Band structures for excited state spectroscopies

By calculating an exchange-correlation potential from the self-energy operator, we show that interpretation of the one-electron band structure appearing in density-functional theory (DFT) calculations as quasiparticle energies is seriously invalid. For example, the well-known error in the minimum band gap of semiconductors and insulators is not caused by the use of the local density approximation (LDA), but is inherent to DFT. Furthermore, the metal-insulator transition undergone when a semiconductor is compressed is not described correctly within DFT, showing that the DFT Fermi surface is not necessarily that of the real system. However, excited state properties can be calculated correctly, by using computational many-body theory. The GW approximation for the self-energy operator gives quasiparticle energies in excellent agreement with experiment. It may also be used to obtain the one-particle Green's function, from which other properties of the system may be found.