The Stone-Wales map for C60

The possible Stone-Wales (pyracylene) rearrangements amongst C60 fullerenes generate a graph in which buckminster-fullerene is linked to 1709 of the other 1811 fullerene isomers. Only one major bottleneck exists on this main map; all routes to icosahedral C60 pass through a single isomer of C2v symmetry. When energies of all isomers computed in the semi-empirical QCFF/PI model are combined with the map, it is found that stability generally decreases with the number of Stone-Wales steps away from the icosahedral isomer and that the 877 most stable isomers are on the main map. Implications of the map for the pentagon and fullerene road models of C60 formation are discussed.