First-principles and semiempirical calculations for centers

The linear muffin-tin orbital method combined with density functional theory (local approximation) and the semiempirical method of the intermediate neglect of the differential overlap (INDO) based on the Hartree-Fock formalism are used for the study of the (Formula presented) centers (O vacancy with two electrons) in cubic and orthorhombic ferroelectric KNbO(Formula presented) crystals. Calculations for 39-atom supercells show that the two electrons are 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 (Formula presented) center in KNbO(Formula presented) resembles electron defects in the partially-covalent SiO(Formula presented) crystal (the so-called (Formula presented) center) rather than usual (Formula presented) centers in ionic crystals like MgO and alkali halides. This covalency is confirmed by the analysis of the electronic density distribution. Absorption energies were calculated by means of the INDO method using the Δ self-consistent-field scheme after a relaxation of atoms surrounding the (Formula presented) center. For the orthorhombic phase three absorption bands are calculated to lie at 2.72 eV, 3.04 eV, and 3.11 eV. The first one is close to that observed under electron irradiation. For the cubic phase, stable at high temperatures, above 708 K, only the two bands, at 2.73 eV and 2.97 eV, are expected.