Classification System for Fullerenes

E. F. Kustov^a, V. I. Nefedov^b, A. V. Kalinin^a, and G. S. Chernova^b

^a Moscow Power Engineering Institute (Technical University), Krasnokazarmennaya ul. 14, Moscow, 111250 Russia

^b Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119991 Russia

Received January 22, 2008

Abstract—The universal classification of nanoshells developed on the basis of group theory makes it possible
to formulate new rules of the composition and structure of fullerenes. The classification shows the possible
numbers of atoms for a given point group of symmetry, their arrangement at the symmetry elements, the number
of nonequivalent groups of atoms in a structure, their coordination numbers, and the angles between bonds. The
suggested formulas of the compositions of nanostructures and their classification is valid for all fullerenes
known thus far and makes it possible to determine the compositions of as yet unknown fullerenes. The compo-
sition of heteroatomic nanoparticles with differently coordinated atoms composed of several shells shifted with
respect to one another in accordance with the lengths and angles of chemical bonds between atoms of these
shells can also be determined. The suggested procedure was used for calculating bridging diatomic nanostruc-
tures, for which a general formula for determining the compositions is derived. The stability of some predicted
structures is supported by accurate quantum-chemical calculations.

DOI: 10.1134/S0036023608090076

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