Carbocations rearrangement is a phenomenon consisting in the riorganization of the structure of a molecule that allows to obtain a carbocation more stabilized (give a look to → carbocations stability). A primary carbocation will therefore rearrange to give a secondary carbocation, while a secondary carbocation will rearrange to tertiary carbocation. Rearrangements generally involve to adjacent carbons and are therefore called 1-2 rearrangements, where a methyl group or just a single hydrogen atom move from the carbon adjacent to the carbocation to the carbocation itself.
The methyl group displacement is called "alkyl shift" whyle the hydogen displacement (although hydride is more suitable, as we're going to see) is called "hydride shift".
Is quite common that a carbocation rearrangment is the reason why a reaction gives a mixture of different products when we are expecting just a single product.
The easiest method to obtain a carbocation is alcohol dehydratation in acid environment.
The imagine makes clear how a (CH3-) group moves (rearrange) on the position occupied by the primary carbocation leaving a positive charge on the carbon to whom was previously bonded. Usually is not physically possible to intercept the carbocation, that quicly eliminates a proton H+ to give the corresponding alkene (observing Zaitsev's rule):
It follows the same modalities of the alkyl shift, but this times an H- ion moves on the carbocation:
Why this time an hydride moves on the carbocation instead of a methyl group? Actually, is not that strange.
It's generally true that the rearrangement is given by the lighter group. In this specific case the carbon in position 2 (adjacent the carbocation) carries three different groups: a propyl, a methyl and an hydrogen. Without any doubt, the ligher of the three and therefore rearranges to give the more stabilized carbocation.
The rearrangements gives the more stabilized carbocation. When the hydride moves on the carbocation the result is a tertiary carbocation, while in the other cases the rearrangement would lead to a secondary carbocation.
Different rearrangements→ ring expansion reaction
In this case we expected the hydride to move on the carbocation, but that is not what actually happens, because prevails the attitude to reach a more stable (energetically) ring, considering that a six terms ring is more stable than a five terms ring. The following elimination gives the corresponding alkene (consider that a double bond can eventually be eliminated through hydrogenation or can be a substrate for different reactions).
The following example is particularly interesting (exceptional) because starting from a seven and five atoms condensed cycles, (quite easily to obtain esperimentally), we arrive to a eight and four atoms condensed cycles. This means that we get a cycle with one more atom and the other with an atom less. This kind of cycles because of their instability are quite difficult to synthesize, and that's why this specific reaction is so important.