facti sumus e rebus stellarum

“It’s like she’s your knight in shining armor and you’re the stupidest princess I’ve ever met.”

Olivia Dean

11 November 2025

Do you ever think about how strange the relationship between symmetry and the physical sciences is? I feel struck every time I study those aspects of theoretical chemistry where symmetry shows up: orbitals, ligand field theory, electronic spectroscopy.

Let's say you have a complex of a d block metal - maybe it's titanium, maybe iron, maybe zirconium, it doesn't matter. You get an electronic spectrum of your complex and it contains some number of peaks of different intensities. If you want to know why the intensities are what they are and where exactly these peaks come from, you need to turn to group theory which will tell you how the electronic states of your metal ion change once this ion is part of your complex; and also why they change and how it's related to the interactions between electrons (momentum!) and how the d orbitals are positioned and what happens when they are transformed by certain symmetry operations.

In a way, this shouldn't be surprising. After all, an orbital is a mathematical beast, just a 3D function to put it simply. Of course this mathematical 3D beast will play the symmetry game according to the rules. But molecules are real, you know what I mean? They aren't abstract mathematical concepts, they are very much real; and yet it's these rules that are responsible for the spectrum you will get when you put your molecule inside a spectrophotometer - and so much more. Don't you think it's amazing? Because it never ceases to amaze me

watching the detectives (2007) dir. paul soter