Trying to Understand Molecular Excited States Notation

[Zernhelt]

Hey guys, I'm an engineering PhD student, and I'm doing some work with laser-induced fluorescence. At the moment, I'm trying to understand some notation about the excited states of nitrogen dioxide. One of the papers I'm looking at, V.M. Donnelly, et al. J. Chem. Phys. 71, 659 (1979), is saying that the transition I'm inducing is \widetilde{A}^{2}B_{2} \leftarrow \widetilde{X}^{2}A_{1}. I'm not entirely sure what any of that means. I assume it's saying that I'm transitioning from the \widetilde{X}^{2}A_{1} state to the \widetilde{A}^{2}B_{2} state, but why the arrow points right to left, I'm not sure. More importantly, I'm not sure what any of the numbers or letters refer to, and what the tilda's mean. I assume some information about the rotational and vibrational states are given (that that's what I'd really like to know), but not knowing the nomenclature, I'm not sure how to read that transition. I'd appreciate it if someone could point me in the right direction. Thanks.

 

[DrDu]

A_1 and B_2 refer to the irreducible representations of the symmetry group of the molecule (C_{2v}) spanned by the electronic wavefunction. The superscript "2" means that the total spin of the electronic wavefunction is s=1/2 (Hence there are 2s+1=2 possible orientations of the spin. I. e., the spin of the single unpaired electron may either point up (m_s=+1/2 or down m_s=-1/2). No idea about the tilde. The states of a given symmetry are usually enumerated A, B, ...X , with A being energetically lowest, then B etc.
Maybe you can learn something from this article:
http://www.sciencemag.org/content/334/6053/208.abstract
or this one:
http://onlinelibrary.wiley.com/doi/10.1002/9780470142813.ch2/summary

 

[Zernhelt]

I think I'm starting to understand. Thanks.