Theoretical Studies of the Fullerenes C34 to

Department of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, UK Received 7 March 1991 in final form 6 April 1991 

An interesting correlation is found between the kinetic stabilities of the fullerenes ] to C70. as determined by simple Hiickel theory HOMO-LUMO energy separations, and the intensities of photoionisation signals from carbon clusters produced by laser vaporisation of graphite. This correlation provides further circumstantial evidence that the observed C34 to C70 clusters are indeed fullerenes, closed carbon cages containing only five- and six-membered rings. 

Clearly, if any such quantitative explanation is to be found, it must take account of the fact that there can be a large number of distinct fullerene isomers for each given C . There are, for example, at least 1812 distinct fullerene isomers for Cso alone (vide infra). Icosahedral C o, which was first discovered by intuition [2], does indeed happen to be the most stable of these. However, since the majority of carbon clusters do not admit such remarkably symmetric closed-shell structures, the most stable C fullerene isomer is generally more difficult to find. Section 2 describes a practical solution to this problem, which amounts to no more than a direct computer search of all possible fullmne structures for each given C . Section 3 then ofTeit a semi-quantitative explanation for fig. 1, based on the relative kinetic stabilities of the fullerenes C34 to C70. 

While large scale ab initio geometry optimisation calculations on the fullerenes are currently impractical, except perhaps in a few high-symmetry cases [10-13], one can at least find the most stable fullerene structure for given C within Huckel x-elec-tron theory [14,15]. In fact this turns out to be quite straightforward, at least for small n, because every possible fullerene structure can be peeled like an orange. 

Moreover similar face spirals can be found for all other fullerenes mentioned in the literature to date. Face spirals for the specific C29, C32, C50 and C70 structures described by Kroto (4,5), for example, are given by 

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Down, Theoretical Studies of the Fullerenes C34 to C70, Chem. Phys. Lett. 181, 105-111 (1991). 

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