Dimethylcyclopropyl carbocation

Cyclopropyl carbocations react rapidly to form allyl carbocations. Explain how this process is allowed. Explain why the allyl carbocation is more stable than the cyclopropyl carbocation. Predict the stereochemistry of the allyl carbocation that is formed from the following c/s-dimethylcyclopropyl carbocation ... 

The opening of a cyclopropyl carbocation to form an allyl carbocation is an electrocyclic reaction involving two electrons. Because it involves an odd number of electron pairs, disrotatory opening is thermally allowed. The allyl carbocation is much more stable than the cyclopropyl carbocation because of resonance stabilization and relief of ring strain, so the allyl carbocation is favored. The thermal ring opening of the c/s-dimethylcyclopropyl carbocation occurs with a disrotatory motion. 

The three C—C bonds of cyclopropane are equivalent since both of the le pair of orbitals are occupied. The two components, however, have different capabilities of interaction with a ring substituent. For example, the dimethylcyclopropyl carbo-cation is more stable in the bisected conformation 11.5a than in 11.5b. In fact, the rotational barrier between the two, as determined by NMR methods, is very large 14kcal/mol) [I I]. As shown in 11.6, this arises simply because the carbocation... 

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