Rules For Aromaticity

by James

in Aromaticity

In the last post we introduced the concept of aromaticity, a property of some unusually stable organic molecules such as benzene. Although some aromatic molecules are indeed fragrant (hello, vanillin! ) the term “aromaticity” actually has nothing to do with smell.  We saw that aromatic molecules:

  • have an extremely high resonance energy (36 kcal/mol for benzene)
  • undergo substitution rather than addition reactions
  • have delocalized pi-electrons

We also gave a few example of other molecules besides benzene which are aromatic, and some which look similar to benzene (e.g. cyclooctatetraene) which are not.

So what are the rules? How can we predict whether a molecule is aromatic or not?

There turn out to be 4 conditions a molecule must meet in order for it to be aromatic.

It’s all or nothing. If any of these conditions are violated, no aromaticity is possible.

  • First, it must be cyclic.
  • Second, every atom in the ring must be conjugated.
  • Third, the molecule must have [4n+2] pi electrons (we’ll explain in depth what that means, below)
  • Fourth, the molecule must be flat (usually true if conditions 1-3 are met, but there are rare exceptions)

Let’s go into more detail.

Condition #1: The Molecule Must Be Cyclic

Determining if a molecule is cyclic is pretty straightforward. Is there a ring? If yes, move to condition #2. If there’s no ring, forget it.

Case in point: (Z)-1,3,5 hexatriene has the same number of pi bonds (and pi electrons) as benzene, but isn’t aromatic. No ring, no aromaticity.

Condition #2: Every atom in the ring must be conjugated

Obviously, being cyclic isn’t a sufficient condition for aromaticity. Just look at cyclohexene, above right. Not aromatic.

In order for aromaticty to exist, there must also be a continuous ring of p-orbitals around the ring that build up into a larger cyclic “pi system”.

One way of saying this is that every atom around the ring must be capable of conjugation with each other .

There are a few alternative ways to say the same thing.

We can also say:

  • “Every atom in the ring must have an available p orbital”, or
  • “Every atom in the ring must be able to participate in resonance”.

Remember that the “available p orbital” condition applies not just to atoms that are part of a pi bond, but also atoms bearing a lone pair, a radical, or an empty p orbital (e.g. carbocations). [See this post on conjugation and resonance if you are unsure].

The key thing  that “kills” conjugation is an sp3 hybridized atom with four bonds to atoms. Such an atom cannot participate in resonance.

This is why the lone pair on pyrrole (below) isn’t as basic as you’d expect a nitrogen to be. Protonation of the nitrogen disrupts the conjugation around the ring, destroying aromaticity in the process. [Note 1]

Advanced note. There’s actually several molecules which are conjugated around the perimeter of the ring but the interior carbons are sp3 hybridized. Still counts as aromatic. [Note 2]

Condition #3: The Molecule Must Have [4n+2] Pi Electrons

The third condition is that the cyclic, conjugated molecule must have the correct number of pi electrons. Benzene and cyclooctatetraene are both cyclic and conjugated, but benzene is aromatic and cyclooctatetraene is not. The difference is that benzene has 6 pi electrons, and cyclooctatetraene has 8. [We’ll explain why this makes a difference in subsequent posts].

Our quick shorthand we often use is to say that benzene has [4n+2] pi electrons and cyclooctatetraene does not.

However, this term [4n+2] causes a lot of confusion in organic chemistry. I’ve known students who will stare at a molecule and try to figure out what “n” is.

“n” is not a property of the molecule!

Commenter Claire had a great way of putting it:

“4n+2 is not a formula that you apply to see if your molecule is aromatic. It is a formula that tells you what numbers are in the magic series. If your pi electron value matches any number in this series then you have the capacity for aromaticity.”

Exactly!  The “magic series” is: 2, 6, 10, 14, 18, 22….. (and counting up from 4 after that). [note 3]

[4n+2] is mathematical shorthand for writing out the series [2, 6, 10, 14, 18, 22…] .

We can generate this series by plugging in whole numbers (“n” = 0, 1, 2, 3, 4… ) to the [4n+2] formula. Those values of “n” have nothing to do with molecules. We are just using them to generate the series.

So for n = 0 , we have [4 (0) + 2] = 2
for n = 1 , we have [4 (1) + 2 ] = 6
for n = 2, we have [4 (2) + 2 ] = 10
for n = 3, we have [4 (3) +2 ] = 14

And so on. See how it generates the series [2, 6, 10, 14…] ? That’s the point of [4n+2].

The numbers in this “magic series” are sometimes referred to as “Hückel Numbers” after Erich Hückel, who proposed this rule back in 1931.

The condition that aromatic molecules must have [4n+2] pi electrons is sometimes called “Hückel’s rule”.

In the figure below, molecules which fulfil Hückel’s rule are in green; those which do not fulfill Hückel’s rule are in red.

Note that we can count electrons in pi bonds as well as electrons from lone pairs (so long as the carbon isn’t already participating in a pi bond – see below). So the cyclopentadiene anion has six pi electrons – 4 from the two double bonds, and two from the lone pair on carbon.

Which Electrons Count As “Pi Electrons”?

