Ab initio calculations of the transfer and aggregation of F centers in CaF ₂

The F center and R center in CaF ₂ crystals have been studied by using density functional theory (DFT) with a hybrid B3PW description of exchange and correlation. Our calculations show that the F-center diffusion barrier is equal to 1.67 eV. During the F-center transfer, the trapped electron is more delocalized than that in the regular F-center case, and the gap between defect level and CB in the α-spin state decreases. The surface F-center investigation shows the trend of F centers to locate near the surface. The association energy calculations of R centers indicate stable aggregations of isolated F centers. During the F-center aggregation, a considerable covalency forms between two neighboring fluorine vacancies with trapped electrons. 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 the 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.