No 1, Vol. 13, 2012, pages 22-36

FROM FOUR TO TWENTY

It is customary to assume that fullerenes are the carbon molecules having a shape
close to a spherical surface which can be composed of regular pentagons combined with
regular hexagons. Earlier we developed a method for calculating electronic and atomic
structure for such fullerenes. Now we suppose that the restriction on fullerenes construction
only from pentagons and hexagons is unnecessary. In other words, we take the term
"fullerene" in a broad sense to mean any shape inscribed into to a spherical surface which can
be composed of carbon atoms, each atom having three nearest neighbors, whenever
discussing hollow carbon clusters. In addition to this definition, we suppose that not only
atoms but also shared electron pairs, forming covalent bonds, are located on one and the same
sphere. From this it follows that the geometry of both the electronic structure as well as of the
atomic structure of fullerenes can be most conveniently constructed and studied with the help
of spherical geometry. We enlarged here the approach developed earlier for usual fullerenes.
The procedure created reveals the hidden symmetry of the shared electron pairs located on the
same sphere as that of carbon atoms. The most interesting result is that we have found
structural isomers of some fullerenes which differed in their surface electronic density.
Keywords: fullerene in a broad sense, shared electron pairs; covalent bonds; spherical geometry; hidden symmetry; structural isomers; surface electronic density |

full paper (pdf, 3088 Kb)