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I would like to know the mechanism of this reaction. In my first attempt to the question, I had replaced the two $\ce{Br}$s by $\ce{CH3}$s by $\ce{S_N2}$ of the organometallic compound but the answer given was the above allene. I think my reaction isn't possible because of too much hindrance. So if that's the case, then what is the mechanism of the actual reaction?

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    $\begingroup$ Lithium-halogen exchange $\endgroup$ – Waylander Jul 11 '18 at 21:20
  • $\begingroup$ Yeah, it's definitely redox with rearrangement. $\endgroup$ – Mithoron Jul 11 '18 at 22:16
  • $\begingroup$ Just to be more explicit, replace one of the bromides with a lithium, i.e., a carbanion. Then, you should be able to draw a rearrangement that gives the allene. $\endgroup$ – Zhe Jul 11 '18 at 22:22
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    $\begingroup$ In this case it is because you have not added any carbons to the molecule. MeLi is not a great nucleophile for alkyl halide in general, principally because lithium-halogen exchange is an alternative pathway. $\endgroup$ – Waylander Jul 12 '18 at 7:40
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    $\begingroup$ Note that the paper referenced states " Tetra-substituted allenes can not be prepared by the reaction of tetraalkyldibromocyclopropane and methyl lithium. " $\endgroup$ – Waylander Jul 12 '18 at 11:37
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This is the Skattebøl rearrangement, the first step is of which is a lithium-halogen exchange to form a carbenoid. A mechanistic study of the rearrangement of monosubstituded lithium bromocyclopropylidenoids found that allene formation can occur either in a concerted (Scheme 2) or step-wise (Scheme 3) fashion depending on the ability of the substituent to stabilize the intermediate carbene$^{[1]}$.

Schemes

The study found that electron donating groups (like the methyl groups in your example) lower the barrier to allene formation. For several EDG-substituted species, the free carbene structure 14 could not be found as an energy minimum and all attempts to locate these structures lead directly to allenes. This means the stepwise mechanism does not play a role in the Skattebøl rearrangement for EDG-sbustituded species$^{[1]}$.


$[1]$ Azizoglu, A.; Balci, M.; Mieusset, J.-L.; Brinker, U. H. The Journal of Organic Chemistry 2008, 73 (21), 8182–8188.

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