Analysis of core-valence linearization in $G_{\mathrm{0}}W_{\mathrm{0}}$ calculations

In recent years the $GW$ approach, typically applied as the first order correction to the Kohn-Sham (KS) eigenenergies ($G_{\mathrm{0}}W_{\mathrm{0}}$ approximation), has substantially improved the description of single-particle excitations in weakly correlated semiconductors and insulators. Most of the existing codes are based on the pseudopotential (PP) method. It is well known from ground-state calculations that the linear treatment of the core-valence exchange-correlation interaction is not always valid. However, in the $G_{\mathrm{0}}W_{\mathrm{0}}$-PP scheme, the self-energy is computed from the (pseudo-)valence states only, keeping the core-valence interaction at the KS level. There is no justification for such a ``core-valence linearization'' of the dynamical self-energy, a highly non-linear functional of the total density. Nevertheless, $G_{\mathrm{0}}W_{\mathrm{0}}$-PP results usually agree better with experiments than the all-electron ones. In this talk we analyze the reasons for this disturbing discrepancy and the validity of the ``core-valence linearization'' in the $G_{\mathrm{0}}W_{\mathrm{0}}$-PP scheme. Calculations are performed using our own all-electron $G_{\mathrm{0}}W_{\mathrm{0}}$ code, based on the Wien2k implementation of the FP-(L)APW+lo method. We compare our all-electron results with those obtained by computing the self-energy from the valence states only as well as with $G_{\mathrm{0}}W_{\mathrm{0}}$-PP calculations for selected materials (e.g. Si, NaCl,...).