Introduction and General Considerations

In 1995 a preliminary survey on numbering and nomenclature for fullerenes was published [ref 1]. It described two types of names for fullerenes, one proposed by some workers in the field and another one used by the Chemical Abstracts Service (CAS); and two systems for numbering fullerene skeletons, one proposed in a publication by R. Taylor [ref 2], and one published by CAS [ref 3]. In addition, alternative methods for naming derivatives of fullerenes were discussed. More recently, a document appeared reporting IUPAC recommendations for the nomenclature for the (C₆₀-I_h) and (C₇₀-D_5h(6)) fullerenes and their derivatives [ref 4]. This report was limited to these fullerenes because there are only a small number of known derivatives of only a few other fullerenes.

The present document contains recommendations for the numbering of fullerenes other than (C₆₀-I_h)[5,6]fullerene and (C₇₀-D_5h(6))[5,6]fullerene. The parenthetical prefix gives the carbon content and the point group symbol; the bracketed numbers indicate the ring sizes in the fullerene. The latter is important in fullerenes with rings other than five- and six-membered. The subscript parenthetical (6) following the point group symbol D_5h in the latter name indicates that the five-membered ring on the five-fold symmetry axis is surrounded by six-membered rings. This distinguishes this fullerene from an isomeric (C₇₀-D_5h)[5,6]fullerene having five-membered rings surrounding the five-membered ring on the five-fold symmetry axis designated by the name (C₇₀-D_5h(5))[5,6]fullerene. In the present document, fullerene structures are unambiguously identified by CAS Registry Number and the reference numbers of An Atlas of Fullerenes, if available [ref 5].

The recommendations are largely based on those reported in ref. 4, and can in principle be used for numbering all fullerenes. One of the aims pursued with the development of these recommendations was to devise a numbering method that is simpler than the existing CAS procedures [ref 3], that uses symmetry elements as reference entities, and can be applied "manually" by the chemical public to a structural drawing of a fullerene. It soon became clear that such a method, allowing a relatively easy search for a preferentially contiguous and pretty unambiguous numbering of "small" fullerenes, does not constitute a mathematically robust and absolutely unambiguous numbering procedure for any given fullerene structure - an endeavor that would require computational methods. This antagonism is underpinned by the number of possible C_n isomers which increases overwhelmingly with n: for example, there are 31 924 isomers of (C₈₀)[5,6]fullerene (enantiomeric pairs being counted as one) and contiguous paths of interconnected vertices cannot be found for all of them [ref 5]. On the other hand, the practicability of the present system was tested successfully on sixty-nine fullerenes (including most of the isolated and structurally characterized carbon cages), and it can be expected to perform well in the entire range of "small" fullerenes. It should finally be mentioned that this method conveniently provides the same numberings as the CAS procedure [ref 3] for (C₆₀-I_h)[5,6]fullerene and (C₇₀-D_5h(6))[5,6]fullerene which are the objects of the vast majority of publications on fullerenes.

2. General Considerations on Fullerene Numbering The identification of a well-defined and preferably contiguous helical numbering pathway is the cornerstone of fullerene numbering. Such a pathway represents a double-conical helix in the sense that, starting from a given atom (a "pole" of the spheroid), reaches all the other atoms of the fullerene moving in a clockwise or anticlockwise direction through the two "hemispheres" to reach the opposite "pole". (In a Schlegel diagram with the starting point of the numbering located at the center of the representation, the pathway corresponds to an expanding spiral.) The construction of the pathway starts with the numbering of a whole elementary ring of the fullerene. Then, the numbering proceeds to cover all of the other atoms keeping the pitch of the helix as small as possible (i.e. keeping the movement "as tight as possible") and maintaining its clockwise or anticlockwise directionality.

1. International Union of Pure and Applied Chemistry. "Nomenclature and Terminology of Fullerenes: A Preliminary Report", E.W. Godly and R. Taylor, Pure Appl. Chem. 1997, 69, 1411-1434.

2. R. Taylor, J. Chem. Soc., Perkin Trans. 2 1993, 813-824.

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