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Q9.12(iii):

Explain why the following systems are not aromatic?

(iii) 

Solution :

Theoretical Foundation: Hückel’s Rule for Aromaticity

For a cyclic, planar molecule to be classified as aromatic, it must satisfy the following criteria [Per Hückel’s Criteria]:

  • Cyclic Structure: The molecule must possess a closed ring of atoms.
  • Planarity: Every atom in the ring must be $sp^2$ or $sp$ hybridized, allowing for a continuous p-orbital overlap.
  • Complete Conjugation: There must be a continuous cycle of overlapping p-orbitals throughout the ring.
  • Hückel's Rule ($4n + 2$ $\pi$-electrons): The system must contain $(4n + 2)$ $\pi$-electrons, where $n$ is a non-negative integer ($n = 0, 1, 2, \dots$).

Structural Analysis of the System

The provided structure consists of a cyclooctatetraene ring containing four double bonds, totaling $8$ $\pi$-electrons.

C C C C Cyclooctatetraene ($C_8H_8$)

Step 1: Electron Count Verification

Counting the $\pi$-electrons in the ring:

  • There are 4 double bonds.
  • Total $\pi$-electrons = $4 \times 2 = 8$.
[Per Hückel’s Rule, aromatic systems require $4n + 2$ electrons]. If $n = 1$, $4(1) + 2 = 6$. If $n = 2$, $4(2) + 2 = 10$. Since $8$ does not satisfy the formula, the molecule fails the electron count requirement.

Step 2: Geometrical and Orbital Analysis

The molecule cyclooctatetraene is not planar [Per Steric Strain Analysis]. Due to the bond angles of an octagon, the molecule adopts a "tub-shaped" conformation to minimize angle strain and transannular interactions. By losing planarity, the p-orbitals are unable to maintain continuous parallel alignment, which effectively breaks the conjugation [Per Molecular Orbital Theory].

Criterion Status Justification
Cyclic Yes Closed ring of 8 carbons.
Planar No Molecule adopts non-planar tub conformation.
Conjugated No Non-planarity prevents continuous orbital overlap.
$4n+2$ electrons No Contains $8 \pi$-electrons ($4n$ system).

Final Solution: The system is not aromatic because it possesses $8$ $\pi$-electrons (violating the $4n+2$ rule) and adopts a non-planar "tub" geometry, which prevents the continuous delocalization of electrons required for aromaticity.


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