# Difference between continuously overlapping p orbitals and conjugated pi bonds

Is there any difference between the phrase "continuously overlapping p-orbitals" and "conjugated pi bonds" when referring to aromatic compounds? I've heard both used and I wasn't sure if they mean the same thing.

• Strictly speaking p-orbitals can overlap to form a sigma-bond if the touch end-to-end – Lighthart Mar 20 '15 at 0:17

Interesting question!

To have continuously overlapping p-orbitals, the p-orbitals must be arranged in a cyclic loop. The p-orbitals in benzene are continuously overlapping. The p-orbitals in benzene are also conjugated pi bonds.

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In buta-1,3-diene the p-orbitals form conjugated pi bonds, however, they are not continuously overlapping - there are two "end" carbons that are not connected with each other, there is no continuous loop.

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Let's take it a step further:

Continuously overlapping p-orbitals are not always aromatic.

Example 1: Cyclobuta-1,3-diene (the square planar structure, $\ce{D_{4h}}$) has 4 continuously overlapping p-orbitals but it is not aromatic, it is antiaromatic. For a continuously overlapping system of p-orbitals to be aromatic, it must contain 4n+2 pi electrons.

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Example 2: Have you heard of the Möbius strip? The mathematical (topological) concept has application in chemistry. Imagine a large cyclic loop of p-orbitals where each p-orbital is twisted a few degrees from the preceeding p-orbital. If the loop is large enough, then by the time we come back to the first p-orbital we have twisted the last p-orbital by 180°; there is a phase inversion (node) between the first and last p-orbital. In a Möbius system the p-orbitals are continuous, but not continuously overlapping! Möbius systems are aromatic if they contain 4n pi electrons.

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Continuous pi systems with an even number (0, 2, 4...) of nodes (cyclobutadiene, benzene, etc) are called Hückel systems in order to differentiate then from Möbius systems where there are an odd number of nodes (1, 3, 5...).

Lest you think the Möbius concept is purely theoretical take a look at these two molecules

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Isn't this what makes chemistry fascinating!