Q.The ring systems having the following characteristics are aromatic:

The key idea for classifying these compounds is Benzene Aromatic Stability, governed by Hückel's Rule. A compound is aromatic if it meets three criteria: it is a planar, cyclic system with complete delocalisation of $\pi$-electrons (all ring atoms have unhybridised p-orbitals), and it contains $(4n+2)$ $\pi$-electrons, where $n$ is a non-negative integer.

Here's the classification for each compound:

1. Pyridine: It is a planar, cyclic system with complete $\pi$-electron delocalisation. It has $6$ $\pi$-electrons (from three double bonds; the nitrogen lone pair is in an $sp^2$ orbital and not part of the $\pi$-system). Since $6 = (4 \times 1 + 2)$, it follows Hückel's rule.
2. 1,3,5-Cycloheptatriene: It contains an $sp^3$ hybridised carbon atom, which breaks the continuous delocalisation of $\pi$-electrons around the ring.
3. Cyclopentadienyl anion: It is a planar, cyclic system with complete $\pi$-electron delocalisation. It has $6$ $\pi$-electrons (from two double bonds and the lone pair on the carbanion). Since $6 = (4 \times 1 + 2)$, it follows Hückel's rule.
4. Cyclopentadienyl cation: It is a planar, cyclic system with complete $\pi$-electron delocalisation. It has $4$ $\pi$-electrons (from two double bonds; the carbocation has an empty p-orbital). Since $4$ does not fit the $(4n+2)$ rule, it is not aromatic. …

Aromatic compounds possess exceptional stability due to the cyclic delocalisation of $\pi$-electrons. This special stability, known as aromaticity, is governed by a set of rules, primarily Hückel's rule, which you have provided. To classify each compound, we will systematically check these three criteria:

1. Planarity and Conjugation: The molecule must be a cyclic system and planar, with a continuous ring of conjugated $\pi$ bonds. This means there should be an alternating sequence of single and double bonds, or single bonds adjacent to atoms with lone pairs or empty p-orbitals.
2. Complete Delocalisation: Every atom in the ring must have an unhybridised p-orbital that can overlap with adjacent p-orbitals, allowing for continuous electron flow around the ring. This typically implies $sp^2$ or $sp$ hybridisation for all ring atoms. An $sp^3$ hybridised atom in the ring breaks this continuity.
3. Hückel's Rule: The cyclic, planar, and fully conjugated system must contain $(4n+2)$ $\pi$-electrons, where $n$ is a non-negative integer ($n = 0, 1, 2, \ldots$). If a system is planar and fully conjugated but has $4n$ $\pi$-electrons, it is classified as anti-aromatic, which is a type of non-aromatic compound with destabilising properties.

Let's apply these rules to each compound:

(i) Pyridine

1. Structure: Pyridine is a six-membered heterocyclic ring containing five carbon atoms and one nitrogen atom. It has three double bonds. The nitrogen atom has a lone pair of electrons.
2. Planarity and Conjugation: The ring is planar, and all atoms are $sp^2$ hybridised. The double bonds are conjugated throughout the ring.
3. Complete Delocalisation: All six ring atoms (five carbons and one nitrogen) are $sp^2$ hybridised, each possessing an unhybridised p-orbital perpendicular to the ring. The lone pair on the nitrogen atom resides in an $sp^2$ orbital, lying in the plane of the ring, and therefore does not participate in the $\pi$-electron delocalisation.
4. Hückel's Rule: There are three $\pi$ bonds (double bonds), contributing $3 \times 2 = 6$ $\pi$-electrons. The nitrogen's lone pair is not counted.
   • Number of $\pi$-electrons $= 6$.
   • For $n=1$, $4n+2 = 4(1)+2 = 6$.
   • Since $6$ fits the $(4n+2)$ rule, pyridine is aromatic.

(ii) 1,3,5-Cycloheptatriene

1. Structure: This is a seven-membered carbocyclic ring with three double bonds and one $sp^3$ hybridised $-\text{CH}_2-$ group.
2. Planarity and Conjugation: While it has three double bonds, the presence of the $sp^3$ hybridised carbon atom (the $-\text{CH}_2-$ group) breaks the continuous conjugation around the ring. An $sp^3$ carbon does not have an unhybridised p-orbital available for $\pi$-overlap. This also prevents the ring from being fully planar.
3. Complete Delocalisation: Due to the $sp^3$ carbon, complete delocalisation of $\pi$-electrons throughout the entire ring is not possible.
4. Hückel's Rule: It has $3 \times 2 = 6$ $\pi$-electrons. While $6$ $\pi$-electrons satisfy Hückel's rule, the first two criteria (planarity and complete delocalisation) are not met.
   • Therefore, 1,3,5-Cycloheptatriene is non-aromatic.

(iii) Cyclopentadienyl anion

1. Structure: This is a five-membered carbocyclic ring with two double bonds and a negative charge on one carbon atom.
2. Planarity and Conjugation: The ring is planar. The two double bonds are conjugated with the negative charge. The carbon bearing the negative charge is $sp^2$ hybridised, and its lone pair occupies an unhybridised p-orbital, allowing for continuous conjugation.
3. Complete Delocalisation: All five carbon atoms are $sp^2$ hybridised, each contributing an unhybridised p-orbital. The lone pair on the negatively charged carbon is in a p-orbital, allowing for complete delocalisation around the ring.
4. Hückel's Rule: The two double bonds contribute $2 \times 2 = 4$ $\pi$-electrons. The lone pair (negative charge) contributes $2$ $\pi$-electrons to the delocalised system.
   • Total number of $\pi$-electrons $= 4 + 2 = 6$.
   • For $n=1$, $4n+2 = 4(1)+2 = 6$.
   • Since $6$ fits the $(4n+2)$ rule, the cyclopentadienyl anion is aromatic.

(iv) Cyclopentadienyl cation

1. Structure: This is a five-membered carbocyclic ring with two double bonds and a positive charge on one carbon atom.
2. Planarity and Conjugation: The ring is planar. The two double bonds are conjugated with the positive charge. The carbon bearing the positive charge is $sp^2$ hybridised, and its empty p-orbital allows for continuous conjugation.
3. Complete Delocalisation: All five carbon atoms are $sp^2$ hybridised, each contributing an unhybridised p-orbital (the carbocation carbon has an empty p-orbital). This allows for complete delocalisation.
4. Hückel's Rule: The two double bonds contribute $2 \times 2 = 4$ $\pi$-electrons. The positive charge (empty p-orbital) contributes $0$ $\pi$-electrons to the delocalised system.
   • Total number of $\pi$-electrons $= 4 + 0 = 4$.
   • For $n=0.5$, $4n+2 = 4(0.5)+2 = 4$. Since $n$ must be an integer, $4$ $\pi$-electrons do not satisfy Hückel's rule.
   • A planar, fully conjugated cyclic system with $4n$ $\pi$-electrons is anti-aromatic. Anti-aromatic compounds are highly unstable and are classified as non-aromatic.
   • Therefore, the cyclopentadienyl cation is non-aromatic.

(E) Cycloheptatrienyl (tropylium) cation

1. Structure: This is a seven-membered carbocyclic ring with three double bonds and a positive charge. The formula is $\text{C}_7\text{H}_7^+$.
2. Planarity and Conjugation: The ring is planar. The three double bonds are conjugated with the positive charge. All seven carbon atoms are $sp^2$ hybridised, and the carbon bearing the positive charge has an empty p-orbital, allowing for continuous conjugation. …