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Aromaticity

By James Ashenhurst

Huckel’s Rule: What Does 4n+2 Mean?

Last updated: October 9th, 2019 |

Hückel’s Rule: What Does 4n+2 Mean?  

“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.” – Claire

Table of Contents

  1. If You’re Looking For “n” In A Molecule,  You’re Looking For The Wrong Thing
  2. “n” Is Not A Characteristic Of The Molecule!
  3. In Huckel’s Rule, The Formula (4n+2) Is An Algebraic Expression Of The Series 2, 6, 10, 14… Where ‘n’ Is A Natural Number
  4. Summary: “n” Comes From Algebra, NOT From Chemistry
  5. (Advanced) References and Further Reading

1. Stop Looking For “n” In A Molecule, Because You’re Looking For The Wrong Thing

The other night a student came to me with a question about aromaticity.

“There’s one thing I don’t get”, she said. “They say a molecule has to have 4n+2 electrons to be aromatic.  How do you find ‘n’ ?”

Teachable moment!

2. In the [4n+2] Rule (“Huckel’s Rule”), “n” Is Not A Characteristic Of The Molecule! 

“n” is not a characteristic of the molecule! Let me explain.

In order for a molecule to be aromatic, it has to have the following characteristics:

  • It must be cyclic
  • It must be conjugated (i.e. all atoms around the ring must be able to participate in π-bonding through resonance)
  • It must be flat
And, it must have a certain number of π-electrons. This is known as Huckel’s rule. The number of π electrons must equal one of the numbers in this series:
2, 6, 10, 14, 18….and so on. For example, we can find aromatic molecules with 2 pi electrons, 6 pi electrons, 10 pi electrons, 14 pi electrons, 18 pi electrons, and so on.
But we have never found aromatic molecules with 0, 1, 3, 4, 5, 7, 9, 11, 12, 13, 15, 16, 17 (and so on) pi electrons. Those numbers are not in the series.
To reprise: the number of pi electrons in an aromatic molecule will always be found in the series  [2, 6, 10, 14, 18 …and so on] 
However, there has to be a better way of expressing it than [2, 6, 10, 14, 18… and so on”]. Right?

3. In Huckel’s Rule, The Formula (4n+2) Is An Algebraic Expression Of The Series 2, 6, 10, 14… Where ‘n’ Is A Natural Number

There is! This is where we use algebra. this is where n is going to come in – we are going to use math (algebra) to replace “2, 6, 10, 14, 18… and so on” with a condensed formula. 
2, 6, 10, 14, 18… is an example of an algebraic series.
Algebraically, you can express this with the formula (4n +2), where n is a natural number (0, 1, 2, 3…)
Let’s plug in different values of n (we will put n in bold)
For the formula 4n + 2
For n = 0, we get (4 × 0 + 2) = 2
For n = 1, we get (4 × 1 + 2) = 6
For n = 2, we get (4 × 2 + 2) = 10
For n = 3, we get (4 × 3 + 2) = 14
For n = 4, we get (4 × 4 + 2) = 18
We can keep going, but do you get the idea?
By using the formula [4n +2], we are expressing the same idea as  [2, 6, 10, 14, 18… and so on] but it is a lot more precise.

4. Summary: “n” Comes From Algebra, NOT From Chemistry

Molecules that have the 3 characteristics listed above (cyclic, conjugated, flat) and have this number of π electrons [4n +2] will be aromatic. The letter “n” is not a characteristic of the molecule!


[Thanks to commenters Shawn and Egon Willenhagen for  suggested edits and to Jamey for a correction]


(Advanced) References and Further Reading

  1. CYCLOHEPTATRIENYLIUM OXIDE
    W. von E. Doering and Francis L. Detert
    Journal of the American Chemical Society 1951 73 (2), 876-877
    DOI: 10.1021/ja01146a537
    In this paper, esteemed Harvard chemist William Eggers von Doering succinctly summarized the Huckel rule as 4n + 2 pi electrons (although writes it (2n+4 here) in his synthesis of cycloheptatrienylium oxide (“tropone”).

 

Comments

Comment section

90 thoughts on “Huckel’s Rule: What Does 4n+2 Mean?

  1. I find some students dissatisfied with the idea that n doesn’t actually refer to anything in the molecule. I don’t know what else to tell them. It seems like they can still apply the rule though.

