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The band structure of materials in which both localized and itinerant outer electrons are simultaneously present is discussed. The Franck-Condon Principle is applied, and small and large polar on formation is taken into account. A scheme for estimating the densities-of-states of perfect crystals and doped or non-stoichiometric crystals is suggested, based on the ionic many-body states as a starting point. Screening, covalency, crystalline-field and overlap effects are quantitatively considered. In particular, the band structures of both pure and Li-doped NiO are derived and found to be in agreement with the experimental observations. It is shown that conclusions which are based on ordinary donor and acceptor techniques fail to account for the effects of doping even in a qualitatively correct manner, due to the neglect of important correlation effects.
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