The stability, electronic structure, and optical property of tio ₂ polymorphs

Enthalpies of nine TiO₂ polymorphs under different pressures are presented to study the relative stability of the TiO₂ polymorphs. It is important to include the dispersion correction for van der Waals interaction and the Hubbard U term for the Ti 3d orbital in the DFT-GGA calculation to correctly reproduce the relative stability of rutile, brookite, and anatase. Band structures for the TiO₂ polymorphs are calculated by density functional theory with generalized gradient approximation, and the band energies at high symmetry k-points are corrected using the GW method to accurately determine the band gap. The differences between direct band gap energies and indirect band gap energies are very small for rutile and columbite-structured TiO₂, indicating a quasi-direct band gap character. For optical response calculations, two-particle effects have been included by solving the Bethe-Salpeter equation for Coulomb correlated electron-hole pairs. TiO ₂ with baddeleyite, pyrite, and fluorite structures has optical transitions in the violet light region.