60-ATOM CARBON CAGES

The enumeration of all 60-atom carbon cages associated to trivalent polyhedra with five- and six-sided faces is addressed. This isomer problem is computationally solved to give 1790 cages, with a further resolution into subclasses of cages with differing numbers p of abutting pairs of pentagonal faces. The individual cages are generated, and then there are computed various graph-theoretic invariants, including Huckel MO energies, HOMO-LUMO gaps, Kekule structure counts, and conjugated-circuit counts. Associated properties as a function of p are reported and found to be in concert with earlier qualitative arguments. It is found that the most stable of these cages is the unqiue p = 0 Buckminsterfullerene structure.