We present an implementation of G0W0 and eigenvalue-self-consistent GW (evGW) in the Gaussian and plane waves scheme for molecules. We calculate the correlation self-energy for imaginary frequencies employing the resolution of the identity. The correlation self-energy for real frequencies is then evaluated by analytic continuation. This technique allows an efficient parallel implementation and application to systems with several hundreds of atoms. Various benchmark calculations are presented. In particular, the convergence with respect to the most important numerical parameters is assessed for the benzene molecule. Comparisons with respect to other G0W0 implementations are reported for a set of molecules, while the performance of the method has been measured for water clusters containing up to 480 atoms in a cc-TZVP basis. Additionally, G0W0 has been applied for studying the influence of the ligands on the gap of small CdSe nanoparticles. evGW has been employed to calculate the HOMO–LUMO gaps of linear acenes, linear chains formed of connected benzene rings. Distinct differences between the closed and the open-shell (broken-symmetry) evGW HOMO–LUMO gaps for long acenes are found. In future experiments, a comparison of measured HOMO–LUMO gaps and our calculated evGW values may be helpful to determine the electronic ground state of long acenes.