Dancing resonance or Sigma Resonance:

Dancing resonance is a special stability mechanism which increases stability of carbocations attached directly to the three membered rings. For example Cyclopropylmethyl Carbocation.

In cyclopropane all the carbon is sp3 hybridized and the bond angle for the same should be 109 degree 28′ but the actual bond angle is 60 due to which angle strain develops. So in order to minimize the strain p orbital bents due to which it acquires partial sigma and partial pi bond character which behave like pi bond. And resonance take place between sigma and vacant p-orbitals hence called P-orbitals overlapping or sigma resonance.

We know by Drago’s rule bond angle is directly proportional to the s-character while inversely proportional to p-character.  

Dancing resonance is a hypothetical phenomenon which is reduces strain of the ring, hence the carbocation is more stable.  CH₂⁺ has a vacant p orbital and a very effective overlapping takes place between p-orbital and electron density of cyclopropane, due to this its stability is very high. There is a conjugation between the sigma bond and positive charge.

The exceptional stability of cyclopropane methyl cation can be explained by the concept of dancing resonance concept. The stability of additional cyclopropyl group , is result of more conjugation between the bent orbital of cyclopropyl ring and cationic carbon.

The most stable carbocation known till date in organic chemistry is explain by Dancing resonance.

ILLUSTRATIVE EXAMPLE: Why is the Tropylium carbocation less stable than the tricyclopropylmethyl carbocation?

Why is the Tropylium carbocation less stable than the tricyclopropylmethyl carbocation?

Tropylium is highly stable due to conjugated system, that being resonance stabilized and the number of canonical forms of tropylium is more. But it is less stable than tricyclopropylmethyl carbocation because tricyclopropylmethyl carbocation undergoes a strong  stability mechanism factor that is sigma resonance or dancing resonance  (sigma-tropic rearrangement ).

What is Bredt's rule ?

The Bredt’s rule is relates to bridgeheads with carbon-carbon and carbon-nitrogen double bonds. This rule is  first discussed by german Scholar  Bredt’s  in 1902.

According to Bredt’s rule a bridgehead carbon atom of bicyclo compound cannot be sp2 hybridised or in other word a bridgehead carbon atom cannot be form double bond. unless the ring that contains at least eight atoms 

In Other word Bredt's rule state that planarity is not possible at bridge head carbon of bicyclo compound till one of the ring size is (8) eight member or more.

   

ILLUSTRATIVE EXAMPLE: Bredt's use for the predicting major and minor  product of elimination reactions.