Quasiparticle band structure based on a generalized Kohn-Sham scheme

We present a comparative full-potential study of generalized Kohn-Sham (gKS) schemes with explicit focus on their suitability as starting point for the solution of the quasiparticle equation. We compare ${G}_{0}{W}_{0}$ quasiparticle band structures calculated upon local-density approximation (LDA), screened-exchange, HSE03, PBE0, and Hartree-Fock functionals for exchange and correlation (XC) for Si, InN, and ZnO. Furthermore, the HSE03 functional is studied and compared to the generalized gradient approximation (GGA) for 15 nonmetallic materials for its use as a starting point in the calculation of quasiparticle excitation energies. For this case, the effects of self-consistency in the $GW$ self-energy are also analyzed. It is shown that the use of a gKS scheme as a starting point for a perturbative quasiparticle correction can improve upon the deficiencies found for LDA or GGA starting points for compounds with shallow $d$ bands. For these solids, the order of the valence and conduction bands is often inverted using local or semilocal approximations for XC, which makes perturbative ${G}_{0}{W}_{0}$ calculations unreliable. The use of a gKS starting point allows for the calculation of fairly accurate band gaps even in these difficult cases, and generally single-shot ${G}_{0}{W}_{0}$ calculations following calculations using the HSE03 functional are very close to experiment.