Besides the $Cd$(5*s*) and $F$(2*s*,2*p*) valence states also the shallow $Cd$(4*s*, 4*p*, 4*d*) core states are treated as valence electrons. Inclusion of the $Cd$(4*d*) states is important because they appear in between the $F$(2*s*) and $F$(2*p*) bands. Inclusion of the strongly bound $Cd$(4*s*,4*p*) states (about 100 or 60 eV below the valence band maximum) is not an absolute must but helps a lot to construct *s*- and *p*-pseudopotentials with excellent scattering properties up to very high energies which are needed for a proper treatment of a large number of unoccupied bands in the calculation of the dielectric function. The wave functions are expanded in a plane-wave basis set with a cutoff energy of 950 eV. The DFT/HSE calculations for this cutoff value are fully converged. For GW/BSE calculations the error bar has been estimated at about 0.1 eV. The face-centered cubic (fcc) Brillouin zone (BZ) is sampled by $\Gamma$-point centered meshes with 161616 Monkhorst-Pack *k*-points[@monkhorst] (converging within a few meV). The minimum of the total energy with respect to the volume is obtained by fitting to the Vinet equation of state.[@vinet] For the calculation of the cohesive energies $E_{coh}$, we have subtracted the spin-polarized ground-state energies of the free atoms.

                        