Rules For Aromaticity

Rules For Aromaticity: The 4 Key Factors

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?

Table of Contents

1. Four Key Rules for Aromaticity
2. Condition #1 for Aromaticity: The Molecule Must Be Cyclic
3. Condition #2: Every atom in the ring must be conjugated
4. Condition #3: The Molecule Must Have [4n+2] Pi Electrons
5. Which Electrons Count As “Pi Electrons”?
6. Pyridine and the Benzene Anion
7. Some Examples With 5-Membered Rings
8. Condition #4: The Molecule Must Be Flat
9. Summary: Rules For Aromaticity
10. Notes
11. (Advanced) References and Further Reading

1. Four Key Rules For Aromaticity

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.

2. Condition #1 for Aromaticity: 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.

3. Condition #2 For Aromaticity: 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]

4. Condition #3 For Aromaticity: 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 fulfill 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.

5. Which Electrons Count As “Pi Electrons”, And Which Do Not?

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 oxygen?
• 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….

6. Some Electrons Don’t Count: 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.

7. Some Examples Of Aromatic 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.

8. Condition #4 For Aromaticity: 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, cis, trans, 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.

9. Summary: Rules For Aromaticity

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.

Check out these worked examples 

Notes

Note 1. Fun fact. Pyrrole actually reacts with acid on carbon, not nitrogen!

Note 2. Weird case: the one with aromaticity around the exterior but not on the inside.

Note 3. 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.

(Advanced) References and Further Reading

1. Quantentheoretische Beiträge zum Benzolproblem
   Die Elektronenkonfiguration des Benzols und verwandter Verbindungen
   Erich Hückel
   Zeitschrift für Physik 1931, 70, 204–286
   DOI: 10.1007/BF01339530
   Erich Hückel achieved recognition by elaborating, together with Peter Debye, the theory of strong electrolytes in 1923 and later by applying a simplified version of quantum theory to p-electrons in conjugated molecules, which became known as Hückel molecular orbital (HMO) theory. Although he never explicitly formulated a “4n + 2 rule”, this was obvious from his work. Hückel showed that monocyclic systems with continuous conjugation having 6, 10, 14, etc. p-electrons benefited from extra stabilization and were aromatic. But it is more accurate to refer to the “Hückel 4n + 2 p-electron rule,” rather than to “Hückel’s rule.”
2. Aromaticity Today: Energetic and Structural Criteria
   Mikhail Glukhovtsev
   Journal of Chemical Education 1997, 74 (1), 132
   DOI: 1021/ed074p132
   This paper discusses two of the criteria for establishing aromaticity – planarity and a positive stabilization energy. The latter can be verified by computational methods, as the article demonstrates.
3. Global aromaticity at the nanoscale
   Rickhaus, M., Jirasek, M., Tejerina, L. et al.
   Nature Chem. 12, 236–241 (2020)
   DOI: 10.1038/s41557-019-0398-3
   This paper was published in early 2020 and officially sets the record for the largest aromatic system, with 162 p electrons! Evidence for aromaticity comes from both NMR measurements and experimental (NICS) calculations.
4. Nucleus-Independent Chemical Shifts:  A Simple and Efficient Aromaticity Probe
   Paul von Ragué Schleyer, Christoph Maerker, Alk Dransfeld, Haijun Jiao, and Nicolaas J. R. van Eikema Hommes
   Journal of the American Chemical Society 1996, 118 (26), 6317-6318
   DOI: 10.1021/ja960582d
   This paper is an advanced topic but worth including here, as it is one of Prof. Schleyer’s most highly cited papers. Aromaticity is a difficult concept to accurately define, but one way to empirically measure it is to use computational methods. Here, Prof. Schleyer describes the “NICS effect” as a method of measuring aromaticity, based on magnetic susceptibility exaltation. Aromatic compounds have a ‘ring current’ due to the conjugation of the p orbitals and the presence of delocalized p electrons, and are therefore diamagnetic. This can be measured experimentally or probed computationally.
5. The Cyclodecapentaene System
   Dr. E. Vogel, Dipl.‐Chem. H. D. Roth
   Angew. Chem. Int. Ed. 1964, 3 (3), 228-229
   DOI: 10.1002/anie.196402282
6. Perspektiven der Cycloheptatrien-Norcaradien-Valenztautomerie
   Emanuel Vogel
   Pure Appl. Chem. 1969, 20 (3), 237-262
   DOI: 10.1351/pac196920030237
   The above two papers are on the synthesis and characterization of cyclodeca-1,3,5,7,9-pentaene. The NMR spectrum shows a diamagnetic ring current of the type expected in an aromatic system.
7. Synthesis of 1,6-didehydro[10]annulene. Observation of its exceptionally facile rearrangement to form the biradical 1,5-dehydronaphthalene
   Andrew G. Myers and Nathaniel S. Finney
   Journal of the American Chemical Society 1992, 114 (27), 10986-10987
   DOI: 10.1021/ja00053a059
   Myers (now at Harvard) started his career as a professor at Caltech, and his early papers are gems in physical organic chemistry. This is no exception, and the brevity of this communication belies the extreme difficulty of this experimental work, both in synthesis and characterization. The compound intramolecularly cyclizes via a diradical intermediate at low temperature to naphthalene, and this type of reaction is now known as a “Myers cyclization” after Prof. Myers.
8. HOMO-AROMATIC STRUCTURES
   S. Winstein
   Journal of the American Chemical Society 1959, 81 (24), 6524-6525
   DOI: 10.1021/ja01533a052
   The term ‘homoaromaticity’ was first introduced to chemistry in this paper by organic chemist Prof. Saul Winstein (UCLA). Today, the prefix ‘homo-’ is commonly used in chemistry to denote extension by 1 methylene (-CH₂-) group.
9. UNSATURATED MACROCYCLIC COMPOUNDS. XV.1 CYCLOTETRADECAHEPTAENE
   Franz Sondheimer and Yehiel Gaoni
   Journal of the American Chemical Society 1960, 82 (21), 5765-5766
   DOI: 10.1021/ja01506a061
   [14]annulene has been synthesized but found to be unstable even though it has 14 p electrons as per Hückel 4n + 2 p-electron rule. This is because it cannot achieve planarity, thus proving that planarity is an essential criterion for achieving aromatic stabilization!
10. On the structure and thermochemistry of [18]annulene
    Jerome M. Schulman and Raymond L. Disch
    Journal of Molecular Structure: THEOCHEM 1991, 234, 213-225
    DOI: 10.1016/0166-1280(91)89014-R
    [18]annulene is large enough to minimize steric interactions between the internal hydrogens in a geometry that is free of angle strain. The properties of [18]annulene are consistent with its being aromatic.
11. Ab Initio Density Funtional vs Hartree Fock Predictions for the Structure of [18]Annulene: Evidence for Bond Localization and Diminished Ring Currents in Bicycloannelated [18]Annulenes
    Kim K. Baldridge Prof. Jay S. Siegel
    Angew. Chem. Int. Ed. 1997, 36 (7), 745-748
    DOI: 10.1002/anie.199707451
    An stabilization energy of 18 kcal/mol has been calculated for [18]annulene.