The status of first-principles local density models for the electronic structure of f-element coordination compounds is reviewed. Results obtained by the multiple-scattering scheme and the discrete variational method are discussed, in both relativistic and non-relativistic approaches. We describe the development of self-consistent embedding techniques for molecular cluster representations of crystalline solids. For the 4f-elements, we consider in some detail the simple rock-salt structures, with formula RX and the rare-earth substituted orthovanadates R:YVO(4) and RVO(4). Bonding structure is analyzed, and an interpretation of photoelectron and optical spectra is given.
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