Ab initio calculations for the F-center transfer and R centers in SrF 2 H. Shi a,⇑ , L. Chang a , R. Jia b , R.I. Eglitis c a School of Science, Beijing Institute of Technology, 100081 Beijing, PR China b Department of Mathematics and Natural Sciences, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany c Institute of Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV1063, Latvia article info Article history: Received 17 October 2012 Received in revised form 27 June 2013 Accepted 1 July 2013 Keywords: DFT Electronic structure F center R center Band structure abstract We have simulated the F-center transfer and R center in SrF 2 crystal by using density functional theory (DFT) with a hybrid B3PW description of exchange and correlation. Our calculations show that the F-cen- ter diffusion barrier is equal to 1.84 eV. During the F-center transfer, the trapped electron is more delo- calized than that in the regular F-center case, and the gap between defect level and conduction bands (CB) in the a-spin state decreases. The formation energy calculations of R center show the trend of F centers to aggregate in SrF 2 . During the F-center aggregation, a considerable covalency forms between two neigh- boring 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 for both of a- and b-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. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Alkaline-earth fluorides attract considerable attentions due to their wide band gaps, which are larger than 10 eV, making the Alkaline-earth fluorides have a widely use in ultraviolet (UV) re- gion than quartz. As for SrF 2 crystal the experimentally band gap comes to 11.25 eV [1]. Therefore the SrF 2 crystal has more potential in optical applications and it has attracted considerable attentions both in experimental and theoretical studies [2–23]. It is well known that during the generation of the crystals, the defects and impurities may emerged and they strongly affected the optical and mechanical properties of the crystals. As an poten- tial material of the optical application, the SrF 2 crystal is also af- fected by the internal defects. In order to understand and manipulate the generation of the defects in SrF 2 crystal, some the- ory research must be done. The F center is one kind of the intrinsic color centers in crystal, in this type of crystallographic defect, the anionic vacancy is filled by one or more electrons which depending on the charge of the missing anion in the crystal. As in SrF 2 crystal, the anionic vacancy missed a fluorine atoms so one electron was trapped by the va- cancy. The F center in SrF 2 crystal has been studied by den Hartog, Arends, e.g. with electron paramagnetic resonance (EPR) in 1967 [24] and by Stoneham, Hayes, e.g. with Electron Nuclear Double Resonance (ENDOR) in 1968 [25]. We studied the F center transfer in SrF 2 crystal in our present work and make an approach of the R center in SrF 2 crystal as an extension. The article is organized as follows: Section 2 makes an introduc- tion of the computational method and first principle calculation details. In Section 3, the defect structure, relaxation of the sur- rounding atoms, energetic properties and electronic structure of the F-center transfer and the R centers were discussed. The elec- tron charge and spin density maps, band structures, and DOS plots are illustrated there to help readers to understand the properties of the single F center and their aggregations. 2. Calculation method There are two types about ab initio calculations, one is based on Hartree-Fork (HF) method, the other is based on density functional theory (DFT). As those two method lead to a deviation of the calcu- lation (the first type considerably overestimates the band gap meanwhile the second type underestimates it). So we choose the hybrid exchange–correlation B3PW functional as the base of our ab initio calculations. The hybrid exchange–correlation B3PW functional involving a mixture of nonlocal Fock exact exchange, lo- cal-density approximation (LDA) exchange, and Becke’s gradient corrected exchange functional [26], combined with the nonlocal gradient corrected correlation potential of Perdew and Wang [27–30]. As in our previously calculations about perfect CaF 2 , BaF 2 and SrF 2 crystals, the hybrid DFT-B3PW method gave the best agreement with experiments for the lattice constant, bulk modu- lus, and optical band gap [6,7]. So as in our present calculations 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.07.001 ⇑ Corresponding author. Tel.: +86 010 68916234. E-mail address: shihongting@gmail.com (H. Shi). Computational Materials Science 79 (2013) 527–533 Contents lists available at SciVerse ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci