An accurate exchange-correlation potential for silicon and its discontinuity on adding an electron.

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