Would the carbocation intermediate undergo rearrangement?

Question

I have my concerns regarding option (a) in this question.

During the dehydration step, wouldn't the resulting carbocation intermediate formed in option (a) rearrange?
That is, the ring should contract from a $7$-carbon to a $6$-carbon one because the resulting carbocation would be more stable. But the resulting product would have to be an addition product since elimination now becomes impossible.

I know that this situation can arise because I have tackled it before and the answer was an addition product in that case, but that reasoning contradicts with the official answer key in this question. (The answers are a,b and d).

The shift I called for was the bond between carbon (endocylic with nitrogen) and the carbocation.

Answer 1

Unfortunately, I cannot back this with references at the moment but in my opinion there should be no carbocation formed in the first place and therefore no tendency to undergo any Wagner-Meerwein rearrangements.

Secondary carbocations, while being less unstable than primary ones, are still rather unstable. There are no stabilisation mechanisms that suggest themselves in the reaction conditions (concentrated sulphuric acid) in which the nitrogen will be protonated and therefore unable to stabilise a carbocation in α position. I would assume that the elimination proceeds much more $\mathrm{E2}$-like: likely with no intermediate carbocation at all but if there is one it should be extremely short lived and the neighbouring proton should dissociate practically instantly.

Answer 2

After 3 years perhaps this post requires a fresh look. An Olympiad question is unlikely to want to bog down a participant hunting for myriad rearrangements. Rather than obsess over rearrangements, perhaps one should start at the end of the problem where 1,3,5-cycloheptatriene (6) is the final product. The presence of a cycloheptane ring is not available in structures c and e. However, the remaining structures a, b and d do contain cycloheptane rings and are all candidates as structure C. What is required is the introduction of three double bonds, one by dehydration and two by successive Hofmann eliminations.

Achiral 1 is formed from a upon dehydration while rac-2 arises from b. Compound d leads to two possible alkenes, achiral 3 and rac-4. Bicyclic unsaturated amines 1 - 4 (structures J) are all candidates for successive Hofmann exhaustive eliminations. continued

Historical Note: One of the epimers of alcohol b is tropine, one of the components of atropine. The dehydration of b to alkene 2 and it subsequent oxidation leads to tropinic acid 6 (R=H). Its ester proved to be critical to the young career of Richard Wilstätter. When he performed a single exhaustive methylation on the ester, an ether soluble amine was obtained leading to the conclusion that tropine is a bridged amine. The text below is from his autobiography, From My Life, available through Amazon for the Kindle or online at the Hathi Trust, if you have access. A must read for both aspiring and accomplished chemists.

Answer 3

There are multiple possibilities for this reaction, elimination may not come first, Wagner-Meerwein rearrangements may occur before this. For both A and B, rearrangement occurs before elimination. For D it is straightforward, the -OH will be eliminated and the corresponding alkene will be formed. For B, the -OH will first be protonated, the carbon nitrogen bond of the bridgehead carbon farther away will be broken. The nitrogen atom will then form a bond with the carbon having the -OH2 substituent, the loss of water will follow. This generates D, but a carbocation is in place of the -OH group. This compound can undergo elimination to generate the same alkene as D generated. Your question is pertaining to the lack of rearrangement of the carbocation. It cannot rearrange to one of the tertiary bridgehead carbons, because of Bredt's rule. So when heating in concentrated sulfuric acid, the major elimination product will be the alkene mentioned previously. While B and D proceed through this alkene, A proceeds through a Wagner-Meerwein rearrangement similar to B. This yields a carbocation. This carbocation will rearrange (but not in the context you had) because of angle strain on the adjacent carbon. The rearrangement increases stability and elimination then occurs to yield the same product as B and D. This then undergoes transformation to cycloheptatriene under the conditions provided.