Arenes: Aromatic Systems and the 4n+2 Rule

Benzene, having the molecular formula C6H6, would be consistent with a structure such as cyclohexatriene, having three conjugated double bonds in a six-membered ring. The compound is, however, far more stable than would be predicted for a triene, based on the heat of hydrogenation (the energy evolved when one mole of compound is reacted with H2 in the presence of Pt or Pd catalyst). As shown below, the inclusion of additional double bonds in a compound is generally associated with an increase in the heat of hydrogenation of approximately 25 kcal/mole; benzene, however, has a heat of hydrogenation which is less than that of cyclohexadiene. Further, benzene does not undergo "typical" alkene reactions; it will not react with Br2 to form a dibromide, nor will it react with halogen acids (i.e., HCl) to give alkyl halides.

The rationalization for the unusual reactivity of benzene which is generally accepted today is that the conjugated p-system forms a continuous molecular orbital above and below the plane of the ring, and that this planar, continuous p-system containing six electrons has unusual stability. The delocalization of the electrons is typically shown by writing resonance forms in which the double bonds in benzene compounds can be shown to be distributed equally among all carbon centers (shown below for dibromobenzene). Remember that resonance forms represent structural limits and that the molecule is "never" one form or the other, but is a hybrid of both. To show this, the bonding in benzene compounds is often written as a circle within the ring, although this type of structural representation has its own drawbacks, as we will see when we consider substitution reactions.

The formation of the molecular orbital can be seen below, as the overlap of the six p-orbitals to form the continuous p-system.

   

The resonance description of benzene explains the geometry of the molecule but does not explain the unusual stability of benzene and its derivatives. The stability of benzene is suggested to arise from the fact that the conjugated p-system is planar and contains 4n + 2 electrons (with n = 1), and it is suggested that all compounds having planar, conjugated ¼ systems containing 4n + 2 electrons will share this stability. This property, described originally by Huckel, is referred to as aromaticity. Aromaticity, and unusual stability, will therefore be associated with molecules having 6 (n = 1), 10 (n = 2), 14 (n = 3), 18 (n = 4), etc., electrons. Unshared pairs of electrons on heteroatoms within the ring can also be counted to achieve aromaticity, as shown in the examples below:

It is also essential that the carbon skeleton be planar, as shown for cyclodecapentaene, which has 10 p-electrons, but is not aromatic because the ring hydrogens force the p-system out of planarity.

Lack of planarity is not a problem in [18]annulene (18 p-electrons; 4n +2 where n = 4), where there is sufficient room for the central six hydrogen atoms to fit within the middle of the ring system.