The mid-infrared spectra of large PAHs ranging from C54H18 to C130H28 are determined computationally using Density Functional Theory. Trends in the band positions and intensities as a function of PAH size, charge and geometry are discussed. Regarding the 3.3, 6.3 and 11.2 micron bands similar conclusions hold as with small PAHs. This does not hold for the other features. The larger PAH cations and anions produce bands at 7.8 micron and, as PAH sizes increases, a band near 8.5 micron becomes prominent and shifts slightly to the red. In addition, the average anion peak falls slightly to the red of the average cation peak. The similarity in behavior of the 7.8 and 8.6 micron bands with the astronomical observations suggests that they arise from large, cationic and anionic PAHs, with the specific peak position and profile reflecting the PAH cation to anion concentration ratio and relative intensities of PAH size. Hence, the broad astronomical 7.7 micron band is produced by a mixture of small and large PAH cations and anions, with small and large PAHs contributing more to the 7.6 and 7.8 micron component respectively. For the CH out-of-plane vibrations, the duo hydrogens couple with the solo vibrations and produce bands that fall at wavelengths slightly different than their counterparts in smaller PAHs. As a consequence, previously deduced PAH structures are altered in favor of more compact and symmetric forms. In addition, the overlap between the duo and trio bands may reproduce the blue-shaded 12.8 micron profile.
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