Abstract
Topological information carried by the adjacency matrix is sufficient to build up a systematic model of fullerene stability. Isomers can be enumerated using the ring-spiral algorithm; counting rules for closed electronic shells follow from simple Hückel theory; hexagon neighbour indices describe the distribution of pentagon-induced strain, and sterically favoured cages can be identified at each number of atoms. A full analysis is made for 120-atom cages. Competition between electronic and steric effects rationalises the scarcity of properly closed shells amongst experimentally isolated higher fullerenes. C60 and C70 are the only known properly closed shells below C180 to have minimum steric strain.
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Fowler, P.W., Austin, S.J., Manolopoulos, D.E. (1994). Competing Factors in Fullerene Stability. In: Prassides, K. (eds) Physics and Chemistry of the Fullerenes. NATO ASI Series, vol 443. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0984-0_4
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