Huckel Rule

Introduction

The German chemist and physicist Erich Huckel determined the Huckel Rule in 1931. He proposed that the aromatic rings follow four norms to be an aromatic compound. The first is that it should be cyclic and the second thing it should be planer, the third thing it conjugates, and the fourth one it must follow the Huckel rule. An aromatic compound has $\mathrm{4n\:+\:2\:pi\:electrons}$. The n in the formula is a positive integer. Aromatic compounds have $\mathrm{sp^{2}\:hybrodization}$.

What is the Huckel Rule?

The huckel’s rule is an algorithm that combines the number of pi electrons in an aromatic ring and determines whether a ring is aromatic or non-aromatic. It is defined by the formula 4n+2. If the value of N obtained is in the whole number. Apart from that, the compound must follow these criteria to be an aromatic compound.

• The aromatic compound must be cyclic.

• The compound should be a planner means it has $\mathrm{sp^{2}}$ hybridization.

• The compound conjugates mean the pi electrons can resonate over an entire ring making it conjugate.

• Fourth it must follow Huckel's rule of aromaticity.

Aromatic Compounds	Huclel’s Rule (4𝑛 + 2)
Non-aromatic compounds	Mobius System (𝟒𝒏)

Contribution to Aromatic Compounds:

Not all the compounds are cyclic, planar and conjugate are stable and aromatic The aromaticity in a compound makes it more stable. we can understand more by the example of cyclobutadiene and benzene ring.

• In cyclobutadiene, it is cyclic, planar, and conjugate but unstable as it does not follow the huckel's rule. In cyclobutadiene, it has a total of 4 pi electrons.

$$\mathrm{4n\:+\:2\:=\:=\:4}$$

$$\mathrm{4n\:=\:4\:-\:2}$$

$$\mathrm{n\:=\:\frac{2}{4}}$$

$\mathrm{n\:=\:\frac{1}{2}}$ it is a fractional value,

So, it does not follow Huckel’s rule, and it is highly unstable and it is antiaromatic.

• In the Benzene Ring, it is cyclic, planar, conjugate, and let's check whether it follows Huckel’s Rule or not. It has 6 pi electrons.

$$\mathrm{4n\:+\:2\:=\:6}$$

$$\mathrm{4n\:=\:6\:-\:2}$$

$$\mathrm{4n\:=\:4}$$

$$\mathrm{n\:=\:\frac{4}{4}}$$

n=1, the value of n is a whole number means it follows the huckel’s rule and is a stable compound.

Why 4n+2 Electrons?

According to Huckel’s Orbital theory, a compound is stable when the electrons present in the orbitals are paired. The aromatic compounds are more stable than the antiaromatic or non-aromatic compounds. Aromatic compounds follow Huckel's rule and have 4n pi electrons in their orbital.

In benzene, there are 6 pi electrons, with sp2 hybridization. The first two electrons in the s-orbital are in the lowest energy level and the remaining 4 pi electrons are in the p-orbital. They are in the further one up the energy level.

• All the electrons are in the bonding orbitals no one is in the antibonding orbital.

• Application of Huckel Rule in Benzene Ring.

$$\mathrm{4n\:+\:2\:=\:6}$$

$$\mathrm{4n\:=\:6\:-\:2}$$

$$\mathrm{4n\:=\:4}$$

$$\mathrm{n\:=\:\frac{4}{4}}$$

$$\mathrm{n\:=\:1}$$

The 1 is a whole number and follows the huckel’s rule.

• We can also find if a compound is aromatic or not if a compound has an odd number of electron pairs i.e (1,3,5,7,9,11…etc.)

• If the number of electrons in a compound has 2, 6,10,14, and 18 electrons in their orbitals it follows Huckel’s Rule.

Few Examples of Huckel’s Rule

Aromaticity in Naphthalene:

Naphthalene molecule

In a naphthalene molecule, the number of electrons is 10 pi electrons. It is cyclic, planar, and conjugated. We have to check by the 4n+2 formula.

$$\mathrm{4n\:+\:2\:=\:10}$$

$$\mathrm{4n\:=\:10\:-\:2}$$

$$\mathrm{4n\:=\:8}$$

$$\mathrm{n\:=\:\frac{8}{4}}$$

$$\mathrm{n\:=\:2}$$

The value of n is 2 which is a whole number, which means naphthalene follows the huckel’s rule and is aromatic.

