Ab initio infrared vibrational modes for neutral and charged small fullerenes (C20, C24, C26, C28, C30 and C60)

We calculate the infrared (IR) absorption spectra using DFT B3LYP(6-311G) for a range of small closed-cage fullerenes, Cn, n=20, 24, 26, 28, 30 and 60, in both neutral and multiple positive and negative charge states. The results are of use, notably, for direct comparison with observed IR absorption in the interstellar medium. Frequencies fall typically into two ranges, with C-C stretch modes around 1100-1500 cm(-1) (6.7-9.1 mu m) and fullerene-specific radial motion associated with under-coordinated carbon at pentagonal sites in the range 600-800 cm(-1) (12.5-16.7 mu m). Notably, negatively charged fullerenes show significantly stronger absorption intensities than neutral species. The results suggest that small cage fullerenes, and notably metallic endofullerenes, may be responsible for many of the unassigned interstellar IR spectral lines. This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.