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Systematics of fullerenes and related clusters

Qualitative theoretical treatments of the fullerene family of molecules can be used to count possible isomers and predict their geometric shapes, point groups, electronic structures, vibrational and NMR spectroscopic signatures. Isomers are generated by the ring-spiral algorithm due to D. E. Manolopoulos. Geometrically based magic number rules devised by the present author account for all electronically closed π shells within the Hiickel approximation and these ‘leapfrog’ and ‘cylinder’ rules apply to the wider class of ‘fulleroid’ structures constructed with rings of other sizes. Extrapolations from the theory of carbon clusters are described for doped fullerenes, metallocarbohedrenes, fully substituted boron-nitrogen heterofullerenes and decorated-fullerene models for water clusters.