Figure 1

Basis-set extrapolated $G_0{W}_0$@PBE fundamental gaps of solid lithium hydride, diamond, and the molecular crystals ${\mathrm{NH}}_3$ and ${\mathrm{CO}}_2$ as function of the supercell size. The blue circles are the gaps computed without the correction; see Eq. (21) together with Eq. (22), where the blue line represents the linear regression. The intercept of the regression line with the ordinate determines the supercell extrapolated gap which is indicated by the dashed gray line. By the green dots, we show the gaps being computed with the periodic correction from Eq. (21) together with Eq. (59) where the dashed green lines are simple connections of the data points to guide the eye. It is observed that the corrected gaps are much closer to the supercell extrapolated gap compared to the noncorrected gaps.