Density functional theory has been employed to calculate the harmonic frequencies and intensities of a range of polycyclic aromatic hydrocarbon (PAH) cations that explore both size and electronic structure effects on the infrared spectroscopic properties of these species. The sample extends the size range of PAH species considered to more than 50 carbon atoms and includes several representatives from each of two heretofore unexplored categories of PAH cations: (1) fully benzenoid PAH cations whose carbon skeleton is composed of an odd number of carbon atoms (C(odd) PAHs); and (2) protonated PAH cations (HPAH+). Unlike the radical electronic structures of the PAH cations that have been the subject of previous theoretical and experimental work, the species in these two classes have a 'closed'-shell electronic configuration. The calculated spectra of circumcoronene, C54H18, in both neutral and (radical) cationic form are also reported and compared with those of the other species. Overall, the C(odd) PAHs spectra are dominated by strong CC stretching modes near 1600 cm(-1) and display spectra that are remarkably insensitive to molecular size. The HPAH+ species evince a more complex spectrum consistent with the added contributions of aliphatic modes and their generally lower symmetry. Finally, for both classes of closed-shell cations, the intensity of the aromatic CH stretching modes is found to increase with molecular size far out of proportion with the number of CH groups, approaching a value more typical of neutral PAHs for the largest species studied.