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The linear muffin-tin-orbital method combined with density functional theory(local approximation) and the semiempirical method of the intermediate neglectof the differential overlap (INDO) based on the Hartree-Fock formalism are usedfor the study of the $F$ centers (O vacancy with two electrons) in cubic andorthorhombic ferroelectric KNbO$_3$ crystals. Calculations for 39-atomsupercells show that the two electrons are considerably delocalized even in theground state of the defect. Their wave functions extend over the two Nb atomsclosest to the O vacancy and over other nearby atoms. Thus, the $F$ center inKNbO$_3$ resembles electron defects in the partially-covalent SiO$_2$ crystal(the so-called $E^{\prime}_1$ center) rather than usual $F$ centers in ioniccrystals like MgO and alkali halides. This covalency is confirmed by theanalysis of the electronic density distribution. Absorption energies werecalculated by means of the INDO method using the $\Delta$ self-consistent-fieldscheme after a relaxation of atoms surrounding the $F$ center. For theorthorhombic 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 electronirradiation. 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.Comment: 7 pages, including 4 postscript figures; with minor changes, as will  appear in Phys. Rev.

physical review. b, condensed matter

First-principles and semiempirical calculations for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math>centers in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>KNbO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

First-principles and semiempirical calculations forFcenters inKNbO3