Periodic System of Fullerenes: the Column of Three-Fold Symmetry

Abstract

We have studied possible ways of growing the fullerenes having initial three-fold symmetry. Beginning with the basic fullerenes C8, C14 and C20, which belong to the ∆n = 4, 6 and 8 series of the periodic table of fullerenes, we obtained intermediate fullerenes are C10, C12, C16 and C18; which fill up the gaps between the basic ones. The intermediate fullerenes are imperfect or semi-perfect. The imperfection is connected either with extra ‘interstitial’ or ‘vacancy’ carbon dimers, both types of dimers playing the role of defects. Only the basic fullerenes have the symmetry of the corresponding column, the intermediate fullerenes having no such symmetry. Considering these fullerenes as imperfect due to defects, one can define them as the fullerenes conserving three-fold topological symmetry. These features are also inherent to other more massive fullerenes which create different families and incorporate fullerenes from C8 to C56. We have calculated their energies and discussed possible reasons of their dependence on a fullerene size and shape.