of spin-orbit coupling on the energy bands has been considered extensively in Ref. , where the spin-orbit effect, in the case of $CdF_{2}$, slightly decreases the gaps by about 0.05 eV only. Thus spin-orbit effects will be neglected in the present paper.

We performed the calculations using different *XC* functionals. The local density approximation (LDA) has been used for the *XC* energy, as given by Ceperley and Alder, and parametrized by Perdew and Zunger.[@ceperley; @perdew] In addition, the generalized-gradient approximation (GGA) in the parametrization of Perdew, Burke, and Ernzerhof (PBE) is used.[@perdewburkeernzerhof] Moreover, we considered also a revised version of the PBE functional which gives better results in solids which we shall refer to as PBEsol[@perdew2008] from now on.

The lattice structure of $CdF_{2}$, as well as of all the other fluorides, is a cubic one with the space group *$Fm\overline{3}m$*, with three ions per unit cell, i.e., one cation $Cd$ placed in the origin and two anions $F$ situated at $\pm(\frac{1}{4}a, \frac{1}{4}a,\frac{1}{4}a)$.[@wyckoff] In the crystal the $F^{(-)}$ ions form a simple cubic sublattice surrounded by a face-centered cubic lattice of $Cd^{(++)}$ cations. All fluorides with cations belonging to the II and IIB groups are stable in this crystallographic structure.[@cadelano]

