Chemical Bonding in Cyclic-cluster Model Local Properties of Composite Crystalline Oxides

2 Chemical Bonding in Cyclic-cluster Model Local Properties of Composite Crystalline Oxides 

Unlike light-metal oxides, the investigation of the electronic structure of crystalline heavy-metal oxides is a difficult task because of their composite crystal structure. Thus, it is necessary to use approximations both for the crystal-structure description and for the choice of one-electron Hamiltonian. 

It is necessary to investigate the electronic structure of defect-containing metal oxides to understand their physical and chemical properties. However, the first step of such an investigation is connected with the calculation of the electronic structure of perfect nondefective crystal. The analysis of ionic and covalent components of the chemical bonding in perfect crystal allows one to propose realistic models describing the defects in these compounds. 

The calculations of local properties of metal-oxide electronic structure [571,581-583] were made in the cychc-cluster model, in the CNDO approximation. As in the CNDO approximation AOs are supposed to be orthogonalized by the Lowdin procedure (see Chap. 6), the definitions of local properties given in Sect. 9.1.1 for nonorthog-onal basis, have to be modified. In particular, the overlap population (9.9) becomes zero in the CNDO approximation, so that the electronic population is defined only by diagonal density matrix elements In (9.6) and in the bond-order definition 

For comparison the crystallographic valencies in copper-oxide compounds, calculated for the experimental bond lengths, are given in brackets. 

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