Many-body perturbation theory vs. density functional theory: a systematic benchmark for band gaps of solids

We benchmark many-body perturbation theory against density functional theory (DFT) for the band gaps of solids. We systematically compare four GW variants—G0W0 using the Godby-Needs plasmon-pole approximation (G0W0-PPA), full-frequency quasiparticle G0W0 (QPG0W0), full-frequency quasiparticle self-consistent GW (QSGW), and QSGW augmented with vertex corrections in W (QSGŴdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Ghat{W}$$end{document})—against the currently best-performing and popular density functionals mBJ and HSE06. Our results show that G0W0-PPA calculations offer only a marginal accuracy gain over the best DFT methods, however, at a higher cost. Replacing the PPA with a full-frequency integration of the dielectric screening improves the predictions dramatically, almost matching the accuracy of the QSGŴdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Ghat{W}$$end{document}. The QSGW removes starting-point bias, but systematically overestimates experimental gaps by about 15%. Adding vertex corrections to the screened Coulomb interaction, i.e., performing a QSGŴdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Ghat{W}$$end{document} calculation, eliminates the overestimation, producing band gaps that are so accurate that they even reliably flag questionable experimental measurements.