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.

What is the Inversion of Amines ?

Inversion of amines takes place at room temperature and required 64 k j per mole energy.

An amine such as ethyl methyl amine has a tetrahedral (sp3) nitrogen atom, and the nitrogen lone pair in an sp3 orbital. However this tetrahedral amine structure is not static. It is found that the nitrogen atom inverts. The lone pair disappears from one face, moves through the nucleus, and reappears on the opposite face. The lone pair repels the ethyl group, the hydrogen atom, and the methyl group, so as the lone pair reappears, these groups move away. As the lone pair is tunneling through the nucleus, the nitrogen has just three attachments so this nitrogen atom is trigonal planar with sp2 hybridization. Overall flipping of amines is called as inversion of Amine. This magical act is also known as quantum mechanical tunneling.

The tetrahedral amine structures are in equilibrium. Furthermore, these structures are enantiomers. All physical properties of enantiomers are identical except for the direction in which they rotate plane polarized light). From this we can conclude that the two enantiomeric amines are present in equal amounts and have equal stability .

There are two conditions in which a inversion of nitrogen atom does not take place.

1: No Lone Pair:

2: Ring Strain:

When the amine nitrogen is not part of a ring, this bond angle change is easily and inversion takes place. However, if the nitrogen atom is part of a three-membered or a four-membered ring then inversion is significantly retarded by strain.

Effect of Inversion on basicity of amines:

The rate of nitrogen inversion also correlates with, among other things, hybridzation. But in cases where these "other things", such as ring constraints, limit nitrogen inversion, then the rate of nitrogen inversion may not correlate with hybridization. So the rate of nitrogen inversion does not always correlate with hybridization and is therefore not a good indicator of lone pair "availability".

 It is clear that basicity of amines reduced by inversion of amines.

ILLUSTRATIVE EXAMPLE (1): 1-Azabicyclo[2,2,1]heptane is more basic than triethylamine why?.

 SOLUTION:  1-Azabicyclo[2,2,1]heptane is more basic than triethylamine . Because in case of triethylamine the lone pair of electrons is less available in the latter due to rapid nitrogen inversion. Nitrogen inversion is not possible in the bicyclic amine.

ILLUSTRATIVE EXAMPLE (2): Which of the following compound is more basic?

SOLUTION: Option (A) is least basic because Option (B) and (C) both have restriction of inversion hence more basic while option (C) is least basic than option (B) due to –I effect of N-atom to another reduce availability of lone pair of nitrogen atom.

ILLUSTRATIVE EXAMPLE (3):The correct order of decreasing basicity of the compounds is :

SOLUTION:  III > II > IV > I

In Case of Option (III) their is restriction of inversion take place at bridge head nitrogen atom hence it is most basic than (II), while (II) is more basic then (VI) because its lp does not delocalized  while lp of (IV) is delocalized with ring hence less basic  but (I) is least basic to all due to presence of three strong  -I group.

Silicon Carbide(SiC): Carborundum:

Silicon carbide (SiC) is a compound of silicon and carbon. It is extremely rare on Earth in mineral form (moissanite) and it has semiconductor properties. It has a bluish-black appearance. It has a large number of crystalline forms.

Preparation: When Silica treated with carbon at around 2000℃ to 2500℃ give carbide

Properties:(1) SiC also known as carborundum which is very hard .(2) Silicon carbide is inert and not attack by even HF.
(3) Silicon carbide when treated with NaOH give silicates and carbonate .

(4) Silicon carbide is covalent carbide.

(5) Silicon carbide has a high sublimation temperature and is a good heat conductor. It's expansion with increase in temperature is low. Also, it has high electric field breakdown strength.

(6) Silicon carbide exhibits the phenomenon of polymorphism, and hence has a large number of crystalline forms. Alpha silicon carbide is the most common polymorph and has a hexagonal crystal structure, while Beta Silicon Carbide has zinc blende structure.