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?
 A: 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. 
