Abstract
The structure of stable phases is investigated using first-principle calculations based on the functionals: LDA, GGA and newly developed general-purpose heavily constrained and appropriately normalized meta GGAfunctional (SCAN). The purpose of this study is to theoretically study the atomic displacements and band gap of the cubic, tetragonal, orthorhombic, rhombohedral perovskite phases for the comparison LDA, GGA-PBE and meta-GGA functionals using the density functional theory method. The obtained data of the density of states (DOS) showed that the values of the band gap energies are underestimated, and the DOS values show that the upper part (valence band) mainly consists of O 2p orbitals, the lower part (conduction band) consists of Ti 3d orbitals. The rhombohedral phase has a mixed composition of Ti states in the conduction band with a greater degree of 3dz2 than 3dxy. The values of the energies of the band gap (Egap) and the density of states show reasonable agreement with experimental and theoretical data. The LDA functional and, to a lesser extent, the GGA - PBE functional can also provide fairly accurate information about atomic displacements in these crystals. The values calculated by the SCAN functional do not differ much from the GGA and LDA functionals.