First-principles calculations of surface H centers in BaF₂

H center, a hole trapped at an interstitial anion site, placed on the (111) surface of Barium fluoride BaF₂ has been studied by using density functional theory (DFT) with hybrid exchange potentials, namely, DFT-B3PW. Two different configurations of surface H center are investigated carefully. Both surface H -center systems have strong relaxations because of the surface effect. In the configuration that the interstitial fluorine atom is within the surface, named case 1 in this paper, the unpaired electron is almost equally distributed onto the two atoms of the H center, which is quite different from the bulk H -center case. The other configuration with one of the F atoms of the H center located above the BaF₂ (111) surface (case 0) has a more polarized charge distribution as compared to that obtained in the bulk case and case 1. The calculation on total energies of different surface H -center configurations implies that H centers have a trend to locate near the surface. The creation of a surface H center in BaF₂ results in a new β -hole band located at the Γ point 3.99 and 2.70 eV, for the cases 0 and 1, respectively, above the top of valence bands. According to our calculations on density of states, the constituents of the defect bands are cleared and the β -hole band is primarily composed of pz orbitals localized on the H center.