Contradictory theoretical results for oxygen vacancies in SrTiO 3 (STO) were often related to the peculiar properties of STO, which is a d 0 transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, density functional theory (DFT) within the extended Hubbard DFT + U + V approach, including onsite as well as intersite electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via density-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT + U + V provides a better description of stoichiometric STO compared to standard DFT or DFT + U , the band gap and crystal field splitting being in good agreement with experiments. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with experiments as well as results obtained with the most frequently used hybrid functionals, however, at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.

The bulk structure, the relative stability, and the electronic properties of monoclinic, tetragonal, and cubic ZrO(2) have been studied from a theoretical point of view, through periodic ab initio calculations using different Gaussian basis sets together with Hartree-Fock (HF), pure Density Functional Theory (DFT), and mixed HF/DFT schemes as found in hybrid functionals. The role of a posteriori empirical correction for dispersion, according to the Grimme D2 scheme, has also been investigated. The obtained results show that, among the tested functionals, PBE0 not only provides the best structural description of the three polymorphs, but it also represents the best compromise to accurately describe both the geometric and electronic features of the oxide. The relative stability of the three phases can also be qualitatively reproduced, as long as thermal contributions to the energy are taken into account. Four low-index ZrO(2) surfaces [monoclinic (-111), tetragonal (101 and 111), and cubic (111)] have then been studied at this latter level of theory. Surface energies, atomic relaxations, and electronic properties of these surfaces have been computed. The most stable surface is the cubic one, which is associated to small relaxations confined to the outermost layers. It is followed by the monoclinic (-111) and the tetragonal (101), which have very similar surface energies and atomic displacements. The tetragonal (111) was instead found to be, by far, the less stable with large displacements not only for the outermost but also for deeper layers. Through the comparison of different methods and basis sets, this study allowed us to find a reliable and accurate computational protocol for the investigation of zirconia, both in its bulk and surfaces forms, in view of more complex technological applications, such as ZrO(2) doped with aliovalent oxides as found in solid oxide fuel cells.