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Marvo Sharks

Acid Catalysed Ring Expansion – Mechanism?

Ring expansion of vinyl cyclobutane -

enter image description here

Could someone please help me with a detailed mechanism for the above conversion?

It is the acid-catalyzed rearrangement of 4,7,7-trimethylbicyclo[3.2.0]hept-3-en-6-one to 3,3-dimethyl-6-methylidenebicyclo[2.2.1]heptan-2-one.

I couldn't find the mechanism anywhere, and couldn't propose a good one either.Please help.

P.S.As one of the users in the comments is interested in seeing my best effort, I'll explain my thought process-As the carbonyl oxygen is the most nucleophilic, it is the first to be protonated in acidic medium. Furthermore, this species has a resonating structure (less contributing, but the only one that can lead to a ring expansion, I believe) – one obtained by shifting the π bond towards oxygen – a carbocation. After this, I'm clueless. I think, that the expansion could have something to do with the hydrogen at alpha position to the sp² hybridised carbon atom in the five membered ring – as the product has an exocyclic double bond.

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