  Phonon density of states calculation shows that a new TiO2 polymorph with
tridymite structure is mechanically stable. Enthalpies of 9 TiO2 polymorphs
under different pressure are presented to study the relative stability of the
TiO2 polymorphs. 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, columbite
and baddeleyite TiO2, indicating a quasi-direct band gap character. The band
gap energies of baddeleyite (quasi-direct) and brookite (direct) TiO2 are close
to that of anatase (indirect) TiO2. The band gap of the newly predicted
tridymite-structured TiO2 is wider than the other 8 polymorphs. For optical
response calculations, two-particle effects have been included by solving the
Bethe-Salpeter equation for Coulomb correlated electron-hole pairs. TiO2 with
cotunnite, pyrite, and fluorite structures have optical transitions in the
visible light region.
