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Aromaticity: Aromatic or not?

Aromatic or not: The Frost Circle

According to Hückel's rule, an aromatic compound must have (4n + 2) π electrons that form an uninterrupted π electron cloud. In addition, it must be planar and cyclic. If the compound is not planar and cyclic then it is also not aromatic. The bonding π MO (molecular orbitals) of an aromatic compound are fully occupied, while the antibonding and non-bonding π MO are fully unoccupied.

Whether or not a compound is aromatic may be determined by the so-called Frost circle - a simple method used to estimate the relative π orbital energies of both planar and cyclic compounds with an uninterrupted π electron system: To begin with, the structure of the cyclic compound is placed inside a circle with one of its vertices pointing downwards. A short horizontal line is then added to each of the molecular structure's vertices, along with a horizontal dashed line that runs right through the circle's and molecule's center.

Fig.1
Relative energies of benzene's π molecular orbitals - depicted by a Frost circle.

Finally, all π electrons are distributed among the short horizontal lines at the molecule's vertices, which represent the π MO. The distribution is started off with the lowest line (energy-poorest π MO) and continued on with the next highest line. Each MO (line) is occupied by two electrons before the following MO ever receives an electron (according to Hund's rule). The short lines beneath the central horizontal dashed line represent bonding π MO, while the short lines above the central dashed line represent antibonding π MO. Likewise, the short lines that are right on the central dashed line represent non-bonding π MO. Consequently, the molecule is aromatic only if all the lines below the central dashed line contain two electrons. In addition, all the lines that are on or above the central dashed line must be empty. That is, the molecule is aromatic if all bonding π MO are fully occupied, while all non-bonding and antibonding π MO are unoccupied. In benzene, for instance, all three bonding π MO are occupied by six π electrons, while none of the energy-rich, antibonding π MO is occupied by an electron. Ions may also be aromatic: The tropylium ion (cycloheptatrienyl cation), for example, possesses six π electrons, which occupy all three bonding π MO, such as is the case with benzene.

Fig.2
Tropylium ion (left) and benzene (right): Examples of aromatic compounds in the Frost circle.

The cycloheptatrienyl anion contains eight π electrons. Two of these occupy antibonding π MO. 1,3,5,7-Cyclooctatetraene is an example of a non-aromatic compound, as two of its eight π electrons are located in non-bonding π MO. As a result, neither the cycloheptatrienyl anion nor 1,3,5,7-cyclooctatetraene are aromatic compounds.

Fig.3
Fig.4

Exercise: Aromatic or not: The Frost circle

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