Aromaticity in Pentalene:

Pentalene

is also a cyclic compound, planar and conjugated with sp2 hybridization, and has 8 pi-electrons.

$$\mathrm{4n\:+\:2\:=\:8}$$

$$\mathrm{4n\:=\:8\:-\:2}$$

$$\mathrm{4n\:=\:6}$$

$$\mathrm{n\:=\:\frac{6}{4}}$$

$$\mathrm{n\:=\:\frac{3}{2}}$$

We have calculated the value and found the value of n is 3/2 which is a fraction. Even though it follows all other criteria of aromaticity, but it does not follow the Huckel Rule. So, it is not aromatic.

Application of Huckel Rule

• Huckel Rule helps us find the stability of the monocyclic hydrocarbon compounds. In cyclopentadienyl anion, 𝐶5𝐻5− it has 6 pi electrons, and it follows the Huckel Rule. Hence it is a stable compound.

• It helps us define whether a compound is aromatic or nonaromatic by 𝑡ℎ𝑒 $\mathrm{4n\:+\:2}$ Rule.

• The cations and anions of some compounds follow the Huckel rule. They can show different stability. An example of such a pyrrole has 4 electrons and a lone pair that contribute to the pi bond. We get 6 pi electrons which follow the huckel’s rule. Hence pyrrole is an aromatic compound.

• In Cyclopentadienyl anion there are 6 pi- electrons. 4 electrons are of two pi- bond and a pair of anions. The total value of pi-electrons is 6 which follows the Huckel rule. Hence it is an aromatic compound.

Exceptions of Huckel’s Rule

There are few exceptions to Huckel's Rule.

• The planar compounds are not very stable but cyclobutadiene 𝐶4𝐻4 is a planar, cyclic, and non-aromatic compound but it is stable below 35-kelvin Temperature.

• Another exception is the polycyclic compound Pyrene which is an aromatic compound but does not follow the Huckel rule.

Pyrene

• One more exception is Trans-Bicalicene which is an aromatic cyclic compound having 8 pi-electrons but does not follow the Huckel Rule.

Trans-Bicalicene

Conclusion

In the above tutorial, we have studied Huckel’s Rule which helps us find out whether the compound is aromatic or non-aromatic. A cyclic compound that follows four criteria that it is planar having $\mathrm{sp^{2}}$ hybridization, and its electrons resonate in the whole ring defined, it is cyclic and follows the Huckel rule of 4𝑛 + 2 is an aromatic compound but there are few exceptions like pyrene, trans-bicalicene that are aromatic but do not follow the Huckel’s Rule. It helps us find out the stability of the compound.

FAQs

1. What are antiaromatic compounds?

It follows the 4n Mobius System. They are cyclic, planar, and conjugate but are highly unstable. Example: Cyclobutadiene which has 4 pi electrons.

2. Explain that the Cylcopentadiene anion is an aromatic compound?

Cyclopentadiene anion is a cyclic, planar compound with a lone pair, the negative charge of the carbon form $\mathrm{sp^{3}}$ hybridization, to stabilize the aromatic ring it changed to $\mathrm{sp^{2}}$ hybridizations, and the lone pair delocalized over the ring.

3. Why is Cyclopropenyl Cation aromatic?

Cyclopropenyl cation is a cyclic compound and has $\mathrm{sp^{2}}$ hybridization. It has three carbon atoms and 2pi electrons. The cation of the cyclopropenyl has a parallel and planar p-orbital and follows all the criteria of an aromatic compound.

4. What is an aromatic compound?

An aromatic compound is hydrocarbons with sigma and delocalized pi-electrons between the carbons of a ring.

5. What are the uses of aromatic compounds?

The aromatic compounds are highly stable and used in medicines, pesticides, fuel formation, paints, detergents, etc.