Crystal field theory cubic

Thus, for a transition metal ion in a simple cubic lattice, crystal field theory predicts that the (/-orbitals are split into two types, one consisting of two members, henceforth referred to as the eg set, of higher energy than the remaining three, which are also degenerate and referred to as the t2g set. The labels eg and t2g are given because of their transformation properties in the group Of, which describes the site symmetry of an ion in a simple cubic lattice.19... 

A prediction of crystal field theory as outlined in the preceding subsections is that the crystal field splitting parameter, A, should be rather critically dependent upon the details of the crystal lattice in which the transition metal ion is found, and that the splittings of the /-orbital energies should become larger and quite complicated in lattices of symmetry lower than cubic. The theory could not be expected to apply, for example, to the spectra of transition metal ions in solution. 

Tables of compatibility relations for the simple cubic structure have been given by Jones (1962, 1975), and similar tables can be compiled for other structures, as shown by the examples in Tables 17.2 and 17.5. Compatibility relations are extremely useful in assigning the symmetry of electronic states in band structures. Their use in correlation diagrams in crystal-field theory was emphasized in Chapters 7 and 8, although there it is not so common to use B SW notation, which was invented to help describe the symmetry of electronic states in energy bands in crystals (Bouckaert el al. (1936)).

In this section we shall develop the electrostatic crystal-field theory to a sufficient extent to give an account of its stereochemical implications particularly with reference to the distortions from cubic symmetry which are characteristic of certain groups of transition-metal compounds. The treatment is not meant to be complete and the reader is referred to the many reviews (SI, 72, 97, 102, 106) for detailed references, derivations, qualifications, disputations, and applications. 

Continuing studies have shown that Co decay in MgO can produce Fe+, Fe " ", and Fe " daughter charge states in proportions dependent on the particular sample preparation and the temperature of the Mossbauer measurement [49]. Dilute concentrations of Fe ( 0-03 at. %) in MgO show a small quadrupole splitting at low temperature [50, 51]. This can be interpreted in terms of crystal-field theory assuming the presence of random strains in the crystal although the Fe site symmetry may be perfectly cubic... 

The theory of CF originates from the early work of Bethe (1929). A number of complete review articles have appeared which describe theoretical models and experimental effects of CF in rare earths (Fulde 1979). For crystal fields of cubic symmetry the spin Hamiltonian with reference to the fourfold axis can be expressed conveniently in the operator-equivalent form (Hutchings 1964, Stevens 1967)... 

The structures of spinels, A B2 4, are determined not only by the radius of the ions involved but also by the crystal field stabilization energies of the cations that occupy octahedral or tetrahedral holes in the cubic close-packed lattice of oxide ions. These structures offer an opportunity to combine a knowledge of crystal field theory obtained in earlier chapters with the knowledge of solid-state structures covered in this chapter. 

Each Cn-NH3 coordinate covalent bond is a a bond formed when a lone pair in an sp8 orbital on N is directed toward an empty s/PS orbital on Cr8+. The number of unpaired electrons predicted by valence bond theory would be the same as the number of unpaired electrons predicted by crystal field theory. 62. The coordination compound is face-centered cubic, K+ occupies tetrahedral holes, while PtC occupies octahedral holes. 63. In order from 0 NH3 ligands to 6 NHj ligands KjfPtCl j, K[Pta5(NH3)],PtCl (NH3)2, [PtOjOSIHYjjCl, [Pta2(NH3)ja2, [Pta(NH3)5ici3, [Pt(NH3),]cy... 

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. 

Of major importance in either theory is the crystal field (or ligand field) parameter Dq, where lODq is the energy separation between the 6g and t2g d orbitals in a cubic environment (2, 12, 23). The term cubic environment covers 4-coordinate tetrahedral, 6-coordinate octahedral, and 8-coordinate cubic complexes. The g subscripts are not necessary for a tetrahedral environment which lacks a center of symmetry. Henceforth, for simplicity, these subscripts will be dropped. 

---