When Do Ring Expansions in Alicyclic Carbocations Occur?

[loom91]

Hi,

I'm having some difficulty predicting favourable rearrangements in alicyclic carbocations. When, why and how does a ring in a carbocation expand? I've seen some drawings (not sure whether they are correct though) where tertiary carbocations undergo ring expansion to a secondary carbocation. This seems very strange to me. For example, consider the attached reaction. We were asked to predict the product in an exam. The given solution is also attached. How can this happen? Also, why do carbocations rearrange so easily? Thanks.

Molu

 

[GCT]

Thermodynamically, the product is more stable then the reactant which contains a cyclopropane ring; versus a more open ring system (cyclohexane and cyclopropane). Subsequent methyl and hydride migrations may result in the product, although I would need to draw out the mechanism to understand whether this is actually the case.

 

[Gokul43201]

The reaction mechanism for this problem is fairly guessable, and can be achieved (from my best guess, and Organic is my poorest subject, so take what I say with a pinch of salt) with only one of those uncomfortable tertiary-to-secondary shifts.

I would imagine that in general, for a pair of fairly complex alternatives, it would be hard to actually know which is more stable - as in a case like this one, you'd have to have a good quantitative intuition for comparing steric energy (and possibly, energy contributions from n resonances) with hyperconjugation energy (and contributions from inductive stabilization).

How on Earth can you be expected to have a good idea for something like that?

Well, for the most part, isn't that how chemistry is? Someone does a gazillion reactions, finds equilibrium constants and estimates contributions from various factors. I imagine if you look through a large number of known reactions, you'll find you get a good sense for what is preferred and what isn't. Or, if you're lucky, someone may have done this already and put out some rules of thumb.

PS: As for the solution to the posted problem, you know the rules...

 

[loom91]

The reaction mechanism for this problem is fairly guessable, and can be achieved (from my best guess, and Organic is my poorest subject, so take what I say with a pinch of salt) with only one of those uncomfortable tertiary-to-secondary shifts.

I would imagine that in general, for a pair of fairly complex alternatives, it would be hard to actually know which is more stable - as in a case like this one, you'd have to have a good quantitative intuition for comparing steric energy (and possibly, energy contributions from n resonances) with hyperconjugation energy (and contributions from inductive stabilization).

How on Earth can you be expected to have a good idea for something like that?

Well, for the most part, isn't that how chemistry is? Someone does a gazillion reactions, finds equilibrium constants and estimates contributions from various factors. I imagine if you look through a large number of known reactions, you'll find you get a good sense for what is preferred and what isn't. Or, if you're lucky, someone may have done this already and put out some rules of thumb.

PS: As for the solution to the posted problem, you know the rules...

Is there any general rule-of-thumb about when relieving angle strain in ring takes precedence over inductive/hyperconjugative stabilisation of the tertiary variety over the secondary one? Also, I think ring expansions can't happen simply through migrations. There would have to be sigmatropic rearrangements. If that is the case, wouldn't it also be necessary to consider symmetry rules? Thanks.

Molu

 

[Gokul43201]

If there was, I don't expect I'd know about it.

Yes, I think ring expansions are sigmatropic, but again, you shouldn't be listening to me. Mostly, I'm bumping this up, hoping chemistree takes a look at it.

 

[chemisttree]

Sigmatropic rearrangements are those that result in the formation of a new sigma bond. Not very useful as an adjective if you are trying to understand mechanisms.

Symmetry is not applicable here as you would expect in Diels-Alder type reactions since the system does not involve concerted addition across conjugated pi systems.

Obviously a ring expansion has occurred since a three-member ring is no longer present. But has it expanded into a 5-member or 6-member ring?

Add the HCl across the double bond (markovnikov, of course) and see where the cation should reside. I found it to be on the tertiary carbon of the cyclopropyl ring or, after two hydride migrations, on the tertiary carbon of the 5-member ring. After that nothing makes any sense. Every path I examined either had a 5-bonded carbon intermediate or required several sequential hydride shifts to achieve something reasonable.

I found that if the original 5-member ring had one double bond in conjugation with the one exo to the cyclopropyl ring, the predicted product is very straightforward to rationalize. Did you get the structure correct in your original post?

Did your teacher provide a rationalization for the answer? I suspect not...