Question: Use the inscribed polygon method to show the pattern of molecular orbitals in cyclonona-1,3,5,7-tetraene and use it to label its cation, radical, and anion as aromatic, antiaromatic, or not aromatic.

The inscribed polygon method can be employed to anticipate the energies of cyclic and conjugated compounds.Another name for the inscribed polygon is the frost circle.

Molecular orbitals can be categorized into two types, and they include bonding molecular orbital (BMOs) and anti-bonding molecular orbital (ABMOs).

Antibonding molecular orbitals possess elevated energy than bonding molecular orbitals.

The molecular orbital pattern of cyclononatetraenyl cation can be given as:

Cyclononatetraenyl cation

This particular cation contains $8\mathrm{\pi }$ electrons and is antiaromatic.The eight electrons of the cation are filled in the bonding molecular orbital. Two degenerate molecular orbitals of the cation are not completely filled.

The molecular orbital pattern of cyclononatetraenyl radical can be given as:

Cyclononatetraenyl radical

The given radical has $9\mathrm{\pi }$ electrons and is not aromatic. The nine electrons of the radical are filled in the bonding molecular orbital. One degenerate molecular orbital of the radical is not completely filled.

The molecular orbital pattern of cyclononatetraenyl anion can be given as:

Cyclononatetraenyl anion

The given radical has $10\mathrm{\pi }$ electrons and is not aromatic. All the bonding molecular orbitals are filled in this molecular orbital representation of the anion.