# Trying to Understand Molecular Excited States Notation

• Zernhelt
In summary, the speaker is an engineering PhD student working with laser-induced fluorescence and is trying to understand the notation for excited states of nitrogen dioxide. They are unsure about the numbers and letters used and the meaning of the tildes. They ask for clarification and receive an explanation that A_1 and B_2 refer to the irreducible representations of the molecule's symmetry group and the superscript "2" indicates a spin of 1/2. They also receive recommendations for further reading on the topic.
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.

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.
http://www.sciencemag.org/content/334/6053/208.abstract
or this one:
http://onlinelibrary.wiley.com/doi/10.1002/9780470142813.ch2/summary

Last edited:
I think I'm starting to understand. Thanks.

## 1. What is molecular excited states notation?

Molecular excited states notation is a way of representing the electronic configuration of a molecule in its excited state. It is a shorthand notation that uses numbers and letters to indicate the energy levels and orbitals of the electrons in a molecule.

## 2. Why is it important to understand molecular excited states notation?

Understanding molecular excited states notation is important for studying the electronic properties and behavior of molecules. It can help scientists predict how molecules will react and interact with other molecules, as well as understand the role of excited states in chemical reactions.

## 3. How is molecular excited states notation different from ground state notation?

Molecular excited states notation differs from ground state notation in that it includes additional energy levels and orbitals to represent the excited state of a molecule. Ground state notation only includes the lowest energy configuration of a molecule.

## 4. How is molecular excited states notation determined?

Molecular excited states notation is determined through experimental techniques such as spectroscopy, which measures the energy levels of molecules. The notation is also based on theoretical calculations and models that help predict the electronic configuration of molecules in their excited states.

## 5. Are there any limitations to molecular excited states notation?

While molecular excited states notation is a useful tool for understanding the electronic properties of molecules, it does have some limitations. It may not accurately represent the complex behavior of highly excited molecules or molecules with multiple electronic transitions. Additionally, the notation may vary depending on the specific theoretical model or experimental techniques used.

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