Electronic structures in ${\mathrm{VO}}_2$susing the periodic polarizable point-ion shell model and DV-Xα method

Electronic structures in the metallic ${\mathrm{VO}}_2$ phase above the metal-insulator (MI) transition temperature of ${\mathrm{T}}_{\mathrm{c}}$ and the insulating phase below ${\mathrm{T}}_{\mathrm{c}}$ have been investigated using the combination of the three-dimensional periodic shell model and the discrete-variational (DV)-Xα cluster method. Besides the correlation effect for ${\mathrm{d}}_{\mathrm{\parallel }}$ electrons, the Hamiltonian in the insulating phase includes the Anderson's attractive potential due to the electron-phonon interactions which stabilize the three-dimensional periodic distribution of ${\mathrm{V}}^{4+}$ -${\mathrm{V}}^{4+}$ dimers. The shell model estimates the electron-phonon coupling constant and provides direct theoretical evidence that the dimers are stable in the low-temperature phase. The DV-Xα cluster method calculates the electron energies in [${\mathrm{V}}_2$ ${\mathrm{O}}_{10}$ ${]}^{\mathrm{-}12}$ clusters and the value for the intersite repulsive nearest-neighbor d-d Coulombic interaction which quantifies the correlation effect for ${\mathrm{d}}_{\mathrm{\parallel }}$ electrons. The electron-phonon interaction effect and the correlation effect for ${\mathrm{d}}_{\mathrm{\parallel }}$ electrons are found to split d band into the empty upper and the occupied lower Hubbard bands and also to result in an obvious energy gap between these bands in the insulating phase. In the metallic phase, the nonresolved d band overlaps the π band and they construct a partially filled conduction band. These calculations explain well the MI transition in ${\mathrm{VO}}_2$ and, in particular, the electron-phonon interaction assessed by the periodic shell model is an indispensable contribution in the stabilization of the insulating phase.