A DFT study of the stoichiometric and reduced anatase (0Â 0Â 1) surfaces

Here we report a systematic study on the structural and energetic properties of the stoichiometric and reduced anatase (0 0 1) surfaces by using periodic density functional calculations. Structural and energetic properties for different surface models are investigated, as well as their stability as a function of the slab thickness. The calculations indicated that a 3 × 3 × 6 model is adequate to describe the pure and reduced anatase TiO2 (0 0 1) surfaces. Our calculations on the reduced system have demonstrated that the outermost oxygen vacancy, in the first atomic layer, is the most stable defect. A comparison between (0 0 1) and (1 0 1) surfaces reveals that defect creation is easier on the former. Thus, a higher vacancy concentration on that surface is expected. On the other hand, calculations at higher vacancy concentrations show repulsive interactions among defects what might inhibit further vacancy creation. The electronic structure has been examined by means of DFT+U methodology. The Hubbard U parameter influences considerably the location of defect states in the Ti 3d band and is essential to correctly describe the electronic structure. We conclude that the value U = 4.0 eV is a correct choice, which produces mid states in the band gap, a charge density localization and increases geometry deformation because of repulsive interactions, but effects on energetics are limited.