    1. Well, it’s not so much that it doesn’t refer to anything… the original description is just missing an implied “…where n can be any natural number”

      1. You can work out the number of pi electrons from the molecule (x)
        Then working backwards using Huckel’s Rule –> (4n+2) = x
        (x-2)/4 = n

        If n is a natural number (0,1,2,3…) and the structure is a planar monocycle with an uninterupted cyclic pi-cloud then the molecule is aromatic.

      2. n is just any natural number which is used to satisfy the 4n 2 rule.
        1. Count the number of pi electrons.
        2. If that number becomes equal 4n 2 for any value of n then that compound is aromatic(or in other words if the number of pi electrons come in the series – 2, 6, 10, 14, 18….. then that compound will be aromatic)..
        Hope all understand what I mean.

  2. I find this a little bit confusing. How do i get that the molecule is flat? I always thought that the fact that the aromatic molecule is planar is caused by aromaticity itself (or even distribution of electrons in the rings above and below aromatic core). From this article it seems to me like the planarity is something like prerequisite (i think of prerequisite like that it must be cyclic and conjugated). I’m not sure if i explained my problem properly but if you got some of my idea, can you please explain it?

    1. Good question. It’s generally a good assumption that if the molecule fits the first three criteria, the molecule is flat, unless there is some steric impediment to it doing so. One notable exception is one of the isomers of [10]-annulene (see figure 3 in this page) which cannot lie flat due to steric clash between the hydrogens.

  3. Thanx for this post; there is a lot of confusion about the Hueckel rule. I personally like azulene more for the 10-electron example, as each individual ring does not conform the Hueckel rule, while your example still has to separate rings with each 6 π electrons. Another aspect of this is that ‘aromatic’ bonds, those in the delocalized bond system, have a bond length somewhere in between that of a single and of a double bond.

  4. Huckel model is obsolete. See

    ARKIVOC, 2008, Part xi, p. 24 – 45

    According to above comments the very aromatic hydrocarbon pyrene is anti-aromatic because it includes 16 pi electrons?

    1. According to above James’ amusing comments regarding ‘algebraic sens of n’ the aromatic hydrocarbon pyrene is anti-aromatic because it includes 16 pi electrons! Also, the non-existent hexazine should be quite stable because his Huckel aromaticity!
      Huckel model became obsolete many years ago, see, for instance, ARKIVOC, 2008, Part xi, p. 24-45

      1. Yes, it’s worth noting that the Huckel model starts to fall apart for even moderately complex polyaromatic hydrocarbons, so thank you for pointing that out. However, as far as the most common examples students will encounter in an introductory class (i.e. the intended audience of this site), the Huckel model is fine. By all means learn the exceptions once you’ve mastered the basics.

    1. Dear Adil! The term aromatic is an old name used for those compounds having pleasant odor, although they are not in the category what we call as “Aromaticity”.

  5. It should read:
    For n = 0, we get (4 × 0 + 2) = 2
    For n = 1, we get (4 × 1 + 2) = 6
    For n = 2, we get (4 × 2 + 2) = 10
    For n = 3, we get (4 × 3 + 2) = 14

  6. I have little confusion … n is not the characteristic of a molecule so what is it???
    all have same value of n’ or every molecule has different n’ value how we can find the value of ‘n???

        1. No, its the number of electrons in the pi-bonds. Take benzene, for example, we construct this as alternating pi bonds in a six membered ring. If the pi, bonds are alternating, then we know that there must be half the number of double bonds as there are single (3 in this case). So, we find that that the number of electrons in the pi bonds are 3×2 (because there are two electrons in every double bond), so we see that the 6 electrons in the pi bonds, satisfies the 4n+2 rule. Another way to put the 4n+2 rule is that if you set 4n+2 equal to the number of electrons in the pi bond and solve for n, you will find that n will be a whole number. Therefore n must be a whole number that satisfies this equation 4n+2=x, where x = the number of electrons in the pi bonds. The reason for this is probably related to quantum mechanics, since n must be a whole number, it must be a quantized value of some kind…that’s just a guess though.

  7. Hi I’m confused on the last structure: I don’t see how the last dicyclic structure has 10 pi electrons. At the tertiary carbons that the cycloheptane and cyclopentane are connected to: aren’t there no space for electrons? Or they don’t have Hydrogens, which I’ve been counting as electrons for the previous examples.

    1. Sophia !the last structre has 10 pi bond because it contain 5 double bond and each double bond contain 2 pair of electron so they become 10 pi electron.

