$8.4-8.7$ eV).[@orlowski; @raisin] The best accordance with experiments is found within the scQP-GW scheme with a high level of accuracy. In Fig. \[fig:2\] we present the calculated DOS within different schemes. As is clear from this figure the VB regions after the HSE03 and PBEsol methods seem very similar while discrepancies arise for the CB region between the results after the two methods (higher value of the gap after the HSE03 scheme).

Similarities for the VB regions appear also between the result after the $G_{0}W_{0}$ and scQP-GW schemes. The latter method does operate a further opening of the gap. In the upper part of Fig. \[fig:2\], the HF DOS is reported. It determines a (too) large overestimate of the band gaps (about 16 eV at $\Gamma$) and valence bands are only partially (the shallow ones) similar to those calculated after the other methods. This HF band gap overestimate resembles a similar behavior taking place in other systems.[@hl; @strinati] Notice that the *d*-electrons of $Cd$ play an important role. Indeed, they are present inside the valence bands in the energy range displayed in Fig. \[fig:1\], and give rise to flat bands/sharp peaks near -5 eV, due to the localized character of 