Ab initio calculations of the oxygen-vacancy dipoles and M centers in CaF₂

We performed ab initio calculations of complex defects in CaF₂ namely oxygen-vacancy (OV) dipoles and F₂ centers (M centers) by means of the hybrid B3PW method, in which Hartree-Fock exchange is mixed with density functional theory (DFT) exchange functionals, using Becke's three parameter method, combined with the non-local correlation functionals by Perdew and Wang. Our calculated optical absorption bands for the OV center (6.40 eV, 6.52 eV and 6.66 eV) are in good agreement with the complex experimental 6.7 eV absorption bands consisting of at least two elementary peaks with separation of 0.48 eV. The defect levels induced by the oxygen impurity between the conduction and valence bands consist mainly of oxygen p orbitals and are split into three bands. Vacancy s orbitals form the vacancy band near the fermi-energy. Several configurations of the (OV)₂-dimer were calculated. The association energy for the most favorable one is 0.55 eV. The results for the M center, the simplest aggregation of two F centers, show that the β band absorption in CaF₂ is predominantly due to the presence of M centers. The direct optical gap for M centers in CaF₂ is 2.22 eV and is in good agreement with the corresponding experimental value of 2.38 eV.