LDA      PBE    PBEsol         OTheory               Expt.
  ------------------- -------- ------- -------- --------------------- --------------------
  $a_{\circ}$ (Å)       5.30    5.49     5.39     5.39[@kudrnovsky]    5.365.39[@deligoz]
  $B_{\circ}$ (GPa)    126.70   93.80   108.50   123.00[@kudrnovsky]    114.60[@deligoz]
  $B'_{\circ}$          4.76    4.88     4.85     4.85[@kudrnovsky]             
  $E_{coh}$ (eV)       -12.07   -9.55   -10.39                                  

  : Structural data for $CdF_{2}$ are given: lattice constant $a_{\circ}$, bulk modulus $B_{\circ}$ and its pressure derivative $B'_{\circ}=dB_{\circ}/dP$, and cohesive energy $E_{coh}$. Three local and semilocal *XC* functionals are used, as discussed in the text. Other theoretical results and experimental references are reported in column ”OTheory” and in column ”Expt.”, respectively.[]{data-label="table: lattice constant"}

Comparing experimental measurements[@kudrnovsky] with results calculated with different *XC* functionals, see Table \[table: lattice constant\], the best results are obtained within the PBEsol scheme. Therefore we have decided to use from now on the PBEsol lattice constant of $5.39$ Å  consistently for all calculations (ground-state, one- and two-particles excitations). This is an important point since band structure test calculations on DFT level for different lattice constants show that the gap value changes by about +0.1 eV (-0.1 eV) when going from the PBEsol to the LDA (PBE) lattice constant.

Quasi-particle excitations {#sec:computational}
==========================

The Kohn-Sham (KS) eigenvalues of the DFT scheme cannot be interpreted as energies of single-particle/quasiparticle (QP) electronic excitations and, 