That seems straightforward enough. However, complications can arise when we have atoms in the ring which both participate in pi bonding and also have a lone pair. For example,

  • how do we count electrons in the benzene anion (below left) or pyridine? Do we count the lone pair electrons as Pi electrons, giving a total of 8? Or do we ignore them?
  • What about furan (middle) which has two lone pairs on oxgyen?
  • What about pyrrole, with its lone pair on nitrogen, or imidazole, with two nitrogens?

In order to answer these questions, it’s important to remind ourselves of how p orbitals contribute to aromaticity in benzene.

In benzene, each p orbital is arranged at right angles (90°) to the plane of the ring. Each p orbital contains a single electron. We can verify the total number of pi electrons in benzene  by counting the pi bonds: 3 pi bonds times two electrons = 6 pi electrons total.  

Note that the C-H bonds are at 90° to the pi system. If there was a lone pair where the C-H bond is, then it wouldn’t be able to interact with the pi system at all. Which brings us to….

Pyridine and the Benzene Anion

The benzene anion has a lone pair on one of the carbons. This lone pair can’t be in a p orbital, since the p-orbital is participating in the pi system. Instead, it’s at 90 degrees to the pi system, in the plane of the ring.

In other words, the lone pair on carbon doesn’t count as a pair of pi electrons since it can’t overlap with the pi system.

The same is also true for pyridine, where the lone pair is also at right angles to the pi system.

So while in each case you might be tempted to say that they have 8 pi electrons, the correct answer is 6. This is a Hückel number, and both of these molecules are in fact aromatic.

The bottom line: each ring atom can contribute a maximum of one p orbital toward the pi system.

Some Examples With 5-Membered Rings

Some molecules with five-membered rings can also present ambiguities.

The cyclopentadiene anion (below)  has a lone pair on one of the carbons. Can this lone pair contribute to the pi system?

Since that carbon is not involved in any pi-bonding, the answer is yes.

The total number of pi electrons for the cyclopentadiene anion equals 2 (from the lone pair) plus the 4 electrons in the two pi bonds, giving us a total of 6. This is a Hückel number and the cyclopentadiene anion is in fact aromatic.

A similar situation arises for pyrrole. The nitrogen bears a lone pair but  is not involved in a pi bond (unlike pyridine, above). Therefore it can contribute to the pi system and this gives us a total of 6 pi electrons once we account for the 4 electrons from the two pi bonds.

A curious case is furan, where the oxygen bears two lone pairs. Does this mean that furan has 8 pi electrons? No! 

Why not? Because as we noted above, each atom can contribute a maximum of one p-orbital towards the pi system. In furan, one lone pair is in a p orbital, contributing to the pi system; the other is in the plane of the ring. This gives us a total of 6 pi electrons. Furan is aromatic. (So is thiophene, the sulfur analog of furan).

Finally there is imidazole, which has two nitrogens. One nitrogen (the N-H) is not involved in a pi bond, and thus can contribute a full lone pair; the other is involved in a pi bond, and the lone pair is in the plane of the ring. This also gives us a total of 6 pi electrons once we account for the two pi bonds.

 

Condition #4: The Molecule Must Be Flat

The fourth condition for aromaticity is that the molecule must be flat (planar).

Aromaticity is such a stabilizing property (worth 20-36 kcal/mol) that generally a molecule that is

  • cyclic
  • conjugated
  • has [4n+2] pi electrons

will also be flat.  Give a molecule a large enough potential energy well, and it will fall into it eventually.

It’s a bit like the punch line to the old (crude) joke about why dogs adopt a certain energetically favourable conformation:  “Because they can”.  

As with certain vertebrates, the only thing that preventing a molecule that fulfills the first three conditions from being flat is if the flat conformation is incredibly strained.   One example in this category is the molecule known as [10]-annulene, an isomer of which is drawn below left. In the trans, cistrans, cis, cis isomer, the molecule is cyclic, conjugated, and has 10 pi electrons, but the two marked hydrogens bump into one another when attempting to adopt a flat conformation.

The molecule is prevented from adopting planarity due to this punitive Van Der Waals strain , and is therefore not aromatic. 

Interestingly, if the hydrogens are removed and replaced with a bridging CH2 group, the strain is relieved and the pi bonds can adopt a planar conformation. The molecule below right shows the expected properties of an aromatic molecule.

Summary

This post went through the four conditions a molecule must meet to be aromatic.

Generally, determining if a molecule is cyclic and conjugated isn’t what trips people up.

It’s the damn pi electron-counting!

So in the next post, we’ll play the game show “Is This Aromatic?” with a series of different contestants and try to demonstrate a relatively quick n’ easy plan for determining if an unknown molecule is aromatic or not.

After that, we’ll look at the molecular orbitals and attempt to understand what exactly is so special about the Hückel series.

Thanks to Matt Knowe for assistance with this post. 


 

 Fun fact. Pyrrole actually reacts with acid on carbon, not nitrogen!

 Weird case: the one with aromaticity around the exterior but not on the inside.

It should be noted that Huckel’s rule starts to break down for higher numbers of pi electrons (>20) in polycyclic systems. I’m not going to go into the details here. The wikipedia article covers it well.

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{ 2 comments… read them below or add one }

Paul

I’m glad but kind of surprised that you didn’t mention homoaromaticity. Big can o’ worms. Have you deliberately tagged it as “hackles” rule?

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James

Homoaromaticity is the kind of thing that deserves a footnote, since it’s so interesting but probably not required for the average reader. Thanks for the tip about “hackles rule” : – )

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