An increasing number of observations show that non-classical isomers may play an important role in the formation of fullerenes and their exo- and endo-derivatives. A quantum-mechanical study of all classical isomers of C , C , and C , and all non-classical isomers with at most one square or heptagonal face, was carried out. Calculations at the B3LYP/6-31G* level show that the favored isomers of C , C , and C have closely related structures and suggest plausible inter-conversion and growth pathways among low-energy isomers. Similarity of the favored structures is reinforced by comparison of calculated ring currents induced on faces of these polyhedral cages by radial external magnetic fields, implying patterns of magnetic response similar to those of the stable, isolated-pentagon C molecule. © 2016 Wiley Periodicals, Inc.
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