Hückel’s rule is a simple application of LCAO. It states that a fully conjugated cyclic molecule requires 4n+2 pi electrons, where n is any integer, to be to be considered an aromatic compound. That means the number of pi electrons in conjugation must be 2, 6, 10, 14, etc.
How to determine n
Before we even try to find “n,” we should confirm that the other three rules of the Four Rules of Aromaticity are satisfied. The variable “n” stands for the number of pi electrons found in the would-be aromatic portion of a molecule. The pi electrons can be found in pi bonds (like those in alkenes and alkynes) and in lone pairs.
Once the first three rules are satisfied, we can count the number of pi bonds. Determining if a molecule is cyclic is super easy: “Is it a ring? Yes? Then it’s cyclic.” Conjugation is pretty easy to determine once you’ve learned what to look for. Planarity is a little bit more nuanced, but you can generally assume planarity in molecules given by professors.
Let’s look at benzene, which satisfies all four rules:
1. Cyclic: √
2. Fully conjugated: √
3. Planar: √
4. Huckel’s rule √
Benzene Four Rules
Benzene is cyclic, all carbons have sp2 hybridization, it’s a planar ring, and it has six pi electrons. Six is a Huckel’s rule number, so that makes it aromatic! Benzene is far from the only aromatic molecule, however; there are tons.
Aromatic vs antiaromatic
If a molecule satisfies rules 1-3 BUT has a 4n number (Breslow’s rule) of electrons, it’s what we call antiaromatic. Antiaromatic molecules are very unstable molecules that often decompose on their own.
If a molecule doesn’t satisfy any of rules 1-3, it’s considered nonaromatic.
Let’s count some pi-electrons in some practice problems and assume that each molecule is planar. Remember:
- if the molecule has a Huckel’s rule number of pi electrons (4n+6) it’s aromatic
- if it has 4n pi electrons, it’s antiaromatic
- if it doesn’t satisfy rules 1, 2, or 3, it’s antiaromatic.
Let’s determine whether the molecules below are aromatic, antiaromatic, or nonaromatic.
Three-membered Ring
- The one on the left is nonaromatic because it breaks rule 2; it’s not fully conjugated.
- The one in the middle has a 4n number of pi electrons (where n=1), so it’s antiaromatic. The carbanion can resonate with the double bond, which means the molecule is fully conjugated. This is an antiaromatic ion.
- The one on the right is fully conjugated and has a 4n+2 number of pi electrons (where n=0), so it’s aromatic. The carbocation has an empty orbital that the double bond’s electrons can resonate with. This is an aromatic ion.
That wasn’t so bad, right? Let’s look at a couple more:
Seven-membered Ring
- The one on the left is antiaromatic because it has a 4n number of pi electrons ; it’s not fully conjugated.
- The one in the middle has a 4n number of pi electrons (where n=1), so it’s antiaromatic. The carbanion can resonate with the double bond, which means the molecule is fully conjugated. This is an antiaromatic ion.
- The one on the right is fully conjugated and has a 4n+2 number of pi electrons (where n=0), so it’s aromatic. The carbocation has an empty orbital that the double bond’s electrons can resonate with. This is an aromatic ion.
Heteroatoms
Non-carbon atoms (heteroatoms) can “choose” to donate a lone pair (electrons in non-bonding orbitals) to complete conjugation and make a molecule aromatic. If, however, donating the lone pair would make the molecule antiaromatic the heteroatom would “choose” to not donate its lone pair.
Let’s take a quick look at two classic heterocylic aromatics: pyridine and pyrrole.
Pyridine and pyrrole
It’s easy to see that pyridine is aromatic because there are three pi bonds in alternation, but it’s a bit more difficult to tell that pyrrole is also aromatic. It’s donating its lone pair into the ring: 
Nitrogen donating its lone pair
On the left the molecule could be considered nonaromatic (assuming the lone pair is isolated from the ring. On the right the lone pair is participating as pi electrons in the ring, and that brings the number to six. Six is a 4n+2 number where n=1.
