Predictive GW calculations using plane waves and pseudopotentials

We derive a finite-basis-set correction for quasiparticle (QP) energies in the GW approximation and many-body correlation energies in the random phase approximation. Since the correction requires only knowledge of the ground-state density distribution, it is straightforward to implement in any plane-wave code and significantly improves convergence at negligible computational cost. The expression also indicates that QP energies might converge to the wrong value using the projector augmented wave (PAW) method since the overlap densities of occupied orbitals and high-energy, plane-wave-like orbitals are inaccurately described. The error is shown to be related to the incompleteness of the partial waves inside the atomic spheres. It can be avoided by adopting norm-conserving partial waves. G0W0 and GW0 results based on such norm-conserving PAW potentials are presented for a large set of semiconductors and insulators. Accurate extrapolation procedures to the infinite-basis-set limit and infinite-k-point limit are discussed in detail.