Huckel’s Rule: 4n + 2 Rule and Aromaticity

What is Huckel’s Rule?

Huckel’s Rule is used in order to estimate the aromatic qualities of any planar ring-shaped molecule in the field of organic chemistry. The supporting quantum mechanics required for the formulation of this rule was solved first by the German physical chemist and physicist Erich Armand Arthur Joseph Huckel in the year 1931.

The Huckel 4n + 2 Pi Electron Rule

A ring-shaped cyclic molecule is said to follow the Huckel rule when the total number of pi electrons belonging to the molecule can be equated to the formula ‘4n + 2’ where n can be any integer with a positive value (including zero).

Examples of molecules following Huckel’s rule have only been established for values of ‘n’ ranging from zero to six. The total number of pi electrons in the benzene molecule depicted below can be found to be 6, obeying the 4n+2 𝛑 electron rule where n=1.

Huckel's Rule Confirms Benzene Aromaticity

Thus, the aromaticity of the benzene molecule is established since it obeys the Huckel rule.

This rule is also justified with the help of the Pariser-Parr-Pople method and the linear combination of atomic orbitals (LCAO) method.

Generally, aromatic compounds are quite stable due to the resonance energy or the delocalized electron cloud. For a molecule to exhibit aromatic qualities, the following conditions must be met by it:

  • There must be 4n + 2 𝛑 electrons present in a system of connected p orbitals (where the electrons are delocalized) belonging to the molecule.
  • In order to meet the first condition, the molecule must have an approximately planar structure wherein the p orbitals are more or less parallel and have the ability to interact with each other.
  • The molecule must have a cyclic structure and must have a ring of p orbitals which doesn’t have any sp3 hybridized atoms.

Other examples of aromatic compounds that comply with Huckel’s Rule include pyrrole, pyridine, and furan. All three of these examples have 6 pi electrons each, so the value of n for them would be one.

Stability of Monocyclic Hydrocarbons

The stability of monocyclic hydrocarbons, their cations, and their anions can be understood with the help of the Huckel Rule. A great example of such a monocyclic hydrocarbon is benzene.

It can be observed that benzene tends to undergo substitution reactions wherein the number of pi electrons remains the same in the product. Benzene does not tend to take part in addition reactions which would cause it to lose its pi electrons. However, catalysts are generally a prerequisite for the benzene molecule to participate in a substitution reaction. This stability of the pi electron system belonging to benzene is often referred to as ‘aromaticity’.

Considering the example of cyclopentadiene, its corresponding anion (cyclopentadienyl anion) can easily be generated since it has six pi electrons and is quite stable. On the other hand, the cation of cyclopentadiene only has four pi electrons, which implies that it does not exhibit aromaticity as per Huckel’s rule. This cation is quite difficult to generate, especially when compared to its acyclic counterpart – the acyclic pentadienyl cation.

Thus, Huckel’s rule is very useful in the estimation of the aromaticity (and therefore the stability) of ring-shaped molecules of planar structures.

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