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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?

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  • $\begingroup$ This will be (somewhat) easier to answer if you specify the source where you saw this notation (which you should always do anyways). $\endgroup$ – Emilio Pisanty May 14 '17 at 16:58
  • $\begingroup$ @EmilioPisanty This is just from an exam question from my university. I've assumed the notation they refer to here is universal. $\endgroup$ – Ilya Lapan May 14 '17 at 17:51
  • $\begingroup$ 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. $\endgroup$ – Emilio Pisanty May 14 '17 at 18:01
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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.

Generally, term symbols are brief summaries of the angular momentum properties of a particular atomic or molecular state, which along with some (usually) experimentally determined constants allow you to parametrize vibrational and rotational state energies and transition probabilities.

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  • $\begingroup$ Yeah, this is pretty much it, though it's sometimes accompanied by superscripts that indicate parity(ish), as seems to be the case with the sigma state in the OP. $\endgroup$ – Emilio Pisanty May 14 '17 at 17:59
  • $\begingroup$ Yes, good point. The big superscript I believe denotes overall parity. $\endgroup$ – Will C May 14 '17 at 18:03

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