Quasiparticle GW calculations for solids, molecules and 2D materials

We present a plane wave implementation of the G0W0 approximation within the projector augmented wave method code GPAW. The computed band gaps of ten bulk semiconductors and insulators deviate on average by 0.2 eV (~ 5 %) from the experimental values - the only exception being ZnO where the calculated band gap is around 1 eV too low. Similar relative deviations are found for the ionization potentials of a test set of 32 small molecules. The importance of substrate screening for a correct description of quasiparticle energies and Fermi velocities in supported 2D materials is illustrated by the case of graphene/h-BN interfaces. Due to the long range Coulomb interaction between periodically repeated images, the use of a truncated interaction is found to be essential for obtaining converged results for 2D materials. For all systems studied, a plasmon pole approximation is found to reproduce the full frequency results to within 0.2 eV with a significant gain in computational speed. As alternative to G0W0, the efficient local GLLBSC potential yields significantly better results than the PBE0 hybrid. For completeness, we provide a mathematically rigorous and physically transparent introduction to the notion of quasiparticle states.