A comparative study of the atomic and electronic structure of F centers in ferroelectric KNbO₃: Ab initio and semi-empirical calculations

The linear muffin-tin-orbital method combined with density functional theory (in a local density approximation) and the semi-empirical method of the intermediate neglect of the differential overlap (INDO) based on the Hartree-Fock formalism are used for the supercell study of the F centers (O vacancy with two electrons) in cubic and orthorhombic ferroelectric KNbO₃ crystals. The two electrons are found to be considerably delocalized even in the ground state of the defect. Their wave functions extend over the two Nb atoms closest to the O vacancy and over other nearby atoms. Thus, the F center in KNbO₃ resembles much more electron defects in the partly covalent SiO₂ crystal (the so-called E₁′ center) rather than usual F centers in ionic crystals like MgO and alkali halides. This covalency is confirmed by the analysis of the electronic density distribution. The absorption energies were calculated by means of the INDO method using the △SCF scheme after a relaxation of atoms surrounding the F center. For the orthorhombic phase three absoprtion bands are predicted, the first one is close to that observed experimentally under electron irradiaton.