Excess electron states in reduced bulk anatase TiO₂: Comparison of standard GGA, GGA+U, and hybrid DFT calculations

The removal of lattice O atoms, as well as the addition of interstitial H atoms, in TiO₂ is known to cause the reduction in the material and the formation of " Ti3+ " ions. By means of electronic structure calculations we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of TiO₂. The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defect-induced states in the gap, and the polaronic distortion around the defect have been investigated with different theoretical methods: standard density functional theory (DFT) in the generalized-gradient approximation (GGA), GGA+U methods as a function of the U parameter, and two hybrid functionals with different admixtures of Hartree-Fock exchange. The results are found to be strongly dependent on the method used. Only GGA+U or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are experimentally observed in reduced titania. The corresponding electronic states are localized on Ti 3d levels, but partly delocalized solutions are very close in energy. These findings show the limited predictive power of these theoretical methods to describe the electronic structure of reduced titania in the absence of accurate experimental data.