The nine methyl groups of nonamethylcyclopentyl cation 1 all interconvert with a barrier of 7 kcal mol-1. However, at low temperature only partial scrambling occurs: there are two sets of methyl groups, one containing five groups and the other containing four methyl groups. The barrier for this scrambling is only 2.5 kcal mol-1. While this behavior was found more than 20 years ago, Tantillo and Schleyer1 only now have offered a complete explanation.
The ground state structure of 1 is shown in Figure 1 and has C1 symmetry. The two pseudo-axial methyl groups adjacent to the cationic center show evidence of hyperconjugation: long C-C bonds and Me-C-C+ angles of 100°.
The transition state TS1¸also in Figure 1, is of Cs symmetry. This transition state leads to interchange of the pseudo-axial methyls, and interchange of the pseudo-equatorial methyls, but no exchange between the members of these two groups. The M06-2x/6-31+G(d,p) and mPW1PW91/6-31+G(d,p) estimate of this barrier is 1.5 and 2.5 kcal mol-1, respectively. This agrees well with the experiment.
Figure 1. B3LYP/6-3+G(d,p) optimized geometries.
A second transition state TS2 was found and it corresponds with a twisting motion that interconverts an axial methyl with an equatorial methyl. This TS has Cs symmetry (shown in Figure 1) and the eclipsing interaction give rise to a larger barrier: 7.3 (M06-2x/6-31+G(d,p)) and 6.7 kcal mol-1 (mPW1PW91/6-31+G(d,p)). So twisting through TS2 and scrambling through TS1 allows for complete exchange of all 9 methyl groups.
An interesting point also made by these authors is that these three structures represent the continuum of cationic structure: a classical (localized) cation in TS2, a bridged structure in TS1 and hyperconjugated cation in 1.
(1) Tantillo, D. J.; Schleyer, P. v. R. “Nonamethylcyclopentyl Cation Rearrangement Mysteries Solved,” Org. Lett. 2013, 15, 1725-1727, DOI: 10.1021/ol4005189.