### Hückel's Rule

*p*orbitals, have planar geometry, and have a Hückel number of electrons. Hückel's rule states that compounds having 2, 6, 10, 14, … [$4n+2$] $\pi$ electrons (and satisfying the first three rules) are aromatic.

An aromatic molecule is a molecule that is cyclic, has a continuous circle of *p* orbitals, has planar geometry, and has a Hückel number [$4n+2$] of $\pi$ electron. **Hückel's rule** is a rule that states that the number of delocalized electrons in the $\pi$ cloud in an aromatic ring is equal to [$4n+2$], where *n* is zero or a positive integer. Hückel's rule applies to monocyclic compounds.

**molecular orbital theory**(or MO theory) is a solution of the Schrödinger equation that describes the probable location of an electron relative to the nuclei in a molecule and so indicates the nature of any bond in which the electron is involved. The Schrödinger equation is used in quantum mechanics to identify atomic energy levels. According to MO theory, aromaticity results when all the $\pi$ molecular bonding orbitals are completely filled and all the $\pi$ molecular nonbonding orbitals are completely empty.

#### Benzene Pi Cloud

**Frost circles**, also referred to as the polygon method, is a method to predict bonding $\pi$ molecular orbitals, which indicate aromaticity. There are seven steps in using Frost circles to determine aromaticity.

1. Draw a circle.

2. Draw a polygon inside the circle. The polygon should have the same number of sides as the number of carbon atoms in the cyclic structure. One of the vertices of the polygon must be down inside the ring.

3. Every time a vertex of the polygon intersects the ring, a short horizontal line is drawn to indicate a molecular orbital (MO).

4. Draw a dotted line halfway through the circle, and then erase the circle and the polygon. The resulting structure is the molecular orbital diagram of the ring.

5. The horizontal lines above the dotted line are antibonding molecular orbitals, and the horizontal lines below the dotted lines are bonding molecular orbitals.

6. Determine the total number of $\pi$ electrons from the structure. Start filling the electrons into the molecular orbitals starting at the bottom. Fill in one electron in each molecular orbital on a single level before filling in a second electron in each orbital. Once all the molecular orbitals on a level are completely filled, then start filling in the next energy level. Keep filling orbitals in this method until all electrons have been used.

7. If the highest level has an odd number, the compound is nonaromatic. If the highest level is completely filled and below the dotted line, the compound is aromatic. If the highest level is completely filled and above the dotted line, the compound is antiaromatic.#### Frost Circle

### Antiaromatic and Nonaromatic Compounds

*p*orbitals, have planar geometry, and do not have a Hückel number of electrons. Nonaromatic compounds either are not cyclic, are not planar, or do not have a continuous circle of

*p*orbitals. Annulenes, ions, heterocyclics, and polycyclics can all be aromatic if they fulfill all of the rules of aromaticity.

Aromatic molecules are cyclic, have a continuous circle of *p* orbitals, have planar geometry, and have a Hückel ($4n+2$) number of electrons. An **antiaromatic** molecule is a molecule that is cyclic, has a continuous circle of *p* orbitals, has planar geometry, and does not have a Hückel number of electrons but instead has [$4n$] $\pi$ electrons. Antiaromatics are more than just "not aromatic" or nonaromatic; they are highly unstable. A **nonaromatic** is a molecule that is not cyclic or planar or does not have a continuous circle of *p* orbitals.

An **annulene** is any of a class of completely conjugated cyclic hydrocarbons (such as benzene or cyclooctatetraene) that are monocyclic. Conjugated compounds have alternating single and double bonds. A **heterocyclic** is any molecule relating to, characterized by, or being a ring composed of atoms of more than one kind. **Polycyclic** refers to molecules with more than one ring structure. A **polycyclic aromatic compound** (or benzenoid aromatic compound) is a compound that has more than one ring structure and is aromatic. A benzenoid is a molecule that has a six-membered ring structure or aromatic properties of benzene. Annulenes, ions, heterocyclics, and polycyclics can all be aromatic if they fulfill all four rules of aromaticity.

_{18}H

_{18}or [18]annulene, is an example of an aromatic molecule that follows Hückel's rule ($4n+2$). Applying Hückel's rule when $n=4$ gives a total of 18 electrons, confirming that [18]annulene is aromatic. However, cyclobutadiene, C

_{4}H

_{4}or [4]annulene, is antiaromatic because it does not follow Hückel's rule ($4n+2$). It is a cyclic, each atom in the system has a

*p*orbital perpendicular to the ring, and it has a planar geometry, but it has a total of $4\pi$ electrons. Applying Hückel's rule when $n=1$ gives a total of 4 electrons, confirming that [4]annulene is antiaromatic.