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Q9.12(iii):

Explain why the following systems are not aromatic?

(iii) 

Solution :

Step 1: Structural Analysis of the Molecule

The system presented is cycloheptatrienyl radical/anion derivative, specifically a seven-membered ring with three conjugated double bonds and a radical (or lone pair/charge) on the remaining carbon. Based on the chemical structure, we identify this as the cycloheptatrienyl species ($C_7H_7$).

Step 2: Verification of Huckel's Rule ($4n + 2$ $\pi$ electrons)

To determine aromaticity, we apply Huckel's Rule, which states that a planar, cyclic, conjugated system must possess $(4n + 2)$ $\pi$ electrons, where $n$ is an integer ($0, 1, 2, \dots$).

  • Number of $\pi$ electrons in the conjugated system: The molecule has 3 double bonds, contributing $3 \times 2 = 6$ electrons. Depending on the specific state of the 7th carbon (radical vs anion), we evaluate the electron count.
  • If the system is a radical ($C_7H_7^\bullet$), there are $6 + 1 = 7$ $\pi$ electrons.
  • If the system is a neutral hydrocarbon with localized electrons, it fails the requirement for continuous cyclic conjugation.
  • Setting the equation: $4n + 2 = 7 \implies 4n = 5 \implies n = 1.25$.

[Per Huckel's Rule, for a system to be aromatic, $n$ must be an integer. Since $n = 1.25$ is not an integer, the system fails the $\pi$-electron count requirement].

Step 3: Geometry and Planarity Analysis

For a molecule to be aromatic, it must be planar to allow for the effective overlap of $p$-orbitals across the ring. Cycloheptatrienyl systems often undergo "tub" or non-planar distortions to minimize steric hindrance and torsional strain.

C1 C2 C3 C4 C5 C6 C7

Step 4: Comparison Table of Aromaticity Criteria

Criterion Aromatic Requirement Status of Given System
Cyclic Conjugation Required Incomplete/Broken
$\pi$ Electron Count $4n + 2$ $7$ (Violates $4n + 2$)
Planarity Must be planar Non-planar (Tub shape)

Conclusion

The system is non-aromatic because it fails the primary requirements of Huckel's Rule. Specifically, it contains $7$ $\pi$ electrons (in the radical state), which does not satisfy the $(4n+2)$ condition, and the cyclic conjugation is interrupted by the $sp^3$ hybridized carbon or the geometric inability to maintain a planar configuration for continuous overlap of $p$-orbitals.

Final Solution: The system is not aromatic because it possesses $7$ $\pi$ electrons, violating the Huckel $(4n + 2)$ rule, and fails to maintain the necessary planar cyclic conjugation for resonance stabilization.


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