A first-principles energy-band study of the metallic rutile phase of V${\mathrm{O}}_2$ using a general crystal potential and an expansion of the Bloch functions in a linear combination of atomic orbitals is reported. The results are compared with previous work and experimental optical, x-ray absorption and emission, and x-ray photoelectron spectroscopy data. We obtain a large density of states at the Fermi energy; the Fermi surface is found to be determined by the two lowest $d$ bands, at the bottom of the "$t_{2g}$" manifold which is split by the orthorhombic field; the lowest-band Fermi surface possesses some nesting features corresponding to a nesting vector $\overrightarrow{\mathrm{q}}=\Gamma R$. A calculation of the generalized susceptibility in the constant-matrix-element approximation shows the existence of a maximum at the zone boundary $R$. We suggest that the formation of a charge-density wave with wave vector $\overrightarrow{\mathrm{q}}=\Gamma R$ accompanied by a periodic lattice distortion is thus possible; the subsequent condensation of phonons at the point $R$ could then explain the crystallographic phase transition observed at $T=339\mathrm{}$ K.

• Received 6 June 1977

DOI:https://doi.org/10.1103/PhysRevB.16.3338