  Aims. In this work we determine the effects of anharmonicity on the
mid-infrared spectra of the linear polycyclic aromatic hydrocarbons (PAHs)
naphthalene, anthracene, tetracene and pentacene recorded using the free
electron laser FELIX. Methods. Comparison of experimental spectra obtained
under supersonic jet conditions with theoretically predicted spectra was used
to show if anharmonicity explicitly needs to be taken into account. Results.
Anharmonic spectra obtained using second-order vibrational perturbation theory
agree on average within 0.5% of the experimental frequencies. Importantly, they
confirm the presence of combination bands with appreciable intensity in the 5-6
$\mu$m region. These combination bands contain a significant fraction of the IR
absorption, which scales linearly with the size of the PAH. Detection and
assignment of the combination bands are a preliminary indication of the
accuracy of far-IR modes in our anharmonic theoretical spectra. Detailed
analysis of the periphery-sensitive CH out-of-plane band of naphthalene reveals
that there is still room for improvement of the VPT2 approach. In addition, the
implications of our findings for the analysis of the aromatic infrared bands
are discussed.
