Molecular Orbital Theory: Conjugation and Aromaticity

MO theory and conjugated pi bonds

The advantage of using MO theory to understand bonding in organic molecules becomes more apparent when we think about pi bonds.  We find that the theory predicts that when we have a connected series of sp² carbons, the pi bonds are said to be “conjugated.”   In a conjugated system the pi bonds can be delocalized over the whole series of atoms, and this leads to additional stabilization.  Note: Other second row sp² atoms, such as oxygen and nitrogen, can also participate in this delocalization, as can sp hybridized atoms.  If the conjugated system occurs in certain types of ring, such as a six-carbon benzene ring, it leads to exceptionally high stabilization called aromaticity, which we will discuss in section 13.5.

Aromaticity

Molecular orbital theory is especially helpful in explaining the unique properties of aromatic compounds such as benzene:

3D interactive model of benzene

Although benzene is most often drawn with three double bonds and three single bonds, in fact all of the carbon-carbon bonds iare exactly the same length (138 pm). In addition, the pi bonds in benzene are significantly less reactive than ‘normal’ pi bonds, either isolated or conjugated. Something about the structure of benzene makes its pi bonding arrangement especially stable. This ‘something’ has a name: it is called ‘aromaticity’.

What exactly is this ‘aromatic’ property that makes the pi bonds in benzene so stable? In large part, the answer to this question lies in the fact that benzene is a cyclic molecule in which all of the ring atoms are sp²-hybridized. This allows the pi electrons to be delocalized in molecular orbitals that extend all the way around the ring, above and below the plane. For this to happen, of course, the ring must be planar – otherwise the p orbitals couldn’t overlap properly. Benzene is indeed known to be a flat molecule.

Do all cyclic molecules with alternating single and double bonds have this same aromatic stability? The answer, in fact, is ‘no’. The eight-membered cyclooctatetraene ring shown below is not flat, and its π bonds react like ‘normal’ alkenes.

Clearly it takes something more to be aromatic, and this can best be explained with molecular orbital theory. Let’s look at an energy diagram of the pi molecular orbitals in benzene.

Quantum mechanical calculations tell us that the six pi molecular orbitals in benzene, formed from six atomic p orbitals, occupy four separate energy levels. pi₁ and pi₆* have unique energy levels, while the pi₂ – pi₃ and pi₄*- pi₅* pairs are degenerate, meaning they are at the same energy level. When we use the aufbau principle to fill up these orbitals with the six pi electrons in benzene, we see that the bonding orbitals are completely filled, and the antibonding orbitals are empty. This gives us a good clue to the source of the special stability of benzene: a full set of bonding MO’s is similar in many ways to the ‘full shell’ of electrons in the atomic orbitals of the stable noble gases helium, neon, and argon.

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 (pi₁ and pi₈*) have unique energy levels, while the other six form degenerate pairs. Notice that pi₄ and pi₅ are 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 pi 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 or group to be considered aromatic:

Rule #4 is known as the Hückel rule, named after Erich Hückel, a German scientist who studied aromatic compounds in the 1930’s. If n = 0, the Hückel number is 2. If n = 1, the Hückel number is 6 (the Hückel number for benzene). The series continues with 10, 14, 18, 22, and so on. Cyclooctatetraene has eight pi electrons, which is not a Hückel number. Because six is such a common Hückel number, chemists often use the term ‘aromatic sextet’.

Benzene rings are ubiquitous in biomolecules and drugs – below are just a few examples.

Recall that a benzene ring with a hydoxyl substituent -such as seen in the tyrosine structure above – is called a phenol.

Heterocycles – cyclic structures in which the ring atoms may include oxygen or nitrogen – can also be aromatic. Pyridine, for example, is an aromatic heterocycle. In the bonding picture for pyridine, the nitrogen is sp²-hybridized, with two of the three sp² orbitals forming sigma overlaps with the sp² orbitals of neighboring carbon atoms, and the third nitrogen sp² orbital containing the lone pair. The unhybridized p orbital contains a single electron, which is part of the 6 pi-electron system delocalized around the ring.

another image of orbitals in pyridine

Pyridoxine, commonly known as vitamin B₆, and nicotine are both substituted pyridines.

Pyrrole is a five-membered aromatic heterocycle.  In pyrrole, the lone pair electrons on the sp²-hybridized nitrogen are part of the aromatic sextet (contrast this to pyridine, where the lone pair occupies one of the sp² hybrid orbitals).

Why don’t we assume that the nitrogen in pyrrole is sp³-hybridized, like a normal secondary amine? The answer is simple: if it were, then pyrrole could not be aromatic, and thus it would not have the stability associated with aromaticity. In general, if a molecule or group can be aromatic, it will be, just as water will always flow downhill if there is a downhill pathway available.

Imidazole is another important example of an aromatic heterocycle found in biomolecules – the side chain of the amino acid histidine contains an imidazole ring.

In imidazole, one nitrogen is ‘pyrrole-like’ (the lone pair contributes to the aromatic sextet) and one is ‘pyridine-like’ (the lone pair is located in an sp² orbital, and is not part of the aromatic sextet).

Fused-ring structures can also fulfill the Hückel criteria, and often have many of the same properties as monocyclic aromatic compounds, including a planar structure. Indole (a functional group on the side chain of the amino acid tryptophan) and purine (found in guanine and adenine nucleotide bases) both have a total of ten pi electrons delocalized around two rings.

The nucleic acid bases of DNA and RNA – guanine, adenine, cytosine, thymine, and uracil – are all aromatic systems, with the characteristic aromatic properties of planarity and delocalized p electron density. When you study the structure and function of DNA and RNA in a biochemistry or molecular biology course, you will see that the planar shape of the bases plays a critically important role.