The atomic, electronic structure and phonon frequencies have been calculated in cubic and low-temperature tetragonal SrTiO3 phases at the ab initio level. We demonstrate that the use of the hybrid exchange-correlation PBE0 functional gives the best agreement with experimental data. The results for the standard generalized gradient approximation (PBE) and hybrid PBE0 functionals are compared for the two types of approaches: a linear combination of atomic orbitals (CRYSTAL09 computer code) and plane waves (VASP5.2 code). The relation between cubic and tetragonal phases and the relevant antiferrodistortive phase transition is discussed in terms of group theory and is illustrated with analysis of calculated soft-mode frequencies at the $\Gamma${} and R points in the Brillouin zone. Based on phonon calculations, the temperature dependence of the heat capacity is in good agreement with experiment.

The DFT+U calculations were employed in a detailed study of the strong electron correlation effects in a promising nuclear fuel—uranium mononitride (UN). A simple method for solving the multiple minima problem in DFT+U simulations and insure obtaining the correct ground state is suggested and applied. The crucial role of spin–orbit interactions in reproduction of the U atom total magnetic moment is demonstrated. Basic material properties (the lattice constants, the spin- and total magnetic moments on U atoms, the magnetic ordering, and the density of states) were calculated varying the Hubbard U-parameter. By varying the tetragonal unit cell distortion, the meta-stable states have been carefully identified and analyzed. The difference in the magnetic and structural properties obtained for the meta-stable and ground states is discussed. The optimal effective Hubbard parameter U_eff = 1.85 eV reproduces correctly the UN anti-ferromagnetic ordering, and only slightly overestimates the experimental total magnetic moment of the U atom and the unit cell volume.

We compare two approaches to the atomic, electronic, and magnetic structures of $\mathrm{La}\mathrm{Mn}{\mathrm{O}}_3$ bulk and the (001), (110) surfaces—hybrid B3PW with optimized LCAO basis set (CRYSTAL-2003 code) and GGA-PW91 with plane-wave basis set (VASP 4.6 code). Combining our calculations with those available in the literature, we demonstrate that combination of nonlocal exchange and correlation used in hybrid functionals allows to reproduce the experimental magnetic coupling constants $J_{ab}$ and $J_c$ as well as the optical gap. Surface calculations performed by both methods using slab models show that the antiferromagnetic (AF) and ferromagnetic (FM) (001) surfaces have lower surface energies than the FM (110) surface. Both the (001) and (110) surfaces reveal considerable atomic relaxations, up to the fourth plane from the surface, which reduce the surface energy by about a factor of 2, being typically one order of magnitude larger than the energy difference between different magnetic structures. The calculated (Mulliken and Bader) effective atomic charges and the electron density maps indicate a considerable reduction of the Mn and O atom ionicity on the surface.

We present and discuss results of the density functional theory (DFT) for perfect UO₂ crystals with He atoms in octahedral interstitial positions therein. We have calculated basic bulk crystal properties and He incorporation energies into the low temperature anti-ferromagnetic UO₂ phase using several exchange–correlation functionals within the spin-polarized local density (LDA) and generalized gradient (GGA) approximations. In all DFT calculations we included the on-site correlation corrections using the Hubbard model (DFT+U approach). We analysed a potential crystalline symmetry reduction from tetragonal down to orthorhombic structure and confirmed the presence of the Jahn–Teller effect in a perfect UO₂. We discuss also the problem of a conducting electronic state arising when He is placed into a tetragonal antiferromagnetic phase of UO₂ commonly used in defect modelling. Consequently, we found a specific monoclinic lattice distortion which allowed us to restore the semiconducting state and properly estimate He incorporation energies. Unlike the bulk properties, the He incorporation energy strongly depends on several factors, including the supercell size, the use of spin polarization, the exchange–correlation functionals and on-site correlation corrections. We compare our results for the He incorporation with the previous shell model and ab initio DFT calculations.

We have performed a detailed analysis of the magnetic (collinear and non-collinear) order and the atomic and electron structures of UO₂, PuO₂ and UN on the basis of density functional theory with the Hubbard electron correlation correction (DFT + U). We have shown that the 3-k magnetic structure of UO₂ is the lowest in energy for the Hubbard parameter value of U = 4.6 eV (and J = 0.5 eV) consistent with experiments when Dudarev's formalism is used. In contrast to UO₂, UN and PuO₂ show no trend for a distortion towards rhombohedral structure and, thus, no complex 3-k magnetic structure is to be anticipated in these materials.