Ab initiocalculations of theCaF2electronic structure andFcenters

Abstract

We present and discuss the results of calculations of the $\mathrm{Ca}{\mathrm{F}}_{2}$ bulk and surface electronic structure. These are based on the ab initio Hartree-Fock method with electron correlation corrections and on density-functional theory calculations with different exchange-correlation functionals, including hybrid exchange techniques. Both approaches use the localized Gaussian-type basis set. According to our calculations the ab initio Hartree-Fock method considerably overestimates $(20.77\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ 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 $(8.72\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, generalized gradient approximations by Perdew and Wang $(8.51\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$, and Perdew, Burke, and Ernzerhof $(8.45\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ underestimate it. Our results show that the best agreement with experiment $(12.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ can be obtained using a hybrid Hartree-Fock and density-functional theory exchange functional, in which Hartree-Fock exchange is mixed with density-functional theory exchange functionals, using Beckes three-parameter method, combined with the nonlocal correlation functionals by Perdew and Wang $(10.96\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. We also present calculations of $\mathrm{Ca}{\mathrm{F}}_{2}$ (111), (110), and (100) surfaces. Our calculated surface energies confirm that the $\mathrm{Ca}{\mathrm{F}}_{2}$ (111) surface is the most stable one, in agreement with the experiment. The characterization of $F$ centers in $\mathrm{Ca}{\mathrm{F}}_{2}$ is still a question of debate. In order to understand the behavior of the material with respect to its optical properties, we performed ab initio calculations to determine the electronic structure, atomic geometry, and formation energy of $F$ center in $\mathrm{Ca}{\mathrm{F}}_{2}$.