Structure and energetics of stoichiometric TiO₂ anatase surfaces

We present an ab initio density-functional investigation of the structure and energetics of several stoichiometric 1 × 1 low-index surfaces of anatase, a TiO₂ polymorph ∼9% less dense and ∼1.2 kcal/mol less stable than rutile. Although our calculations do not reproduce the relative ordering of the two phases that is observed experimentally, the calculated bulk structural and elastic properties of both polymorphs are in excellent agreement with the experiment, suggesting that surface relaxations are correctly described as well. As expected, the surface energies of anatase appear to be related to the presence of undercoordinated Ti atoms: the surfaces with fourfold-coordinated Ti atoms have a larger energy than those with fivefold-coordinated Ti. Furthermore, we find that the average surface energy of a TiO₂ anatase macroscopic crystal is smaller than that of rutile. Finally, patterns in the relaxation of the surface atoms which are common to different surfaces are analyzed.