Periodic unrestricted Hartree-Fock study of corundumlike ${\mathrm{Ti}}_2$${\mathrm{O}}_3$ and ${\mathrm{V}}_2$${\mathrm{O}}_3$

The ground-state electronic and magnetic properties of rhombohedral ${\mathrm{Ti}}_2$${\mathrm{O}}_3$ and ${\mathrm{V}}_2$${\mathrm{O}}_3$ have been investigated by ab initio all-electron periodic Hartree-Fock calculations. Both unrestricted open-shell and restricted closed-shell methods have been employed, with basis sets of atomic orbitals represented by contracted Gaussian-type functions. The ${\mathrm{t}}_{2\mathrm{g}}$ degeneracy of d electrons is removed by the rhombohedral field, giving rise to orbital ordering between ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\pi }}$ levels. The self-consistent-field variational solutions are spin-polarized insulating states with single (${\mathrm{a}}_{1\mathrm{g}}$) and double (${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\pi }}$) electron occupations for ${\mathrm{Ti}}_2$${\mathrm{O}}_3$ and ${\mathrm{V}}_2$${\mathrm{O}}_3$, respectively. Conducting or semiconducting states, with different relative energies of ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\pi }}$ bands, have also been obtained by changing the c/a ratio of the hexagonal unit cell. The charge transfer into ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\sigma }}$ levels is discussed and compared to the ${\mathrm{Cr}}_2$${\mathrm{O}}_3$ and ${\mathrm{Fe}}_2$${\mathrm{O}}_3$ behavior.