Accurate Exchange-Correlation Potentials for Semiconductors and Their Connections With The Quasiparticle Energies

We obtain accurate density functional theory exchange and correlation potentials V xc(r) and their gap discontinuities from an exact relationship with the self-energy. Using the GW approximation is calculated for Si, FaAs, AlAs and diamond. A comparison with V xc (LDA) shows that each case is equivalent to 80% of the LDA bandgap error is attributable to the neglect of and only equivalent to 20% is due to the LDA itself. A discussion of the form of in real space illustrates the physical origin of.