17.8: Frost Circles for Different Conjugated Systems

The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.

By looking at the Frost circles, it is observed that the number of bonding MO is always odd, and the required number of π electrons in the bonding MO is either 2 or 6. The number of electrons perfectly satisfies the 4n + 2 rule of aromaticity. Hence, the compounds with completely filled bonding MO are aromatic.

In the case of four-membered cyclobutadiene with 4π electrons and eight-membered cyclooctatetraene with 8π electrons, the bonding MO are completely filled, and each of the non-bonding MO is singly occupied. The presence of electrons in high-energy non-bonding MO makes them unstable and not aromatic. However, the five-membered cyclopentadienyl anion, six-membered benzene, and seven-membered cycloheptatrienyl cation have 6π electrons, and the corresponding bonding MO are fully occupied and stable, so they are aromatic.

Overall, molecules having completely filled bonding molecular orbitals are considered aromatic, whereas compounds with electrons in orbitals other than bonding are not aromatic.

According to Huckel's rule, benzene is stable and aromatic, while cyclobutadiene and cyclooctatetraene are unstable and not aromatic.

The aromaticity of these compounds can be understood from their Frost circle diagrams.

The Frost circle for benzene has six π molecular orbitals. All the low-energy bonding orbitals are fully occupied with six π electrons, while the high-energy antibonding orbitals are empty. Therefore, benzene is stable and aromatic.

The Frost circles for cyclobutadiene and cyclooctatetraene have four and eight π  molecular orbitals, respectively.

The bonding orbitals are fully occupied for both of the compounds, while the nonbonding orbitals are singly occupied. The antibonding orbitals are empty.

As is evident, the presence of π electrons in high-energy nonbonding orbitals makes the two compounds unstable and not aromatic.

Overall, a given molecule is considered aromatic when all of the π electrons are paired in bonding molecular orbitals. Compounds with electrons in orbitals other than bonding are not aromatic.