Ring expansion means rearrangement

This time the cation is formed by protonation of an alkene, not departure of a leaving group, but writing a mechanism should now be a straightforward matter to you. 

Though the rearrangement step transforms a stable tertiary cation into a less stable secondary cation, relief of strain in expansion from a four- to a five-membered ring makes the alkyl migration favourable. In 1964, E.J. Corey published a synthesis of the natural product a-caryophyllene alcohol that made use of a similar ring expansion. Notice the photochemical [2+2] cycloaddition (Chapter 35) in the synthesis of the starting material. 

Rearrangement of this tertiary alcohol in acid gives the target natural product. The four-membered ring has certainly disappeared but it may not be obvious at first what has taken its place. 

As usual, numbering the atoms makes clear what has happened carbon 7 has migrated from carbon 6 to carbon 5. Loss of water gives a tertiary carbocation that undergoes rearrangement to a secondary carbocation with expansion of a four- to a five-membered ring. 

that depends. You have now seen a few useful carbocation rearrangements that give single products in high yield. But you have also met at least one reaction that cannotbe done because of carbocation rearrangements Friedel-Crafts alkylation using primary alkyl halides. 

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If the migrating carbon is part of a ring system, the Stevens rearrangement products arise by means of a ring expansion. For example, treatment of pyrrolinium salt 9 with base led to the isolation of a crystalline pyrrolinium ylide that gave the rearranged derivative 10 on further heating.12 Similarly, ylide 11 was smoothly transformed into amino ketone 12.13... 

Scheme 11/19. The Beckmann rearrangement as a mean for ring expansion.

Most such heterobicyclic substrates are fused pyrazines from which the second ring must be removed completely or in part by oxidation, hydrolysis, or some other means to afford the desired monocyclic pyrazine derivatives. However, some such bicyclic substrates do not already incorporate a pyrazine ring, so that more profound processes (like rearrangement, ring expansion, or use of a cosynthon) must be employed to furnish pyrazines. 

Hydrolytic cleavage of the C-O bond of bicyclic, tetracyclic, and steroidal enolates with HF-SbFs induces their isomerization to the corresponding ketones (Scheme 14.41) [104]. Rearrangement of dienones to aromatic compounds is also promoted by HF-SbFs (Scheme 14.42) [105]. Ring expansion of methyl penicilli-nates is achieved by SbCls to give thiazepine derivatives [106]. 1,3-Dithianes derived from ketones and aldehydes are deprotected with SbCls by means of a single-electron-transfer mechanism [107]. 

The ring expansion of substituted piperidines by means of free-radical-induced rearrangements has been used to prepare fully saturated azepines <91T4847>. Ethyl l-benzyl-3-oxo-4-phenyl-selenomethylpiperidine-4-carboxylate (259) is converted into the azepinone (260) by tri-n-butyl tin hydride in benzene under reflux in the presence of AIBN (Equation (21)). The reaction works also with ethyl 3-phenylselenomethyl-4-oxo-piperidine-3-carboxylate, preferably with the benzyl group replaced by a trityl group. 

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