Sixty-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 Hückel MO energies, HOMO‐LUMO gaps, Kekulé 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.