On the formation of the fullerenes

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Abstract
The chemistry by which the closed-cage carbon clusters, C$_{60}$ and C$_{70}$, can be formed in high yield out of the chaos of condensing carbon vapour is considered. Several mechanisms for this process that have been proposed are critically discussed. The two most attractive are the `pentagon road' where open sheets grow following the alternating pentagon rule and the `fullerene road' where smaller fullerenes grow in small steps in a process which finds the buckminsterfullerene (C$_{60}$) local deep energy minimum and to a lesser extent the C$_{70}$ (D$_{\text{5h}}$) minimum. A clear choice between the two does not seem possible with available information.