First-principles calculations of the CaF₂ bulk and surface electronic structure

We present and discuss the results of calculations of the CaF₂ bulk and surface electronic structure. These are based on the ab initio Hartree-Fock (HF) method with electron correlation corrections and on Density Functional Theory (DFT) calculations with different exchange-correlation functionals, including hybrid exchange techniques. Both approaches use the localised Gaussian-type basis set. According to our calculations the ab initio HF method considerably overestimates (20.77 eV) the optical band gap, whereas the density functional calculations based on the Kohn-Sham equation with a number of exchange-correlation functionals, including local density approximation (LDA) (8.72 eV), generalized gradient approximations (GGA) by Perdew and Wang (PW) (8.51 eV), and Perdew, Burke, and Ernzerhof (PBE) (8.45 eV) under-estimate it. Our results show that the best agreement with experiment (12.1 eV) can be obtained using a hybrid HF-DFT exchange functional, in which Hartree-Fock exchange is mixed with DFT exchange functionals, using Beckes three parameter method, combined with the non-local correlation functionals by Perdew and Wang (B3PW) (10.96 eV). We also present calculations of CaF ₂(111), (110), and (100) surfaces. Our calculated surface energies using the hybrid B3PW method confirm that the CaF₂(111) surface is the most stable one, in agreement with the experiment.