The energetic costs of widening the classical fullerene definition to
include carbon cages with octagonal as well as pentagonal and hexagona
l faces are investigated theoretically. Relative energies of all 16 C-
40 and 620 C-48 cages that can be assembled with one face octagonal, 1
4 pentagonal and all others hexagonal are calculated within two indepe
ndent semi-empirical models and compared with the 295 C-40 and 2664 C-
48 one-square, one-heptagon and classical-fullerene cages. All isomers
are local minima on the potential surface, and many non-classical str
uctures fall within the energy range spanned by the classical fulleren
es. Penalties for introduction of a single non-classical face increase
in the order heptagon < square < octagon, estimated for C-48 as 58 -
123, 108 - 236, and 329 - 450 kJ mol(-1), respectively, depending on m
odel. The energy variation across the range of classical and non-class
ical structures is rationalised by extension of the isolated-pentagon
rule: when large ring is present, structures of low energy maximise th
e number of its contacts with pentagons and minimise the pentagon-pent
agon adjacencies.