approach*

For first-principles excited-state calculations, there exist in the literature various schemes to do “self-consistent” GW calculations at different levels going beyond the one-shot G₀W₀ approach. For single-particle excitations (e.g., the quasiparticle bandgap in semiconductors), a straightforward self-consistent update of both the single-particle Green’s function G and the screened Coulomb interaction W within the random-phase approximation (RPA) for the self-energy generally gives less satisfactory results than those from the G₀W₀ approach as compared to experiments. This is because the dielectric screening is underestimated within RPA using quasiparticle energies and the error will be accumulated, since electron-hole interactions (excitonic effects) are neglected in the RPA polarizability. In this work, we investigate the importance of electron-hole interactions in modifying W in the GW self-energy. The theoretical formalism is presented, along with first-principles results for various semiconductors.