A conflation of concepts: Conformation and pericyclic.

This is an interesting result I got when studying the [1,4] sigmatropic rearrangement of heptamethylbicyclo-[3.1.0]hexenyl cations. It fits into the last lecture of a series on pericyclic mechanisms, and just before the first lecture on conformational analysis. This is how they join.

The experiment it relates to[1] may well be a contender for the top ten list of most influential experiments ever conducted in chemistry. At -40°C, the ¹H NMR spectrum of this species has three peaks, at δ2.06, 1.57 and 1.13 ppm with an integral ratio of 15:3:3. The five basal methyls are averaged to 2.06 ppm, whereas those marked above as Me_a and Me_b exhibit distinct separate resonances. At -90°C, the five basal methyls split into peaks at δ2.48, 2.02, 1.66, in the integral ratio of 6:3:6. This indicates a process that is slow at the lower temperature but becomes fast (on the NMR time scale) at the higher temperature. The process must retain the individual identity of Me_a and Me_b.

The explanation is of course that a pericyclic [1,4] sigmatropic shift occurs. As a four electron process, this must have one antarafacial component, and this is by far easier to achieve by inverting the configuration at the migrating carbon centre. To convince oneself that this process does indeed retain the individual identity of Me_a and Me_b, an IRC of the reaction can be computed (ωB97XD/6-311G).

The energy profile is smooth and springs no surprises. The barrier is about right for the temperatures noted above.

But the RMS gradient norm along the IRC is unexpected. 

1. Between the limits IRC ± 9, the profile is that of a reaction, involving bonds breaking and forming.
2. In the range IRC ± (9 – 15), unexpected features appear (hidden intermediates if you check this post). A whole plethora of them. This is the conformational region where the methyl flags start waving (and no bonds are formed or broken). If you watch the animation above very carefully, you will note that the methyl groups start rotating at the start and at the end of the migration, at a stage when the ring has an allyl cation. This delocalised cation has a different impact upon the conformation of the methyl groups from that of the transition state, where the charge now resides largely on the migrating carbon, and the ring now has just a neutral butadiene. This latter imparts a different conformational preference upon the methyl groups. You can see an orbital analysis of these effects at this post.
3. But perhaps the most surprising aspect of all of this is that each methyl flag waves at a different time from the others; first one waves, then the second and then the third. The two remaining basal methyls (attached to sp³ carbons) do not wave at all.

So this classic reaction is not just a pericyclic exemplar, it also illustrates nicely and concisely the conformational analysis of methyl groups interacting with an unsaturated system. Two for the price of one so to speak.

References

1. R.F. Childs, and S. Winstein, "Ring opening and fivefold degenerate scrambling in hexa- and heptamethylbicyclo[3.1.0]hexenyl cations", Journal of the American Chemical Society, vol. 90, pp. 7146-7147, 1968. http://dx.doi.org/10.1021/ja01027a059