We present a comparative full-potential study of generalized Kohn-Sham schemes (gKS) with explicit focus on their suitability as starting point for the solution of the quasiparticle equation. We compare $G_0W_0$ quasiparticle band structures calculated upon LDA, sX, HSE03, PBE0, and HF functionals for exchange and correlation (XC) for Si, InN and ZnO. Furthermore, the HSE03 functional is studied and compared to the GGA for 15 non-metallic materials for its use as a starting point in the calculation of quasiparticle excitation energies. For this case, also the effects of selfconsistency in the $GW$ self-energy are analysed. It is shown that the use of a gKS scheme as a starting point for a perturbative QP correction can improve upon the deficiencies found for LDA or GGA staring points for compounds with shallow $d$ bands. For these solids, the order of the valence and conduction bands is often inverted using local or semi-local approximations for XC, which makes perturbative $G_0W_0$ 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 $G_0W_0$ calculations following calculations using the HSE03 functional are very close to experiment

The electronic structure of In 2 O 3 polymorphs is calculated from first principles using density functional theory ͑DFT͒ and many-body perturbation theory ͑MBPT͒. DFT calculations with a local exchange-correlation ͑XC͒ functional give the relaxed atomic coordinates of the two stable polymorphs. Their electronic structure, i.e., the band structure and density of states, is studied within MBPT. The quasiparticle equation is solved in two steps. As the zeroth approximation for the XC self-energy the nonlocal potential resulting from a HSE03 hybrid functional is used. In the sense of a self-consistent procedure G 0 W 0 quasiparticle corrections are computed on top. The calculated direct quasiparticle gaps at ⌫ amount to 3.3 eV ͑rhombohedral͒ and 3.1 eV ͑cubic͒. The rhombohedral polymorph is found to exhibit a near degeneracy of the valence-band maxima at the ⌫ point and on the ⌫-L line, while the valence-band maximum of the cubic polymorph occurs near ⌫. Interconduction band transitions are identified as possible origin of conflicting experimental reports, claiming a much larger difference between the direct and indirect gap. The results for gaps, d-band positions, and density of states are compared with available experimental data.

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The bulk and surface electronic structure of In 2 O 3 has proved controversial, prompting the current combined experimental and theoretical investigation. The band gap of single-crystalline In 2 O 3 is determined as 2.93Ϯ 0.15 and 3.02Ϯ 0.15 eV for the cubic bixbyite and rhombohedral polymorphs, respectively. The valence-band density of states is investigated from x-ray photoemission spectroscopy measurements and density-functional theory calculations. These show excellent agreement, supporting the absence of any significant indirect nature of the In 2 O 3 band gap. Clear experimental evidence for an s-d coupling between In 4d and O 2s derived states is also observed. Electron accumulation, recently reported at the ͑001͒ surface of bixbyite material, is also shown to be present at the bixbyite ͑111͒ surface and the ͑0001͒ surface of rhombohedral In 2 O 3 .

Excitonic effects in optical spectra and electron-hole pair excitations are described by solutions of the Bethe-Salpeter equation (BSE) that accounts for the Coulomb interaction of excited electron-hole pairs. Although for the computation of excitonic optical spectra in an extended frequency range efficient methods are available, the determination and analysis of individual exciton states still requires the diagonalization of the electronhole HamiltonianĤ. We present a numerically efficient approach for the calculation of exciton states with quadratically scaling complexity, which significantly diminishes the computational costs compared to the commonly used cubically scaling direct-diagonalization schemes. The accuracy and performance of this approach is demonstrated by solving the BSE numerically for the Wannier-Mott two-band model in k space and the semiconductors MgO and InN. For the convergence with respect to the k-point sampling a general trend is identified, which can be used to extrapolate converged results for the binding energies of the lowest bound states.