Leapfrog fullerenes, Huckel bond order and Kekule structures

Investigation of a sample of 5436 fullerene isomers indicates a relationship between Kekule structures and the molecular orbital theory of these trivalent cages. In leapfrog fullerenes (those constructed by omnicapping and dualising a fullerene parent), the edges of maximal Huckel pi bond order define the Kekule structure with the maximum number of benzenoid hexagons (the Fries structure). For general fullerenes, the bond orders rarely correspond exactly to a Kekule structure: of 1812 C-60 fullerene isomers, for example, only 23 have a Huckel Kekule structure.