Enumeration of Chiral and Positional Isomers of Substituted Fullerene Cages (C~O-C,~)

Enumeration of chiral isomers of substituted fullerene cages (CZO-C~O) is considered using the generalized character cycle index (GCCI) of the alternating representation of the point group of the parent cage. It is shown that there are no chiral isomers for the monosubstituted CZO, c24, C28, C30, c36, and CW fullerene cages but there are chiral isomers for other monosubstituted cages. All cages considered here possess chiral isomers for disubstituted cages. It is shown that the number of positional isomers can be obtained using the GCCI of the totally symmetric representation. We also enumerate the 13C NMR signals of all fullerene cages C Z 4 7 0 .