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Herrn Prof. Dr. H. Hartmann aus Anlaß der 60. Wiederkehr seines Geburtstages in Verehrung gewidmet. Band, Structure Calculations on Nonstoichiometric Vanadium Carbides VCxUsing the augmented-plane-wave (APW ) method the electronic structure of stoichiometric vana dium carbide has been computed previously *. Since only nonstoichiometric cubic phases of vana dium carbide are stable and all experiments are made with such samples, the energy bands have been determined for some nonstoichiometric VCj; phases {x = 0.87; 0.833; 0.79; 0.75) using the APW virtual crystal (VCA) approximation similar to Schoen's work on TiO 7, 10. Our approach differs from his in two aspects: First, the potential is constructed from the self consistent potential of Ref. 1 instead of using atomic data. Thus, the important self consistent procedure is taken into account at least in an approximated form. Second, a more realistic scheme for occupying the states is suggested. Furthermore, an attempt is made to normalize the wave functions in order to obtain the charge distribution in the crystal.The density of states and the partial densities of states corresponding to the quantum numbers n and I have been computed using an LCAO interpolation scheme. The different VC^ phases show a fairly "rigid band structure" . The Fermi energy and the density of states at the Fermi level increase with decreasing carbon content. The calculated APW-as well as the LCAO-charge distribu tion indicate -in accordance with ESCA measurements 32 -that the charge-transfer from vanadium to carbon and the ionicity of VC^ decrease with increasing vacancy concentration. The results of X-ray-emission and heat capacity measurements are discussed in terms of the APW-VCA results.Especially for the X-ray-emission data the agreement between theory and experiment is fair.Einleitung