Classification system for fullerenes

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 composition 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 nanostructures, for which a general formula for determining the compositions is derived. The stability of some predicted structures is supported by accurate quantum-chemical calculations.