A comprehensive theoretical study of the He(I) UV photoionization spectra of coronene, 1.2,6.7-dibenzopyrene, 1.12-benzoperylene, and anthanthrene up to electron binding energies of similar to18 eV is presented with the aid of one-particle Green's function calculations performed using the outer-valence Green's function (OVGF) approach and the third-order algebraic-diagrammatic construction [ADC(3)] scheme, using Dunning's correlation consistent polarized valence basis set of double-zeta quality and the 6-31G basis set, respectively. The deviations from the one-electron OVGF/cc-pVDZ binding energies and experimental results most generally do not exceed 0.3 eV. OVGF/cc-pVDZ pole strengths smaller than 0.85 systematically corroborate a breakdown of the orbital (or one-electron) picture of ionization at the ADC(3)/6-31G level. A comparison has been made with calculations of the lowest doublet-doublet excitation energies of the related radical cations, by means of time-dependent density functional theory (TDDFT) and the Becke-Lee-Yang-Parr (BLYP) functional: Because of systematic and significant underestimations of the lowest [pi(0)* <-- sigma] transition energies in the cations, this approach has led to erroneous identifications of the sigma-ionization onset of the neutral molecules.