Calcium fluoride is a prototypical very large band-gap material, with applications in far-ultraviolet optics. We study the electronic, dielectric, and vibrational properties of CaF2 from first principles, using density-functional theory. The phonon band structure is well reproduced with standard pseudopotentials, except for one optical T-1u mode near Gamma and X. However, the calculated dielectric properties are very poor. Improving the quality of the dielectric constants of the crystal requires a pseudopotential for Ca with additional semicore electrons. We perform a detailed analysis of the static and dynamical charges, as well as the interatomic force constants.
Verstraete, M. J., & Gonze, X. (2003). First-principles calculation of the electronic, dielectric, and dynamical properties of CaF2. Physical review. B, Condensed matter and materials physics, 68(19), 195123:1-195123:7. https://doi.org/10.1103/PhysRevB.68.195123 (Original work published 2003)