Modified Monkhorst-Pack (MMP) special points meshes for Brillouin zone integration are proposed for cubic crystals. The MMP meshes suggested ensure the higher precision of $\mathbf{k}$-points summation and faster and regular convergence of the results of the self-consistent calculations of the electronic structure of crystals. The efficiency of MMP meshes is demonstrated by DFT-GGA (density functional theory - generalized gradient corrections) calculations of $\mathrm{SiC}$ crystal.

The atomic and electronic structure, formation energy, and the energy barriers for migration have been calculated for the neutral O vacancy point defect ($F$ center) in cubic $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ employing various implementations of density functional theory (DFT). Both bulk and $\mathrm{Ti}{\mathrm{O}}_2$-terminated (001) surface $F$ centers have been considered. Supercells of different shapes containing up to 320 atoms have been employed. The limit of an isolated single oxygen vacancy in the bulk corresponds to a 270-atom supercell, in contrast to commonly used supercells containing $\sim 40–80$ atoms. Calculations carried out with the hybrid B3PW functional show that the $F$ center level approaches the conduction band bottom to within $\sim 0.5\mathrm{eV}$, as the supercell size increases up to 320 atoms. The analysis of the electronic density maps indicates, however, that this remains a small-radius center with the two electrons left by the missing O ion being redistributed mainly between the vacancy and the $3d\left(z^2\right)$ atomic orbitals of the two nearest Ti ions. As for the dynamical properties, the calculated migration energy barrier in the low oxygen depletion regime is predicted to be $0.4\mathrm{eV}$. In contrast, the surface $F$ center exhibits a more delocalized character, which leads to significantly reduced ionization and migration energies. Results obtained are compared with available experimental data.

The structural and electronic properties of the neutral and positively charged oxygen vacancies (F and F+ centres) in the bulk and on the (001) surfaces of SrTiO3crystal are examined within the...