# Notation for electronic states of molecules

I came across a question using a notation for electronic states of molecules that I do not understand. The question talks about electrons in molecules of $^{27}$AlH getting excited to $A^1\Pi$ electronic state by colliding with molecules in $X^1\Sigma^+$ ground electronic state. What does the notation for $A^1\Pi$ and $X^1\Sigma^+$ electronic states mean?

• This will be (somewhat) easier to answer if you specify the source where you saw this notation (which you should always do anyways). – Emilio Pisanty May 14 '17 at 16:58
• @EmilioPisanty This is just from an exam question from my university. I've assumed the notation they refer to here is universal. – Ilya Lapan May 14 '17 at 17:51
• In this case, yes, but you never know when there's bits of context that you didn't think were relevant that turn out to be crucial. Always include a link to the source so those can be determined if you've left them out without realising it. – Emilio Pisanty May 14 '17 at 18:01

The first letter is a conventional notation for electronic state ordering in molecules. From this thesis, $X$ denotes the electronic ground state in a diatomic molecule ($\tilde{X}$ in a polyatomic molecule). Excited states with the same total spin quantum number $S$ as the ground state are denoted $A,B,C$ and so on, while excited states with different spin multiplicity from the ground state are denoted $a,b,c$ and so on.
The next set of symbols, e.g. $^3\Pi_0$, is collectively a molecular term symbol. The notation is $^{2S+1}|\Lambda|_{|\Omega|}$, where in a diatomic molecule the quantum number $\Lambda \equiv {\bf L} \cdot {\bf n}$ is the projection of the total electronic orbital angular momentum onto the internuclear axis, and the quantum number $\Omega \equiv {\bf J}_e \cdot {\bf n}$ is the projection of the total electronic angular momentum onto the internuclear axis.