First-principles studies on phase stability of TiO2 by using GGA+U calculations

First-principles calculations on phase stability of three polymorphs of titanium dioxide (TiO2) in rutile, anatase and brookite phases are performed using density functional theory (DFT) and density functional theory plus Hubbard U (DFT+U) methods within generalized gradient approximation (GGA) for Perdew-Burke-Ernzerhof for solids (GGA-PBEsol) functional. The calculated cohesive energy with respect to the volume per formula unit of TiO2 is analyzed to evaluate the phase stability sequence for the TiO2 phases between rutile, anatase, and brookite. The results for the phase stability show good agreement with other theoretical reports. However, the difficult situation occurs for DFT in predicting correctly the phase stability of the rutile, anatase and brookite phases. Thus, the GGA-PBEsol+U for Ti 3d of TiO2 with U = 2, 4, 6 and 8eV are used to determine the effect of U on the phase stability. The DFT+U approach shows good agreement with the existing experimental data for the order of stability of TiO2 which give a good description of the phase stability of TiO2.