  A new implementation of the GW approximation (GWA) based on the all-electron
Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb
interaction is computed within the Random Phase Approximation (RPA) instead of
the plasmon-pole model. Two different ways of computing the self-energy are
reported. The method is used successfully to determine the quasiparticle
energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs,
NaH and KH. To illustrate the novelty of the method the real and imaginary part
of the frequency-dependent self-energy together with the spectral function of
silicon are computed. Finally, the GWA results are compared with other
calculations, highlighting that all-electron GWA results can differ markedly
from those based on pseudopotential approaches.
