Sarah J. Austin

Fullerene isomers of C60. Kekulé counts versus stability

Abstract A count of Kekule structures for all 1812 distinct fullerene isomers of C60 shows that 20 isomers surpass the count of 12500 for icosahedral C60, and demonstrates the lack of correlation between molecular-orbital indices of stability and raw Kekule counts for fullerenes. Analysis of Kekule structures in terms of benzenoid, cyclopentenoid and cyclopentadienoid rings reveals the source of the stability of icosahedral C60 in a localised model to be the fact that uniquely amongst the 1812 structural isomers it has a Fries Kekule structure where all hexagons contain three double bonds and all pentagons none.

The Stone-Wales map for C60

Abstract The possible Stone-Wales (pyracylene) rearrangements amongst C 60 fullerenes generate a graph in which buckminster-fullerene is linked to 1709 of the other 1811 fullerene isomers. Only one major bottleneck exists on this main map; all routes to icosahedral C 60 pass through a single isomer of C 2v symmetry. When energies of all isomers computed in the semi-empirical QCFF/PI model are combined with the map, it is found that stability generally decreases with the number of Stone-Wales steps away from the icosahedral isomer and that the 877 most stable isomers are on the main map. Implications of the map for the pentagon and fullerene road models of C 60 formation are discussed.

Relative stabilities of C76 isomers. A numerical test of the fullerene isolated-pentagon rule

Abstract C 76 has 19151 possible fullerene structural isomers of which up to 55 are compatible with the experimental 19-line 13 C NMR spectrum, but only two have isolated pentagons. Calculations of the relative energies of all 55 candidates within the semi-empirical QCFF/PI model pick out the isolated-pentagon D 2 isomer as the structure of lowest energy for C 76 , confirming previous calculations and providing support for the isolated-pentagon rule. Energy differences between isomers of C 76 are interpreted in the model as torsional strains induced by pentagon adjacencies.

Symmetry properties of the leapfrog transformation for fullerenes and benzenoids

Abstract Application of the leapfrog procedure of omnicapping and taking the dual (inner dual) to a fullerene (benzenoid hydrocarbon) yields a closed-shell fullerene (total resonant sextet benzenoid) with a π configuration that can be predicted from the symmetry spanned by the edges (face centres) of the parent molecule.

The isomer problem for fullerene derivatives: structural proposals for C70H36

Abstract Calculations are performed on the optimal structures and relative stabilities of the experimentally identified but as yet uncharacterized C70H36 molecule. A model in which addition preserves nominal aromaticity is tested against semi-empirical MNDO calculations and found to be inadequate: large aromatic regions on the surface of the C70 cage would demand planarity and, hence, imply large steric strain. A structure with isolated double bonds in the polar caps and conjugation in a cyclopentaphenyl belt is predicted to be more stable by some 300 kJ mol−1 than the nominally aromatic isomers, but the most stable structure found so far, improving by about 85 kJ mol−1 on all previously published proposals, has 17 localized double bonds, one in each polar cap and the others in three bands of five around the C70 cylinder, the low strain of their arrangement apparently outweighing the total loss of π delocalization.

Theoretical characterisation of C70Cl10: the rôle of 1,4-addition across hexagonal rings

Four isomeric structures of decachloro[70]fullerene are compatible with the 13C NMR spectrum and qualitative stability rules; explicit calculation at the semi-empirical level shows the most stable isomer to be that which maximises the number of 1,4-chlorine additions whilst excluding double bonds from pentagons.

Bond-stretch isomerism and the fullerenes

It is argued that because many fullerene molecular graphs admit multiple totally symmetric Kekule structures, the fullerene class of molecules may provide examples of bond-stretch isomerism (π-tautomerism). Calculations on the prototype D2 isomer of C28 demonstrate the existence on the potential surface for 28 carbon atoms of at least three enantiomorphic pairs of fullerene minima of this symmetry, all with the same connectivity. The three patterns of long and short bonds in these isomers are ‘Orthogonal’ in that any one CC bond is formally double in precisely one and formally single in precisely two of the structures.

Closed-shell carbon frameworks: Leapfrog fullerenes and decorated spheriphane hydrocarbons

Two geometrical constructions generate structures with closed A shells from an arbitrary fullerene graph. In the first, closed-shell fullerenes are given by the leapfrog transformation. The starting fullerene is capped on every face and then dualized, producing a new cage of the same symmetry with three times as many atoms, isolated pentagons, and a guaranteed closed shell. Leapfrog fullerenes have n = 60 + 6k (k # 1) atoms, and together with the cylinder series (70 + 30k and 84 + 36k (all k)) they exhaust the known properly closed-shell fullerenes up to Clw. In the second, decoration of a fullerence skeleton replacing each vertex by a (1, 3, 5)-linked C6H3 hexagon produces the spheriphane hydrocarbon series C2mHm where m is 60 + 6k (k # 1). Each molecule has a closed A system, a fixed HOMO-LUMO gap, and a A energy that is independent of the starting isomer.

Is aromaticity a useful concept for C60 and its derivatives? Aromatisation of C60 by regioselective addition

Qualitative symmetry arguments, evidence from bondlengths and energies, and from the addition chemistry of C60 point to a localised description of the π system of this molecule. Regioselective saturation of six double bonds in C60 is predicted to lead to an alternant delocalised (aromatic)π system that is realised in at least one well characterised compound.

Structural Proposals for C70H36

Abstract Calculations are performed on optimal geometries and relative stabilities of 48 new candidates for the structure of the experimentally identified but as yet uncharacterised C70H36 molecule. Three structures with entirely unconjugated π systems, which differ only in the siting of the double bond in each polar pentagon, are more stable than all others by ~ 45 kJ mol−1 in the MNDO model. Localisation alone does not ensure stability, but the low strain of this particular arrangement apparently outweighs the total loss of π delocalisation energy. Presented at Symposium on Expanded Horizons of Fullerene Science and Technology organized by L.Y. Chiang, E. Osawa, H. Terrones and M.Saunders at the IVth International Conference on Advanced Materials, Cancun, Mexico, August 27-September 1, 1995.