  Many-body perturbation theory in the GW approximation is a useful method for
describing electronic properties associated with charged excitations. A
hierarchy of GW methods exists, starting from non-self-consistent G0W0, through
partial self-consistency in the eigenvalues (ev-scGW) and in the Green function
(scGW0), to fully self-consistent GW (scGW). Here, we assess the performance of
these methods for benzene, pyridine, and the diazines. The quasiparticle
spectra are compared to photoemission spectroscopy (PES) experiments with
respect to all measured particle removal energies and the ordering of the
frontier orbitals. We find that the accuracy of the calculated spectra does not
match the expectations based on their level of self-consistency. In particular,
for certain starting points G0W0 and scGW0 provide spectra in better agreement
with the PES than scGW.
