approach*

There are a number of schemes in the literature to do “self-consistent” GW calculations at different levels going beyond the G₀W₀ approximation. 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 generally gives less satisfactory results than those from the G₀W₀ approach as compared to experiment, which is due to an under-screening introduced and accumulated in the treatment of dielectric screening at the random phase approximation (RPA) level, where electron-hole interactions are neglected. In this work, we investigate the importance of electron-hole interactions in modifying W and hence the GW self-energy, as well as in reshaping single-particle excitations at the GW level. We present our theoretical formalism, along with first-principles results for several conventional semiconductors.