      1. You would think it would contain 4 electrons (since a double bond implies that there are double the amount of the number of electrons in a single bond), but its important to note that that the 4n+2 requirement isn’t dependent on the electrons of the double bond, but of the pi bond…there is a difference. A double bond = 1 pi bond + 1 sigma bond. The pi bond refers to sideways orbital overlap of one of the 3 p orbitals, resulting in a shorter bond.

        We are taught that a p orbitals house 6 electrons, but this is wrong. the p sublevel houses 6 electrons. It also has 3 individual p orbitals in it, each containing 2 electrons. If you’re curious as to why, look up the Zeeman effect. So basically because its only one p orbital for each carbon in the bond, there are 2 electrons total in the pi bond, but four in the double.

  8. Sir ,, i am still confused why annulene is not aromatic,,,,how steric hinderence affect it????

  9. Is a compound having more than one ring aromatic even if a single ring is aromatic? For eg. if benzene is linked to another five-membered ring (with no pi-bonds) to form a bicyclic compound, can it be called aromatic?

    1. Yes, what you’re describing is simply a substituted benzene which happens to have substituents which form a ring. Doesn’t change aromaticity.

  10. What if you have a molecule that is made from taking 1 benzene and putting 6 benzene rings around it?

    You get a cyclohexane ring in the center. Does this benzene bonded to 6 other benzene rings change the aromaticity or is the molecule itself still aromatic even though the ring on the inside of the molecule(cyclohexane) is not?

    1. and why can’t 2 aromatic rings bonded to each other keep their pi bond and form an alkyne? I mean surely there are cases of cycloalkynes.

  11. Thank you for that concise and simplified explanation. Perhaps you could give some tips to the people at Khan academy so they can improve their explanation!

  12. Hey James, I have 2 questions about ortho meta para directors and i was wondering if you would be able to answer them.
    1. If you have HSO3 on a ring and add NaOH I believe the OH replaces the HSO3. Would you need to add NaOH and heat, and then H3O and H2O as the total step to accomplish this? or just NaOH and heat?
    2. If you have two ortho/para directors on a ring and one is stronger than the other, say NH2 and CH3, and all other spots are open and you are adding Br2 in say acetic acid, would the Br2 only add to the NH2 directed postions? Or would it go to every spot on the ring?

  13. Actually sorry to say all of you are worng. n in 4n+2pi electron comes from molecular orbital theory where n stand for number of degenerate orbitals. in benzene only one degenerate orbital so n =1. so benzene satisfy huckle rule. same applies to ther members as well.

  14. Thank you ! it was very helpful , however I wanted to know while counting the pi bonds , do the lone pairs of electron play any role ?

      1. How do you know whether or not the lone pair electrons are aligned with the other electrons of the pie system? Thanks a bunch I really enjoy your site!

  15. So the pi electrons are those which make a pi bond?
    Like in benzene it has 3 alternate pi bonds which keep moving so at a time there are only 3 pi bonds…so the electrons which form these pi bonds are 6.
    Am I right?

  16. Sir,
    Can you also tell me why a three carbon ring with a pi bond and alternate “+” charge is aromatic but a three carbon ring with a pi bond and alternate “-” charge is not aromatic?

    1. Count the pi electrons. The first case has two pi electrons (2 in the pi bond, zero in the p orbital of the carbocation), which is a Huckel number. The second case has 4 pi electrons (2 in the pi bond, 2 in the p-orbital of the carbon which bears the negative formal charge). 4 is not a Huckel number. It is not aromatic.

  17. l understand that for a compound to be aromatic using Huckel’s rule,first you should know the number of pi electrons in the compound and if you substitute any integer value into the formula and the result amounts the number of pi electrons in the compound then that integer substituted becomes the value of n for that compound.

  18. This was so helpful, so clear and consice and really helped. Every time I’m stuck on a concept in organic chem, I come to this website, it’s been an absolute life saver. Thank you!

    1. Antiaromaticity is a characteristic of a cyclic molecule with a π electron system that has higher energy due to the presence of 4n electrons in it. Unlike aromatic compounds, which follow Hückel’s rule ([4n+2] π electrons) and are highly stable, antiaromatic compounds are highly unstable and highly reactive.

