\varphi_{k} \rangle,$$ is used in conjunction with the random phase approximation (RPA) dielectric function to calculate the screened Coulomb interaction $W_0$ and the DFT Green’s function $G_0$. This approach called $G_{0}W_{0}$ usually works very well and gives very good results for the GW eigenvalues (band gaps, bandwidths and band dispersions).[@hl; @cappellinissc92] Another GW treatment of the QP band structure is based on the so-called generalized KS schemes (gKS).[@gKS1; @gKS2] The gKS methods have in common that nonlocal exchange-correlation potentials involving partial or screened exact exchange are inserted into the KS equations combined with (semi-)local DFT potentials. From the viewpoint of band structure calculations these gKS schemes can be also considered as oversimplified GW schemes. Hence, they can be considered as an improved starting point (eigenvalues, wave functions) for $G_{0}W_{0}$ calculations. While results are similar for many systems, gKS schemes as a $G_{0}W_{0}$ starting point can provide much improved results for those cases where DFT-LDA or -GGA fails drastically (wrong band ordering, extreme gap underestimates). Since the experimental gap is almost three times as large as the DFT-PBEsol one (a gap correction of about 5 eV is necessary to arrive at the experimental values) a gKS starting point (still leaving a 