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) underestimate 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 CaF2(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.