## Benzene

The structure of benzene is fascinating. Look at all these different attempts to depict it! Let me tell you a tiny bit of the history.

In 1865, August Kekulé argued that benzene is a ring of carbon atoms with alternating single and double bonds. Later, at a conference celebrating the 25th anniversary of this discovery, he said he realized this after having a daydream of a snake grabbing its own tail.

Kekulé’s model was nice, because before this it was hard to see how 6 carbons and 6 hydrogens could form a reasonable molecule with each carbon having 4 bonds and each hydrogen having one. But this model led to big problems, which were only solved with quantum mechanics.

For example, if benzene looked like Kekulé’s model, there would be 4 ways to replace two hydrogens with chlorine! You could have two chlorines next to each other with a single bond between them as shown here… or with a double bond between them. But there aren’t 4, just 3.

In 1872 Kekulé tried to solve this problem by saying benzene rapidly oscillates between two forms. Below is his original picture of those two forms. The single bonds and double bonds trade places.

But there was still a problem: benzene has less energy than if it had alternating single and double bonds.

The argument continued until 1933, when Linus Pauling and George Wheland used quantum mechanics to tackle benzene. Here’s the first sentence in their paper:

As you can see, there were models much stranger than Kekulé’s.

What was Pauling and Wheland’s idea? Use the quantum superposition principle! A superposition of a live and dead cat is theoretically possible in quantum mechanics… but a superposition of two structures of a molecule can have lower energy than either structure alone, and then this is what we actually see! Here’s what Pauling said later, in 1946:

But in reality, benzene is much subtler than just a quantum superposition of Kekulé’s two structures. For example: 6 of its electrons become ‘delocalized’, their wavefunction forming two rings above and below the plane containing the carbon nuclei!

Benzene is far from the only molecule with this property: for example, all the ‘anthocyanins’ I talked about last time also have rings with delocalized electrons:

In general, such molecules are called aromatic, because some of the first to be discovered have strong odors. Aromaticity is an important concept in chemistry, and people still fight over its precise definition:

• Wikipedia, Aromaticity.

One thing is for sure: the essence of aromaticity is not the aroma. It’s more about having rings of carbons in a plane, with delocalized electrons in so-called pi bonds, which protrude at right angles to this plane.

Another typical feature of aromatic compounds is that they sustain ‘aromatic ring currents’. Let me illustrate this with the example of benzene:

When you turn on a magnetic field (shown in red here), a benzene molecule will automatically line up at right angles to the field, and these electrons start moving around! This current loop creates its own magnetic field (shown in purple).

What does this current loop look like, exactly? To understand this, you have to remember that the benzene’s 6 delocalized electrons lie above and below the plane of the benzene molecule.

So, if you compute the electric current above or below the plane of the benzene molecule, it goes around and around like this:

But if you compute the electric current in the plane of the benzene molecule—where the nuclei of the carbon atoms are—you get a much more complicated pattern. Some current even flows backward, against the overall flow!

This current creates its own magnetic field. Outside the benzene molecule, this points the same way as the externally imposed magnetic field, reinforcing it. So, a magnetic field that is strengthened when it goes through benzene. This is called ‘antishielding’—or ‘deshielding’ in this picture from Organic Spectroscopy International:

I want to understand aromaticity and aromatic ring currents better. If I have the energy, I’ll say more in future articles. For example, I want to tell you about ‘Hückel theory’: a simplified mathematical model of aromatic compounds that’s a lot of fun if you like graph theory and matrices.

### References

Please click on the pictures to see where I got them. You can learn more that way! Some came from Wikicommons, via these Wikipedia articles:

• Wikipedia, Benzene.

• Wikipedia, Aromatic ring current.

including the pictures of current vector fields in benzene, created by ‘Hoferaanderl’.

### 14 Responses to Benzene

1. Toby Bartels says:

You left out the ‘u’ in ‘Hückel’ … but you left in the dots! (If you were hand-writing HTML, then perhaps you typed &amp;uml; instead of &amp;uuml;.)

2. Raphael Berger says:

Hi John, glad that you like my pictures. On top I could offer some ideas on antiaromaticity, check out 2.17 here https://pubs.rsc.org/en/content/articlelanding/2021/cc/d1cc03350f. You will come across the Jahn-Teller effect and other intersting stuff.

Raphael (aka Hoferaanderl)

3. You should look into “cation-pi” attractions! https://en.wikipedia.org/wiki/Cation–pi_interaction

The nicotinic acetylcholine receptor is a neat example of a biological example of this effect… which was confirmed by switching in fluorines for hydrogens to change the strength of the effect

4. Perry Metzger says:

Aromatics are quite cool. You mention Hückel but not the 4n+2 rule (which works surprisingly well). Polycyclic aromatics are another really fun topic; graphene is (in some sense) a really big polycyclic aromatic system, and there is tons of interesting chemistry in simpler ones. So-called “bay configuration” polycyclics are generally carcinogens as well. I have a great monograph on polycyclics I could recommend but sadly it’s in a box right now and I can’t remember the author’s name offhand.

• John Baez says:

In my last post, on anthocyanins, I wrote:

I may write more about this if I ever solve some puzzles that are bothering me, like the mathematical origin of Hückel’s rule, which says a planar ring of carbon atoms is aromatic if it has 4n + 2 pi electrons. I want to know where the formula 4n + 2 comes from, and I’m getting close.

I should be able to derive it from Hückel molecular orbital theory; someone must have done this already—like, maybe, Hückel?—but I’m finding it hard to find a clear treatment.

After that I would love to dig into polycyclic aromatics. And my ultimate goal is to understand charge fractionalization in polyacetylene.

If you ever dig up that book or recall its title, please let me know!

• Noah Rahman says:

For charge fractionalization the SSH model is probably your best bet, but Zoltan Soos at Princeton wrote some papers that were good chemistry perspective takes on it

• Raphael says:

If you have a Möbius topology with a single $\pi$ twist you obtain a 4n rule for aromaticity and a 4n+2 rule for antiaromaticity. The same if you get to triplet excited states, if you have both you return back the original Hückel rule. The simple Hückel part of the explanation can be visualized by a “Frost-Diagram” using regular n-polygons.

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