6.9  The Tomato Test

Nefertiti likes organic chemistry and she is excited about the implications of the particle in a box model. Cormorant likes tomatoes. Let’s bring all these enthusiasms  together.

We’re going to look at conjugated polyenes. That means molecules which contain alternating single and double bonds. Here’s the smallest one, buta-1,3-diene:  CH2=CH-CH=CH2.

If you measure the bond lengths between carbon atoms in molecules like these (which you can do very accurately using x-ray diffraction), you find that the double bonds are longer than C=C bonds usually are, while the single bonds are shorter than usual. A bond is a pair of electrons and what underlies these abnormal bond lengths is that one of the electron pairs in each of the double bonds, instead of being purely localised to that pair of carbon atoms, is to some extent spread out  -“delocalised” - over the whole length of the system defined by the alternating double and single bonds. (If you know about organic chemistry, try pushing some curly arrows around to see how this works, or if you know about molecular orbitals formed by overlap of atomic orbitals, picture a continuous run of sideways overlapping p-orbitals. If you prefer not to think about chemistry, you are forgiven).

If we picture electrons as being trapped in this conjugated system but able to move freely within it, you can see that we have something approximately a one-dimensional particle in a box. So we can take the results we have obtained and see what they predict about these conjugated polyenes.

It's not a perfect model, but considering how simple it is, the particle in a box does a pretty good job of explaining what's going on with the delocalised electrons in these compounds. A minor triumph.