Accurate Exchange-Correlation Potential for Silicon and Its Discontinuity on Addition of an Electron

We obtain an accurate density-functional exchange-correlation potential, Vₗ₂ (r), for silicon, from calculations of the self-energy (r, r^', ). No local-density approximation (LDA) is used for Vₗ₂. The band structure with this Vₗ₂ is in remarkably close agreement with that obtained with the LDA, while both differ significantly from the quasiparticle spectrum of. The 50% band-gap error found in LDA calculations is therefore not caused by the LDA but by the discontinuity, , in the exact Vₗ₂ on addition of an electron.