Question

Using MO diagram, explain why cycloctatetraene is very reactive.

Answer 1

Now, let’s do the same thing for cyclooctatetraene, which we have already learned is not aromatic.

The result of molecular orbital calculations tells us that the lowest and highest energy MOs (Ψ₁ and Ψ₈*) have unique energy levels, while the other six come in degenerate pairs. Notice that y₄and y₅are at the same energy level as the isolated 2p_z atomic orbitals: these are therefore neither bonding nor antibonding, rather they are referred to as nonbonding MOs. Filling up the MOs with the eight π electrons in the molecule, we find that the last two electrons are unpaired and fall into the two degenerate nonbonding orbitals. Because we don't have a perfect filled shell of bonding MOs, our molecule is not aromatic. As a consequence, each of the double bonds in cyclooctatetraene acts more like an isolated double bond.

Here, then, are the conditions that must be satisfied for a molecule to be considered aromatic:

1. It must have a cyclic structure.
2. The ring must be planar.
3. Each atom in the ring must be sp²-hybridized, so that π electrons can be delocalized around the ring.
4. The number of π electrons in the ring must be such that, in the ground state of the molecule, all bonding MOs are completely filled, and all nonbonding and antibonding MOs are completely empty.

It turns out that, in order to satisfy condition #4, the ring must contain a specific number of π electrons. The set of possible numbers is quite easy to remember - the rule is simply 4n+2, where n is any positive integer (this is known as the Hückel rule, named after Erich Hückel, a German scientist who studied aromatic compounds in the 1930’s). Thus, if n = 0, the first Hückel number is (4 x 0) + 2, or 2. If n = 1, the Hückel number is (4 x 1) + 2, or 6 (the Hückel number for benzene). The series continues with 10, 14, 18, 22, and so on. Cyclooctatetraene has eight π electrons, which is not a Hückel number. Because 6 is such a common Hückel number, chemists often use the term 'aromatic sextet'.

Benzene is best visualized as a planar ring made up of carbon-carbon sbonds, with two ‘donut-like’ rings of fully delocalized π electron density above and below the plane of the ring (the fact that there is a ring of π electron density on both sides of the molecule stems from the fact that the overlapping p orbitals have two lobes, and the electron density is located in both). This general picture is valid not just for benzene but for all other aromatic structures as well.