On Kekulé structures of buckminsterfullerene

We have examined the 12 500 Kekulé valence structures of C60 and were able to classify them in six classes, belonging to different degrees of freedom (df). There is but one Kekulé structure having the maximal number of df = 10, followed by 80 Kekulé valence structures with df = 9, and so on (see Table 1). In all there are only 158 essentially different Kekulé valence structures out of 12 500 structures of C60. As illustrated on Kekulé structures of df = 9 there are considerable variations in the patterns of CC single and CC double bonds among different Kekulé valence structures, even for structures having the same degree of freedom.