The identification of the carriers of the absorption features associated with the diffuse interstellar bands (DIBs) is a long-standing problem in astronomical spectroscopy. Computational simulations can contribute to the assignment of the carriers of DIBs since variations in molecular structure and charge state can be studied more readily than through experimental measurements. Polyaromatic hydrocarbons have been proposed as potential carriers of these bands, and it is shown that simulations based upon density functional theory and time-dependent density functional theory calculations can describe the vibrational structure observed in experiment for neutral and cationic naphthalene and pyrene. The vibrational structure arises from a small number of vibrational modes involving in-plane atomic motions, and the Franck–Condon–Herzberg–Teller approximation improves the predicted spectra in comparison with the Franck–Condon approximation. The study also highlights the challenges for the calculations to enable the assignment in the absence of experimental data, namely prediction of the energy separation between the different electronic states to a sufficient level of accuracy and performing vibrational analysis for higher-lying electronic states.