Criteria for Aromaticity and the Hückel 4n + 2 Rule

Like benzene, cyclobutadiene and cyclooctatetraene are cyclic compounds with alternate single and double bonds. However, their chemical behavior differs from benzene, as they are unstable and not aromatic. So, what are the structural characteristics of unsaturated compounds categorized as aromatic?  

For the first time, Eric Hückel, a German chemical physicist, derived a set of structural features for a compound to be classified as aromatic. This is now known as Hückel’s rule or the 4n + 2 rule. According to this rule, an aromatic compound must be cyclic, planar, continuously conjugated, having an odd number of pairs of π electrons or 4n + 2  π electrons, where n is an integer (n = 0, 1, 2…).  Therefore, an aromatic compound should have 2 (n = 0), 6 (n = 1), 10 (n = 2), 14 (n = 3), etc., number of π electrons or 1, 3, 5, 7, etc., pairs of π electrons.

For example, 1,3,5-hexatriene and benzene have 6 π electrons; even then, 1,3,5-hexatriene is not aromatic as the p orbitals on the two terminal carbon atoms do not overlap as a bond does not connect these carbons. Therefore, compounds must be cyclic to be aromatic.

Although it is an eight-membered cyclic compound with continuous four π bonds, cyclooctatetraene is unstable and not aromatic. This is because cyclooctatetraene is nonplanar; it adopts a tub conformation. Consequently, an effective overlap of p orbitals to form a closed loop of the π electron cloud is not feasible. Notably,  unlike benzene, it undergoes addition reactions.

For a compound to be continuously conjugated, it must have all the carbons of sp² hybridization with a half-filled unhybridized p orbital on each. For example, 1,3-cyclohexadiene and 1,3,5-cycloheptatriene have sp³ hybridized carbons that do not have an unhybridized p orbital, so continuous overlapping is unachievable. Therefore, they both are not aromatic.

On the other hand, cyclobutadiene, a cyclic, planar compound with continuous conjugation, is unstable and not aromatic. It has 2 pairs of π electrons or 4 π electrons, which does not satisfy the criteria of having 4n + 2  π electrons. Therefore, it is not aromatic.