Band structure and cluster methods for calculations of ideal and defective solids

Two approaches are currently applied in the study of the electronic structure and properties of solids: the so-called cluster and band structure approaches. The former considers as the model a small part of the crystal – a cluster whose electronic structure is studied by one of the methods used to compute the electronic structure of molecules or complexes. Both semiempirical and nonempirical methods of quantum chemistry can be used for the calculations. The principal advantages of this approach are its relative simplicity and the possibility of studying the influences of various kinds of disturbances in the crystal translation symmetry – the presence of impurities, vacancies, phase boundaries, interfaces, etc. – on the electronic structure. The cluster approach has been used in a large number of researches on the electronic structure of refractory compounds – see Gubanov, Kurmaev and Ivanovsky (1984), Ivanovsky, Gubanov, Shveikin and Kurmaev (1983). Calculations show that within the range of its applicability the cluster approach makes it possible to reproduce some properties of refractory compounds with a reasonably high accuracy. These properties are naturally those that are determined by chemical interactions between the nearest-neighbour atoms rather than by the presence of a long-range order. Among such characteristics are, for example, X-ray emission spectra and electronic field gradients at the atomic nuclei of transition elements, see Ivanovsky, Dmitriev and Gubanov (1981).