First-principles simulations on the aggregation of F centers in BaF ₂: R centers

F center (an electron trapped in the fluorine vacancy) and R center (a defect composed of three F centers) in BaF₂crystal, have been studied by using density functional theory (DFT) with hybrid exchange potentials, namely DFT-B3PW. Our calculations show that the F-center transfer barrier is equal to 1.83 eV. During the F-center transfer, the trapped electron is more delocalized than that in the static F-center case, and the gap between defect leveland CB in the α-spin state decreases obviously. The association energy calculations on R centers indicate stable aggregations of isolated F centers. During F-center aggregation, a considerable covalency between two neighbor fluorine vacancies with trapped electrons forms. Three incompletely paired electrons trapped in the R center have an up-down-up spin arrangement and induce three defect levels in the gaps between valence bands (VB) and conduction bands (CB) for both of α- and β-spin polarized band structures respectively. More defect bands lead to more complex electron transitions, which were classified into two F- and four M-like transitions. The DOS calculations clearly reveal the components of defect bands.