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Huckel's Rule of Aromaticity

All organic compounds are composed of carbon and hydrogen atoms. Each carbon atom exhibits teravalency and forms four covalent bonds with same or different atoms. The geometry of each molecule depends on types of covalent bonds present in the molecule and also on hybridization. For example a carbon atom which forms only single covalent bond involves in sp3 hybridization and arranged in tetrahedral geometry. On the other hand, carbon atoms with sp2 hybridization are arranged in trigonal planer geometry with 120° of bond angle. So we can say that all organic compounds have specific molecular and structural formula. 

Hydrocarbons       Cyclohexane     Benzene

Can you differentiate between these molecules! Hexane is an open chain compound in which all six carbon atoms are bonded with each other to form straight chain. Cyclohexane is a cyclic molecule with six carbon atoms bonded with each other through single covalent bonds to form a hexagonal ring. Now compare benzene with cyclohexane.

Both of these molecules have 6 carbon atoms which are bonded in cyclic manner to form a hexagonal ring. But benzene is classified as aromatic compound whereas cyclohexane is an alicyclic compound.  The molecular formula of cyclohexane is $C_{6}H_{12}$ whereas molecular formula for benzene is $C_{6}H_{6}$. It means benzene has less number of H than cyclohexane so it must be an unsaturated compound with either double or triple covalent bonds in the molecule. Unlike alkenes, benzene is a stable aromatic compound which prefers to show electrophilic substitution reactions compare to addition reactions like alkenes. This extra stability in the molecule is due to resonance and conjugation of double bonds in the molecule. 

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Define Hückel Rule of Aromaticity

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To explain the extra stability of aromatic compounds, Erich Hückel postulated a rule in 1931 that is known as Hückel’s rule of aromaticity. This rule helps to predict the extra stability of monocyclic planar compounds in which carbon atoms have un-hybridized p-orbitals. Because of presence of un-hybrid orbitals of carbon atoms, such molecules have a closed bond shell of delocalized π electrons. According to Hückel’s rule, in such planer molecules, the number of π electrons fit a value of 4 n + 2. Here n can be any whole number.

So we can use Hückel's Rule to predict the aromaticity of given compound such as there are three pi-bonds or  six π electrons in benzene molecule with n = 1. Hence benzene is an aromatic compound.

State Hückel’s Rule of Aromaticity

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Aromaticity is the term that is used to describe the extra stability of planer, cyclic conjugated molecules. The presence of conjugated pi-system in molecule causes delocalization of electrons in molecule. Hückel's Rule is used to predict the aromaticity in the molecule. There are certain criteria for Hückel's Rule. The molecule must satisfy these all criteria than only consider as aromatic compound.  

According to Hückel's Rule, a molecule will be aromatic if it is a;
  1. Cyclic molecule, 
  2. Planer molecule in which all bonded atoms lie in same plane,
  3. Conjugated molecule with conjugated pi-electron system,
  4. 4n + 2 π electrons.
This rule can be explained with the help of Hückel's Molecular Orbital Theory. According to Molecular orbital theory, the molecule with all filled bonding molecular orbitals is stable. Like in benzene molecule, two electrons fill the lowest energy molecular orbital, and remaining four electrons fill each subsequent energy level whereas anti-bonding orbitals remain empty. That makes the molecule extra stable. 

Bonding Orbitals

Huckel's Rule of Aromaticity with Examples

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  • Benzene: It has six pi-electrons as there are three pi-bonds in the molecule. If we apply the Huckel's rule of aromaticity, the value of 4n + 2 must be six. So if we put the value of n as 1, 4n+2 will be 6. Hence benzene is an aromatic compound.
  • Cyclopentadienyl anion: Cyclopentadiene is a cyclic diene with two double bonds and five carbon atoms in ring. So there are 4 pi-electrons in the molecule and it is not an aromatic compound as it does not follow Huckel's rule of aromaticity. Now the anion of same molecule; Cyclopentadienyl anion has 4n+2 Ï€ electrons. Hence it is an aromatic ion. We have to check the planarity in molecule also. From C-2 to C-5, carbon atoms are sp2 hybridized so they have planer geometry. Now C-1 has a p orbital therefore Cyclopentadienyl anion has six Ï€ electrons and an aromatic compound. 
Huckel's Rule of Aromaticity
  • Heterocyclic aromatic compounds: A large number of heterocyclic compounds follow the Huckel's rule of aromaticity. Heterocyclic compounds are cyclic compounds with some other atom in carbon ring. Usually N, O and S have tendency to form bond with C to form heterocyclic compounds. Furan, pyridine, pyrrole, thiophene and pyran are some common examples of heterocyclic compounds. 
Hetero Atoms

  • Furan is a heterocyclic compound with –O- atom in the ring. All carbon atoms of furan are sp2 hybridized so are arranged in planer geometry.The oxygen atom of ring has two lone pair of electrons and forms two single covalent bonds with two carbon atoms of the ring. So there are total 6 electrons in the ring which delocalize to make the molecule aromatic. Hence we can say that furan also follow 4n+2 pi electron rule and has 6 pi-electrons in planer ring. 
Furan hybridization
  • Cyclopropyl ion:  Similarly cyclopropyl cation is also an aromatic compound with 2 pi-electrons whereas cyclopropyl anion is not an aromatic compound as it has 4n electrons. 
Cyclopropyl Ion

Explain Huckel's Rule of Aromaticity

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Huckel's rule of aromaticity states that for aromaticity, a compound should be cyclic (no sp3 atoms), planer and with a conjugated system of 4n+2 pi-electrons.  Benzene is the most important and simplest example of this. It is a cyclic, planer hexagonal ring with six pi-electrons which remain delocalized on six carbon atoms.

For aromaticity, it is not necessary that cyclic compound contains only carbon atoms. There are many heterocyclic compounds which have other atoms like O, S, and N etc. The lone pairs of these heteroatom can participate in resonance with pi-electrons of ring that makes the molecule aromatic and satisfy the criteria of 4n+2 rule. With different n values; given numbers of pi-electrons systems will result aromaticity in molecule. 

For the formula 4n + 2
  • n = 0; (4 × 0 + 2) = 2
  • n = 1; (4 × 1 + 2) = 6
  • n = 2; (4 × 2 + 2) = 10
  • n = 3; (4 × 3 + 2) = 14
  • n = 4; (4 × 4 + 2) = 18 pi-electrons
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