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 Mea and Meb 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 Mea and Meb.
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 Mea and Meb, 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.
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.
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Oh! I also calculate this and similar mary-go-round processes: 10.1134/S1070428007080076
When animated, these look like walkers :) http://limor1.nioch.nsc.ru/quant1.html
Very nice animations. Thanks for the links.