Which of the following molecule/species is most stable?

Step 1: Apply Huckel Rule

Aromatic stability (4n+2 pi electrons): more stable than expected. Antiaromatic (4n pi electrons): less stable (destabilized).

Step 2: Count Pi Electrons

• (a) Cyclopropenyl cation $\ce{C3H3^+}$: 3-membered ring, 2 pi electrons (n=0, $4(0)+2=2$). Aromatic. Stable.
• (b) Cyclopentadienyl cation $\ce{C5H5^+}$: 4 pi electrons (4n, n=1). Antiaromatic. Unstable.
• (c) Cyclopropyl carbene/radical: not aromatic.
• (d) Cycloheptatrienyl anion $\ce{C7H7^-}$: 8 pi electrons (4n, n=2). Antiaromatic. Unstable.

Most stable = cyclopropenyl cation (aromatic with 2 pi electrons).

Key Points:

• Cyclopropenyl cation: smallest possible aromatic species (2 pi e, 3-membered ring)
• Antiaromatic species (4n pi e) are highly unstable
• Cyclopentadienyl cation and cycloheptatrienyl anion are both antiaromatic