  19. MY CANCER STATEMENT

    After working for ~63 years in electronics, communications, and satellites fields. I believe that I have discovered the main cause for most Cancers, Alzheimer’s, MS, and other diseases. They all are causes because we are over-saturating our immune systems with trillions and trillions of pi-bonding electrons in caffeine (10) and benzene (6) that creates the large magnetic current energy fields shown below.

    The psychoactive chart didn’t copy and paste, but I have it.

    These magnetic fields can electronically mutate any of your body’s innate and adaptive immune cells, plus your brains glial and neurons cells, and the Hydrogen bonding of your DNA. We have many different microscopic analog and digital voltage levels in our body and the strong caffeine with 10 pi-bonding electrons and benzene with 6 pi-bonding electrons magnetic fields can mutate these microscopic voltages.

    Electron-biologist researcher. Del Parkinson

    This molecule is small enough to fit more than 2000 of these carcinogenic molecules between each of the brains synoptic gaps and mutate them. An 81mg baby aspirin has ~270 quintillion of these carcinogenic molecules. This would add approx one million of these into each cell of your body.

    *Nobody was talked about the magnetic current (Weber) fields or the electrostatic potentials (Newton Dynes) that are created by the carcinogenic caffeine-10 or benzene-6 molecules. I have many reports. Will you help me? Lets talk. Del.

    delparkinson@msn.com 2nd Peter Ch 1 Verse 5-8

  20. Ok, after looking a million places, this site explains it best, but I would like to propose some wording that made it make sense for me.

    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 aromatic. To find how many pi electrons you have, multiply the number of pi bonds by 2 and then compare that number to this formula. It it works out with n as a whole integer, then you have aromaticity. Yes?

      1. n=0 1 2 3 .., what does it mean
        i cant understand
        while in case of benzene n=1 and has 6 pi electrons.
        then from where u bring the value of n
        any rule for the value of n ., how we can understand that n = ? in any molecule ?
        can w right 2 in case of benzene ?

        i have alot of confusion in this plz rply me fast

  21. Flat is important Azonine is an unsaturated heterocycle of nine atoms, with a nitrogen replacing a carbon at one position is aromatic. Oxonine an unsaturated heterocycle of nine atoms, with an oxygen replacing a carbon at one position is not aromatic.
    To What Extent Can Nine-Membered Monocycles Be Aromatic?
    Paul von Rague´ Schleyer,*[a] La´szlo´ Nyula´szi,*[b] and Tama´s Ka´rpa´ti[b]

    1. p orbitals must align themselves in the same plane in order to establish conjugation. If the molecule is not “flat”, i.e. if the orbitals are not aligned in the same plane, then aromaticity is not possible.

  22. Hello, found an error on the page (I believe). In your 2pi 4pi 6pi 8pi small picture examples, it states that the cyclo-octane with the 8pi is Not Aromatic but in fact its Antiaromatic. Not Aromatic would be incorrect!

    1. Hi Ryan – haven’t got to antiaromaticity yet, so I didn’t include that designation. However cyclooctatetraene can wiggle out of being antiaromatic because it is sufficiently flexible to avoid being flat. It adopts a tub shape.

      Thanks for the comment! James

  23. Correction:-

    Algebraically, you can express this with the formula (4n +2), where n is a natural number (0, 1, 2, 3…)

    It should be n is a *whole* number.

    Natural numbers are counting numbers and does not include 0.
    Whole numbers are counting numbers plus 0.

  24. Gone through many other sites, but not one has been able to explain it this well! Thank you for helping me understand as well as for the abundance of other valuable information on your page! Much thanks!

  25. If we put n as a number of pi bonds present in the chemical structure then also we get the one of the number belongs to series
    2,6,10,14,18…… Then also we conclude it is aromatic…. Am i right?

  26. this helped a lot as a student. it should also kindly suggest mentioning that counting Pi bonds is just counting 2 Pi electrons per every double bond. ignore the sigma bonds. i was confused for a bit

  27. Thanks so much foe your useful information but still I have one problem with n
    Can we say the meaning of n is the number of ring or not???

  28. How can we apply Huckel’s Rule when we have a hetroatom with lone pairs in the ring? How should we be counting the number of electrons then?

  29. You are correct to say that n isn’t in the molecule, but yet you fail to show your students how to find the n. Not once did you even teach anything over as to where the n actually comes from. I just started studying this in organic chemistry 2 and I’m still researching this myself. I came to this article thinking I got it down, but yet it still fails to teach students how to find n.

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