Question: Use the inscribed polygon method to show why the cyclopentadienyl cation and radical are not aromatic.

Cyclopentadienyl cation is formed by the loss of hydride ions from cyclopentadiene. Cyclopentadiene and the cyclopentadienyl cation are not aromatic, but cyclopentadienyl anion is aromatic.

The cyclopentadienyl cation formed is planar and contains a cyclic pi-electron cloud above and below the ring. It does not obey Huckel’s$\left(4n+2\right)\mathrm{\pi }$ electron rule, so it is not aromatic. But it obeys $4n\mathrm{\pi }$electron rule, so it is antiaromatic.

To find the aromaticity of cyclopentadienyl cation and radical using the inscribed polygon method, draw the inscribed pentagons with the vertex pointing down, and draw the molecular orbitals (MOs) and add the electrons.

Representation of inscribed polygon method

Cyclopentadienyl cation has four $\mathrm{\pi }$electrons, and all the bonding MOs are not filled; so, it is not aromatic. Cyclopentadienyl radical has five $\mathrm{\pi }$electrons, and all the bonding MOs are not filled; so, it is not aromatic.