The isolated Pentagon Rule (IPR), the special nature of C28 and icosahedral carbon particles

IPR and C28 Nature paper


The origin of this paper was a result by the Rice group which indicated that multiphoton disassociation of C60 proceeded by elimination of C2 groups sequentially i.e. C58 > C56 > C54 etc down to C32 at which point C32 essentially exploded. This led the Rice group to suggest that this was a smallest possible following fullerene. While sitting at our Lewes coffeetable one Sunday afternoon playing with molecular modelling kit I wondered what possible structure of C32 might be. I produced a model and realised it was not C32 but C28 and was suddenly exhilarated because I remembered that we had an experimental run in which the C28 signal was very strong indeed. When I examined the structure of the C28 molecule I had constructed I realised that it might be rather special in that it was tetrahedral and if it added four hydrogen atoms to the for tetrahedral C corner atoms then it still retained four aromatic six-membered rings and the corner atoms would become SP3 and would be relaxed. This suggested that C28 might be a cluster super atom tetravalent analogue of the carbon atom.


Several years later the Rice group published a paper in which they showed this tetravalency conjecture was justified in that they observed U@C28 where the tetravalency was satisfied by an endohedral of Uranium atom.

The Isolated Pentagon Rule IPR

In this paper I also conjectured that C60 was stable because it was a smallest cage which could be constructed with 5 and 6 membered rings in which all the pentagons were isolated. I then wondered when this Isolated Pentagon Rule requirement was satisfied again and found that I could not make one between C60 and C70 and conjectured that if C60 was a stable truncated icosahedron as we have proposed then C70 must be the next special structure. As we had seen that C70 was the next special structure experimentally this seemed to me to be the most convincing circumstantial evidence for the validity of our buckminsterfullerene structural proposa prior to its isolation in 1990.

I knew that the Galveston group had the quantum chemistry experience to verify my conjecture that no IPR structure existed between C60 and C70 and called them up on the telephone. Tom Schmalz told me that they had reached the same conclusion and said they had almost completed the proof of this conjecture.

Our recent work at FSU/Maglab has confirmed these early observations and shown that indeed C28 is very special indeed and can satisfy its tetravalency by trapping a tetravalent individual atom such as Ti, Zr or U

J. Am. Chem. Soc., 2012, 134 (22), pp 9380–9389
Abstract Image

The smallest fullerene to form in condensing carbon vapor has received considerable interest since the discovery of Buckminsterfullerene, C60. Smaller fullerenes remain a largely unexplored class of all-carbon molecules that are predicted to exhibit fascinating properties due to the large degree of curvature and resulting highly pyramidalized carbon atoms in their structures. However, that curvature also renders the smallest fullerenes highly reactive, making them difficult to detect experimentally. Gas-phase attempts to investigate the smallest fullerene by stabilization through cage encapsulation of a metal have been hindered by the complexity of mass spectra that result from vaporization experiments which include non-fullerene clusters, empty cages, and metallofullerenes. We use high-resolution FT-ICR mass spectrometry to overcome that problem and investigate formation of the smallest fullerene by use of a pulsed laser vaporization cluster source. Here, we report that the C28 fullerene stabilized by encapsulation with an appropriate metal forms directly from carbon vapor smallest fullerene under our conditions. Its stabilization is investigated, and we show that M@C28 is formed by a bottom-up growth mechanism and is a precursor to larger metallofullerenes. In fact, it appears that the encapsulating metal species may catalyze or nucleate endohedral fullerene formation.

Icosahedral carbon particles

a simple model building exercise led to the conclusion that closed large fullerenes would have quasi-icosahedral structures. This project was really an arts one in that I wanted to build a large fullerene structure really as a sculpture. To my surprise it was not round like Buckminster Fuller’s Montréal dome but as all the curvature was focused around the pentagons and surface is essentially flat between them this resulted in an explanation of why spheroidal carbon particles have the quasi-icosahedral structures that had been observed. This is a nice example of an arts project resulting in a science breakthrough… An unusual situation.

GiantModel960 new1.2 Onion 4 shell Simulation

formation of quasi-ocosahedral spiral shell carbon particles_1988 NATURE_kroto