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Q9.12(i):

Explain why the following systems are not aromatic?

(i) 

Solution :

Analysis of Aromaticity Requirements

To determine the aromaticity of a cyclic system, we apply Hückel's Rule ($4n+2$ $\pi$-electrons) alongside the structural requirements of planarity, complete conjugation, and cyclic delocalization. The specific system provided, cyclooctatetraene ($C_8H_8$), must be evaluated against these criteria.

Step 1: Structural Evaluation

The molecule in question is cyclooctatetraene. We count the number of $\pi$-electrons involved in the conjugation:

  • Number of double bonds = 4
  • Each double bond contributes 2 $\pi$-electrons.
  • Total $\pi$-electrons = $4 \times 2 = 8$ electrons.

Step 2: Testing against Hückel’s Rule

According to Hückel's Rule, a planar, cyclic system is aromatic if it contains $(4n + 2)$ $\pi$-electrons, where $n$ is an integer ($n = 0, 1, 2, \dots$).

Setting the total $\pi$-electrons equal to the Hückel expression:

$4n + 2 = 8$

$4n = 6$

$n = 1.5$

[Justification: Since $n$ must be an integer, the molecule does not satisfy Hückel's Rule for aromaticity. Instead, it follows the $4n$ rule ($8 = 4 \times 2$), classifying it as anti-aromatic if it were planar.]

Step 3: Geometric Configuration

While the molecule possesses $8$ $\pi$-electrons, which would theoretically make it anti-aromatic and highly unstable if planar, the system avoids this instability by adopting a "tub-shaped" (non-planar) conformation. In this geometry, the $p$-orbitals are not perfectly aligned to allow for full continuous cyclic delocalization.

Tub-shaped Non-planar Conformation Molecule adopts a buckled shape to minimize electronic repulsion

Step 4: Conclusion of Aromaticity Status

The system fails the requirements for aromaticity due to two primary factors:

  1. Electron Count: It contains $8\pi$-electrons, which does not fit the $(4n+2)$ criterion [Per Hückel's Rule].
  2. Geometry: It is non-planar. Aromaticity requires a planar system to ensure effective overlap of $p$-orbitals for cyclic delocalization [By structural criteria of aromatic systems].

Final Solution: The system is non-aromatic because it does not follow the $4n+2$ Hückel rule (having $8\pi$-electrons) and maintains a non-planar "tub" conformation that prevents cyclic delocalization of the $\pi$-electron cloud.


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