Fullerenes isolated pentagon isomers

Table 1. Enumeration of C Fullerene Isomers in the Range n = 20 to 100 (first three columns), and Isolated-Pentagon Isomers in the Range n = 70 to 140 (last three columns)"...

The HNR applies a further filter to the set of isolated-pentagon isomers. It selects at most 44 optimal isomers of any one fullerene in the range 70 < n < 140(Table 3). It has not been proved by exhaustive calculation that these do in fact always include the most stable isomer in all cases, but the HNR does give a qualitativeiustification of the empirical observation that leapfrog and carbon-cylinder isomers beyond C70 are not those found separated from the Kratschmer-Huffman soot. 

As an application the topological coordinate method was used to create a comprehensive catalogue of general fullerene isomers with up to 50 carbon atoms and isolated-pentagon isomers with up to 100 carbon atoms (Fowler and Manolopoulos 1995). It was used also for developing a graph-theoretical procedure for constructing chirality descriptors of fullerenes (Rassat et al. 2003). 

Austin, S. J., Fowler, P. W., Orlandi, G., Manolopou-los, D. E., Zerbetto, F. (1994). Relative stabilities of Cjs isomers - a numerical test of the fullerene isolated-pentagon rule. Chemical Physics Letters, 226(1-2), 219-225. 

Mizorogi, N., Aihara, J. (2003). PM3 localization energies for the isolated-pentagon isomers of the Cs4 fullerene. Physical Chemistry Chemical Physics, 5, 3368-3371. 

Similar calculations were made for the only possible isomer of C70 [11-13] that obeys the isolated pentagon rule [4, 6] and for some of the most stable isomers of the higher fullerenes [11, 14-16]. On the basis of their easily accessible LUMOs and high electron affinities, all stable members of the fullerene family were expected to display very rich cathodic electrochemistry. 

Each fullerene contains 2(10 + A/) carbon atoms corresponding to exactly 12 pentagons and M hexagons. This building principle is a simple consequence of the Euler s theorem. Starting at C20 any even-membered carbon cluster, except C22, can form at least one fullerene structure. With increasing M the number of possible fullerene isomers rises dramatically. The soccer-ball shaped Ceo isomer with icosahedral symmetry (7h) is the smallest stable fullerene, because it is the first to obey the isolated pentagon rule (IPR) [3]. 

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