Accurate exchange-correlation potential for silicon and its discontinuity on addition of an electron

We obtain an accurate density-functional exchange-correlation potential, Vxc(r), for silicon, from calculations of the self-energy Σ(r,r′,ω). No local-density approximation (LDA) is used for Vxc. The band structure with this Vxc is in remarkably close agreement with that obtained with the LDA, while both differ significantly from the quasiparticle spectrum of Σ. The 50% band-gap error found in LDA calculations is therefore not caused by the LDA but by the discontinuity, Δ, in the exact Vxc on addition of an electron.