Torsion angle symbol

Question

I'm reading up on molecular modelling and have come across some terms I should probably have learnt a long time ago but always scared me off a bit with the Greek letters. I guess I'm a big boy now so it's probably time to clarify...

The textbook uses the lowercase symbol omega ($\omega$) for torsion (a.k.a. dihedral) angle while Wikipedia gives the uppercase, $\Omega$, plus both upper and lower case phi ($\Phi$, $\phi$) and psi ($\Psi$, $\psi$) in its description which from reading I'm starting to understand designate particular geometrical cases from the article, though it looks like it might be a little difficult to remember at first.

My textbook also gives in the list of symbols and physical constants [lower case] tau, $\tau$, but I can't see any mention of this on the Wiki page.

Firstly I wanted to ask is the use of upper/lower case totally arbitrary, and secondly is tau just a non-specific way of expressing torsion angle compared to the other 3 (which is the only use I can imagine for it?) Or is this use totally confined to molecular modelling?

Answer 1

It is a habit to assign greek letters (most often lowercase) to angles. In case of "normal" angles, it's mostly $\alpha, \beta, \gamma$, whereas for dihedrals some higher letters, as you mentioned, $\phi, \psi, \omega$. As noted in comments, whatever you use, clearly state what you mean.

The difference between dihedral and torsional angle is more conceptual, then formal. In torsion you discuss rotation around a bond, dihedral is general angle of two planes, as mentioned in the $\ce{CH_4}$ example. The formal expression for both of them is the same, indeed.

To be noted, there are some well known widely used dihedral angles, where you should stick to the common notation. The most prominent example is the protein backbone arrangement, see Ramachandran plot. In this case you should not invent your own notation.