Various phases of TiO2 are studied using the ab initio plane wave appr
oach with soft pseudopotentials. Under pressure when the unit cell red
uces in volume rutile is found to change into a columbite (alpha-PbO2)
phase and in turn into a baddeleyite structure with an associated sli
ght increase in the bulk modulus. The bulk modulus of the baddeleyite
phase depends upon the locations of the oxygen atoms in the unit cell.
Although not nearly as hard as diamond, we suggest such a material co
uld have hardness approaching that of boron nitride. The property of a
fluorite phase that is often considered to derive from the baddeleyit
e phase and as yet not identified is also investigated.