Ab initio calculations of the hydrogen centres in CaF₂ and BaF₂

As an extension of our previous studies dealing with bulk and surface F centres in CaF₂ and BaF₂, we have calculated the hydrogen impurity in CaF₂ and BaF₂ crystals. Our calculated absorption energy for the hydrogen impurity in CaF₂ (8.17 eV) is close to the experimental result (7.65 eV). The band and electronic structures are calculated and compared to the F centre case. We found that insertion of the hydrogen impurity in the bulk does not cause significant relaxation of the neighbouring atoms, but the relaxation of the atoms around the hydrogen impurity at surfaces is not negligible any more. We also observe a strengthening of the surface hydrogen centre and metal chemical bond with respect to the bulk.