A Method for Obtaining Parametrized Bands of Rutile VO2

With the metallic phase of VO2 in view, a method of obtaining parametrized bands, originally due to Slater and Koster, is developed for rutile structures in general. Thirty-four unsymmetrized Bloch states arising from localized 3d, 4s, 4p vanadium orbitals and 2s, 2p oxygen orbitals are projected into symmetric states—by the standard projection operator technique—at various points of symmetry of the BZ. The secular determinant with respect to these symmetric states is then reduced, the degree of reduction depending on the point of symmetry. Typical results are quoted. The paper concludes with some preliminary remarks concerning the connection of the present work with the phenomenological approach of Goodenough based on crystal field theory. In particular the π-like hybrid levels which feature prominently in this latter work are tentatively identified.