## Abstract

We calculate the interacting bandgap energy of a solid within the random-phase approximation (RPA) to density functional theory (DFT). The interacting bandgap energy is defined as E_{g}=E^{RPA}(N+1) +E^{RPA}(N-1) -2E^{RPA}(N), where E^{RPA}(N) is the total DFT-RPA energy of the N-electron system. We compare the interacting bandgap energy with the Kohn-Sham bandgap energy, which is the difference between the conduction and valence band edges in the Kohn-Sham band structure. We show that they differ by an unrenormalized "G_{0}W _{0}" self-energy correction (i.e., a GW self-energy correction computed using Kohn-Sham orbitals and energies as input). This provides a well-defined and meaningful interpretation to G_{0}W_{0} quasiparticle bandgap calculations, but questions the physics behind the renormalization factors in the expression of the bandgap energy. We also separate the kinetic from the Coulomb contributions to the DFT-RPA bandgap energy, and discuss the related problem of the derivative discontinuity in the DFT-RPA functional. Last we discuss the applicability of our results to other functionals based on many-body perturbation theory.

Original language | English |
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Article number | 245115 |

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 70 |

Issue number | 24 |

DOIs | |

Publication status | Published - Dec 2004 |

Externally published | Yes |