http://pubs.acs.org/doi/abs/10.1021/ja302398h

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 proposal prior to its isolation in 1990.  I wanted to publish an image of our ms showing C28 dominant but the request was denied so here can be found one from our recent work at FSU. I also conjectured that Multiplet IPR metastability criteria (MIPR) might operate for fullerenes smaller than C60 such as C50

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. So the IPR was developed simultaneously and independently by the Galveston group which furthermore proved it elegantly. They also proved the MIPR concept in their comprehensively exhaustive theoretical study.

http://pubs.acs.org/doi/abs/10.1021/ja00212a020Capture Schmalz paper