The high interstellar abundances of polycyclic aromatic hydrocarbons (PAHs) and their size distribution are the result of complex chemical processes implying dust, UV radiation, and the main gaseous components (H, C+, and O). These processes must explain the high abundance of relatively small PAHs in the diffuse interstellar medium (ISM) and imply the continuous formation of some PAHs that are small enough (number of carbon atoms NC <~ 35-50) to be completely dehydrogenated by interstellar UV radiation. The carbon clusters Cn thus formed are constantly exposed to the absorption of ~10-13.6 eV UV photons, allowing isomerization and favoring the formation of the most stable isomers. They might tend to form irregular carbon cages. The frequent accretion of interstellar C+ ions could favor further cage isomerization, as is known in the laboratory for C60, possibly yielding most stable fullerenes, such as C40, C44, and C50. These fullerenes are expected to be very stable in the diffuse ISM because C2 ejection is not possible by single UV photon absorption, but could need rare two-photon absorption. It is possible that at least one of these fullerenes or its cation is as abundant as C60 or C60+ in the diffuse ISM, although this abundance is limited by the lack of observed matching features in observed mid-infrared spectra. B3LYP calculations of the visible spectrum for a number of fullerene isomers with 40 <~ NC <~ 50 show that they generally have a few spectral bands in the visible range, with f-values in the range of a few 10-2. This could make such fullerenes interesting candidates for the carriers of some diffuse interstellar bands.
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