There most certainly are errors in these schemes, but they are fiendishly subtle. I strongly recommend that you build models of these transition states. Only by building models was I able to look reliably at “9” with the correct configurations at each chiral C and rotate the molecule so that I could see what product 9 would make.
Scheme 1. The drawing of transition state 9 is inconsistent with the drawings of 10 and 7. As the old man said to the tourists, “you can’t get there from here.”
Minor point: the structure of 10 is ambiguous because the configuration of the quarternary C isn’t spelled out in Scheme 1, but the reaction of 10 with HF shouldn’t affect this C so it is reasonable to assume that same configurations for 10 and 7. Once you make this assumption, you should find that if you push forward from 9, you will end up with the mirror image of 7. Or, if you choose to work backwards from 7, you have to find that it requires the mirror image of 9.
Scheme 1 (partial)
Switching enantiomers on the reader is very annoying, but not evil incarnate. Although 9 is a chiral transition state, it is derived from an achiral reactant so 7 must be obtained as a racemic mixture. Still, if the intent of the drawing is to help the reader understand the reaction, this is a bad drawing. The authors should have made 9, 10, and 7 internally consistent.
Scheme 2. Since 13 is drawn in the same orientation as 6 (the precursor to 9/10/7) and Scheme 1 is the only “explanation” in the paper, one is sorely tempted to invoke Scheme 1 again. Obviously, as we saw above, this will produce the wrong configuration at both chiral carbons in 14. Relying on Scheme 1 is less forgivable here because the authors report >97% ee for the reaction. They owe us a scheme that fits the stereochemistry from start to finish.
But the problem turns out to be even worse because Scheme 1 predicts the wrong diastereomer. Notice that the methyl group in 13 becomes an alkene substituent in 14? If we push 13 through the sequence in Scheme 1, the methyl group occupies a pseudo-axial position in the transition state and a cis alkene is the product. 14 is trans. There is simply no way to account for the conversion of 13 to 14 using Scheme 1.
How can we explain the conversion of 13 to 14? It turns out that the “ring flip conformer” of 9 (not the mirror image of 9) can account for the observed reaction. If we flip the ring, we not only change the configuration at the chiral atoms that are being generated in 14, we also move the methyl group into a pseudo-equatorial position which yields a trans alkene. So, when it comes down to it, it is possible to account for the chemistry that is observed, but Scheme 1 is a useless tool for doing this. One wonders if the authors even used this drawing to think about their chemistry or if its contents were just a slip of the mouse.
The two chair transition states discussed above for 13 are shown below. The one on the left looks like the chair in Scheme 1. The one on the right is the “ring flip conformer”. (Note: the caption says ‘paper 6′ because this was paper 6 in 2009.)
transition state models, compd 13, paper 6
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