For a species to be aromatic, it must satisfy H��ckel's rules:
1. It must be cyclic.
2. It must be planar.
3. It must have a continuous ring of p-orbitals (fully conjugated).
4. It must have $(4n+2)$ $\pi$ electrons in the conjugated system, where $n$ is a non-negative integer.
(A) Cycloheptatrienyl cation:
1. Cyclic: Yes.
2. Planar: Yes.
3. Conjugated: Yes.
4. $\pi$ electrons: 3 double bonds = 6 $\pi$ electrons.
$6 = 4n+2 \implies n=1$, satisfies H��ckel's rule. Aromatic.
(B) Cyclopentadienyl anion:
1. Cyclic, planar, conjugated: Yes.
2. $\pi$ electrons: 2 double bonds (4 $\pi$) + 1 lone pair (2 $\pi$) = 6 $\pi$ electrons.
$6 = 4n+2 \implies n=1$. Aromatic.
(C) Cyclooctatetraene:
1. Cyclic: Yes.
2. $\pi$ electrons: 4 double bonds = 8 $\pi$ electrons ($4n$ type).
3. Planar: No, adopts a non-planar tub shape to avoid anti-aromaticity.
Does not satisfy aromaticity rules. Non-aromatic.
(D) Naphthalene:
1. Cyclic, planar, conjugated: Yes.
2. $\pi$ electrons: 5 double bonds = 10 $\pi$ electrons.
$10 = 4n+2 \implies n=2$. Aromatic.