Calculations are carried out using density functional theory (DFT) to determine the harmonic frequencies and intensities of the neutrals and cations of 13 polycyclic aromatic hydrocarbons (PAHs) up to the size of ovalene. Calculations are also carried out for a few PAH anions. The DFT harmonic frequencies, when uniformly scaled to account primarily for anharmonicity, agree with the matrix isolation fundamentals to within an average error of about 10 cm(-1). Electron correlation is found to significantly reduce the intensities of many of the cation harmonics, bringing them into much better agreement with the available experimental data. While the theoretical infrared spectra agree well with the experimental data for all of the neutral systems and for many of the cations, there still remain discrepancies with the experimental matrix isolation data for some species that are difficult to rationalize entirely in terms of limitations in the calculations. In agreement with previous theoretical work, the present calculations show that the relative intensities for the astronomical unidentified infrared (UIR) bands agree reasonably well with those for a distribution of polycyclic aromatic hydrocarbon (PAH) cations but not with a distribution of PAH neutrals. We also observe that the infrared spectra of highly symmetrical cations such as coronene agree much better with astronomical observations than do those of, for example, the polyacenes such as tetracene and pentacene. The total integrated intensities for the neutral species are found to increase linearly with size, while the total integrated intensities are much larger for the cations and scale more nearly quadratically with size. We conclude that emission from moderate-sized highly symmetric PAH cations such as coronene and larger could account for the UIR bands.