Electronic energy-band structure of the calcium fluoride crystal

Abstract

A self-consistent-field calculation for the electronic energy-band structure of the Ca${\mathrm{F}}_2$ crystal has been performed by using the method of linear combinations of atomic orbitals. The basis set consists of 90 Bloch sums formed by atomic wave functions of Ca and F as well as single-Gaussian orbitals. The valence-band states are composed chiefly of F $2p$ orbitals with both the upper and lower edges at the $X$ point. The x-ray structure factors are obtained from the valence-band wave functions and are compared with the observed values. The conduction states in the energy range of 1-3 eV above the threshold have substantial admixture of the Ca $3d$ orbitals, resulting in high density of states in that region. The calculated band gap is 10.0 eV which is somewhat smaller than the experimental value estimated from the reflectance spectra. Comparison of the calculated joint density of states with experimental optical data is discussed.