Carbon cylinder rule

A survey of the Hiickel spectra of the lower fullerenes rapidly reveals that properly closed n shells are very much the exception rather than the rule most fullerene isomers have pseudoclosed k configurations. The rare occurrences of properly closed shells can be almost entirely described by two magic number rules that are to the fullerenes what the Hiickel 4n + 2 is to monocyclic systems and the Wade n + 1 rule is to boranes. The two are the leapfrog and the carbon cylinder rules. 

I he results of their calculations were summarised in two rules. The first rule states that at least one isomer C with a properly closed p shell (i.e. bonding HOMO, antibonding I. U.MO) exists for all n = 60 - - 6k (k = 0,2,3,..., but not 1). Thus Qg, C72, Cyg, etc., are in lhi-< group. The second rule is for carbon cylinders and states that a closed-shell structure is lound for n = 2p(7 - - 3fc) (for all k). C70 is the parent of this family. The calculations Were extended to cover different types of structure and fullerenes doped with metals. 

Closed-shell fullerenes following the carbon cylinder mle are again rare (just 3 for ft < 100) and again an experimentally characterized fullerene is the parent of an infinite series of properly closed shells. For n < 112 the leapfrog and cylinder rules together exhaust the list of properly closed shells. They are not complete for all n, however, as the next section points out. 

Table 2. Enumeration of C Fullerene Isomers in the Range n < 140 with Sporadic Properly Closed Shells outside the Leapfrog and Carbon-Cylinder Magic-Number Rules...

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