Royal Purple Molecules

My quantum mechanics class had a problem last week aimed at figuring out the color of a porphyrin molecules. Porphyrins are nitrogen-containing ring shaped chelating molecules (here is a picture) and are ubiquitous in biological systems. An iron bound to a porphyrin is the heme in hemoglobin, when a magnesium is bound, it is a key piece of chlorophyll.

The color of porphyrin should not be a mystery, as long as you know some Greek. The name comes from the Greek for purple, and indeed these compounds have vivid red-violet hues.

I asked the students to compute the energy needed to excite one of porphyrin's 18 pi electrons from the highest occupied level to the lowest unoccupied level, assuming that they could model the compound as 18 independent electrons trapped in a square 1000 pm on a side. The answer in the back of the book gave the absorbtion wavelength of 588 nm, which is precisely what you would expect for a purple compound (absorbing visible yellow light). It seemed too good to be true, for such a simple model to give such a good anwer and it was! There is an error in the answer, and the actual value is not in the visible at all, suggesting that the porphyrin is colorless!

The problem was an apt one for me to be grading this morning, as I was waiting to donate some of my own hemes in the form of whole blood at the college's blood drive.