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Abstract
Qualitative aspects of semiempirical energy band calculations are surveyed with the purpose of highlighting the key features of the electronic structures of some insulators, semiconductors and metallic systems. The nodal structure of the electronic orbitals is stressed as the common underlying theme in such effects as: the Peierls distortions of metallic systems; the changing electron counts (due to charge transfer or different d-electron counts); the high-pressure transformations of solids. The range of applicability of semiempirical non-self-consistent band theories is assessed. The discussion is illustrated by several examples.