate the crystal-field splittings of LaCHiPr3"1" under pressure. In addition, Gregorian et al. (1989) derived the parameters of both models and found that both approaches were capable to successfully describe the high-pressure results. 

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 parameterization is easy to discuss for the angular-overlap model for Unearly ligating hgands, since this is parametrically equivalent to the crystal-field model whose merits in this respect, for both d and / period complexes, are indisputable. The more general AOM has more parameters and will therefore be even more flexible for parameterization of experiments. 

It has long been a theoretical puzzle (32, 33) that the crystal-field model works so weU, even though its own interpretation of its parameters has been shown to be physically inadequate. The fact that the crystal-field model for the special case of linearly ligating ligands is parametrically equivalent to the angular-overlap model, whose parameters e g and e)i refer directly to the bonding process, may eventually solve this puzzle. 

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 ... 

The cross relations due to Kibler (1971, 1974, 1975) between the coefficients of the Angular Overlap model e (up to (p effects), the electrostatic model (EM) crystal field parameters, and the superposition model (SM), translate in familiar cjp terminology the contribution of one overlap type A with ligand L to the 5. It is written as... 

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]. 

Another aspect of the relative merits of the angular overlap and crystal field models concerns the radial dependence of the parameters. This is, of course, a matter of particular importance in copper(II) chem-... 

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