## Anthocyanins

As the chlorophyll wanes, now is the heyday of the xanthophylls,
carotenoids and anthocyanins. These contain carbon rings and chains whose electrons become delocalized… their wavefunctions resonating at different frequencies, emitting photons of yellow, orange and red!

Yes, it’s fall. I’m enjoying it.

I wrote about two xanthophylls in my May 27, 2014 diary entry: I explained how they get their color from the resonance of delocalized electrons that spread all over a carbon chain with alternating single and double bonds:

I discussed chlorophyll, which also has such a chain, in my May 29th entry. I wrote about some carotenoids in my July 2, 2006 entry: these too have long chains of carbons with alternating single and double bonds.

I haven’t discussed anthocyanins yet! These have rings rather than chains of carbon, but the basic mechanism is similar: it’s the delocalization of electrons that makes them able to resonate at frequencies in the visual range. They are often blue or purple, but they contribute to the color of many red leaves:

Click on these two graphics for more details! I got them from a website called Science Notes, and it says:

Some leaves make flavonoids. Anthocyanins are flavonoids which vary in color depending on pH. Anthocyanins are not usually present in leaves during the growing season. Instead, plants produce them as temperatures drop. They acts as a natural sunscreen and protect against cold damage. Anthocyanins also deter some insects that like to overwinter on plants and discourage new seedlings from sprouting too close to the parent plant. Plants need energy from light to make anthocyanins. So, vivid red and purple fall colors only appear if there are several sunny autumn days in a row.

This raises a lot of questions, like: how do anthocyanins protect
leaves from cold, and why do some leaves make them only shortly before they die? Or are they there all along, hidden behind the chlorophyll Maybe this paper would help:

• D. Lee and K. Gould, Anthocyanins in leaves and other vegetative organs: an introduction, Advances in Botanical Research 37 (2002), 1–16.

Thinking about anthocyanins has led me to ponder the mystery of aromaticity. Roughly, a compound is aromatic if it contains one or more rings with pi electrons delocalized over the whole ring. But people fight over the exact definition.

I may write more about this if I ever solve some puzzles that are bothering me, like the mathematical origin of Hückel’s rule, which says a planar ring of carbon atoms is aromatic if it has $4n + 2$ pi electrons. I want to know where the formula $4n + 2$ comes from, and I’m getting close.

An early paper by Linus Pauling discusses the resonance of electrons in anthocyanins and other compounds with rings of carbon. This one is freely available, and it’s pretty easy to read:

• Linus Pauling, Recent work on the configuration and electronic structure of molecules; with some applications to natural products, in Fortschritte der Chemie Organischer Naturstoffe, 1939, Springer, Vienna, pp. 203–235.

### 12 Responses to Anthocyanins

1. Lana says:

“Colors are the deeds of light, its deeds and sufferings.” Goethe

2. NoLongerBreathedIn says:

Hückel’s rule says that $4n+2$ is aromatic.

3. morganism says:

there was a kid at ASU, that wrote a paper showing un-zipped benzo rings could be used as a thermoelectric generator. Low eV, but they found that the electrons moving asymmetrically down the carbon chain (an edge that looks just like a graphene edge) produced the charge just because the differential in distance (!) is what produced the voltage. IIRC that’s pretty small scale. Don’t know if they ever looked at phonons, but they were looking for latent heat harvesting at the end.

4. RobT says:

4n+2, not 6n+2

• John Baez says:

Whoops! Yes, I even think I know what the $4n$ is about. When we use Hückel theory to estimate the energy levels of pi electrons in a ring of carbons we can fit 2 electrons in each momentum state thanks to their spin, but we also get two momentum states for each energy because the electrons can be going clockwise or counterclockwise around the ring. So, each energy level typically holds 4 electrons—though this is not true for momentum zero. So we expect different things to happen depending on how many electrons there are mod 4. But I still don’t know what’s so great about it equaling 2 mod 4.

5. bruno says:

Sadly, but predictably, Linus Pauling’s article costs ~30 euros in France, that is around 1e/page, and only 3 less than the whole ebook. It has been downloaded 15 times. How does one say “tuer la poule aux oeufs d’or” in english ?
Bruno

• John Baez says:

If you click on the link I provided and then click on the blue thing that says “PDF”, you should get the book containing Pauling’s paper for free. At least that’s what happens to me! Try clicking this. I get a PDF file of a book, with Pauling’s paper on page 203.

I don’t know what “tuer la poule aux oeufs d’or” means, but some of those words remind me of “killing the goose that lays the golden eggs”, which is a saying in English.

6. Raphael says:

A possibly maths-compatible way to understand aromaticity is via Forst circle diagrams https://www.studyorgo.com/blog/huckel-aromaticity-and-frost-circles/ . The eigenvalues of the Hückel matrices of “polygonal molecules” are the heights of the vertices in a certain setting. The largest “gap” between full and empty levels is then obtained by filling in 4n+2 electrons in a 4n+2 regular polygon “molecule”

• John Baez says:

Thanks! To be happy I need to know where these Forst circle diagrams are coming from, and I think it’s explained here:

• Charles Alfred Coulson, Brian O’Leary and R. B. Mallion, Hückel Theory for Organic Chemists, Academic Press, 1978.

Sometime I would like to write a blog post or two explaining this stuff (which would force me to really understand it).

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