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

Abstract We benchmark many-body perturbation theory against density functional theory (DFT) for the band gaps of solids. We systematically compare four G W variants— G 0 W 0 using the Godby-Needs plasmon-pole approximation ( G 0 W 0 -PPA), full-frequency quasiparticle G 0 W 0 (QP G 0 W 0 ), full-frequency quasiparticle self-consistent G W (QS G W ), and QS G W augmented with vertex corrections in W (QS $$G\hat{W}$$ G W ̂ )—against the currently best-performing and popular density functionals mBJ and HSE06. Our results show that G 0 W 0 -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 QS $$G\hat{W}$$ G W ̂ . The QS G W removes starting-point bias, but systematically overestimates experimental gaps by about 15%. Adding vertex corrections to the screened Coulomb interaction, i.e., performing a QS $$G\hat{W}$$ G W ̂ calculation, eliminates the overestimation, producing band gaps that are so accurate that they even reliably flag questionable experimental measurements.