3.1.6. Systematic numbering for (C₄₀-D₂)[5,6]fullerene

This structure is characterized by three different C₂ axes. One C₂ axis passes through opposite six-membered rings; the other C₂ axes pass through midpoints of opposite bonds. By application of Fu-3.1.2 the axis passing through the ring has highest priority for selection as the reference axis. This axis is shown in Fig. 7a. The numbering should begin from one of the atoms belonging to either one of the two rings that are symmetry-equivalent. The six atoms of the ring form three pairs of symmetry-equivalent atoms: a/a', b/b', and c/c'. Thus, there are only six pathways to be evaluated, clockwise and anticlockwise from a, from b, and from c. The pathway c to b to a does not result in a contiguous helical numbering. All the other five pathways [a to c' to b' (Fig. 7b); a' to b' to c' (Fig. 7c); b' to a' to c (Fig. 7d); b' to c' to a (Fig. 7e); c' to a to b (Fig. 7f)] do result in contiguous numberings and a choice must be made.

Application of Fu-3.1.1 to Fu-3.1.3 is not sufficient to select the preferred numbering, since all numberings terminate at an atom belonging to the ring intersected by the axis. Inspection of the atom-ranking using the new rule Fu-3.1.4 leads to selection of the pathway in Fig. 7e as the correct numbering since it contains the highest ranking atom at the first point of difference (see Table 1). Indeed, the pathway in Fig. 7e begins at a 6,6,5 atom (and thus is preferred over the pathways in Figs. 7b and 7c), and contains a 6,6,5 atom at position 2, whereas both pathways in Figs. 7d and 7f contain a 6,5,5 atom at the same position. The stereodescriptor for the shown enantiomer of this inherently chiral fullerene is (^f,sA) [ref 4]. Note that, once a numbering is discarded, further inspection of atom ranking is not required. Based on different rules [ref 3], CAS selects the pathway in Fig. 7c as the preferred numbering.

3. A.L. Goodson, C.L. Gladys and D.E. Worst, J. Chem. Inf. Comp. Sci. 1995, 35, 969-978.

4. International Union of Pure and Applied Chemistry, Division of Organic Chemistry, Commission on Nomenclature of Organic Chemistry. "Nomenclature for the (C₆₀-I_h) and (C₇₀-D_5h(6))[5,6]fullerenes (IUPAC recommendations 2002)", Pure Appl. Chem. 2002, 74, 629-695.

5. P.W. Fowler and D.E. Manolopoulos, An Atlas of Fullerenes, Clarendon Press, Oxford, 1995