Symmetry analysis for localized function generation and chemical bonding in crystals:: SrZrO3 and MgO as examples -: art. no. 075138

Different criteria of localization of one-electron states in crystals are discussed and relations between them are established. A new localization criterion determined only by the localized orbital (LO) itself is formulated. The importance of the symmetry analysis in the procedure of the generation of maximally LOs in crystals is shown. It is suggested that the numerical parameters of the LOs corresponding to the valence energy bands of the crystal can be used in the theory of chemical bonding only if these functions form bases of irreducible representations of site symmetry groups of atoms and bonds in crystals. General considerations are illustrated on the examples of LOs corresponding to the valence energy bands in SrZrO3 and MgO crystals. There is in SrZrO3 a LO describing a partly covalent bond between oxygen and zirconium atoms with the degree of covalency K=0.46. When applied to the MgO crystal the suggested approach confirms a purely ionic nature of chemical bonding in this crystal.