Isotope dependence of Dunham Parameters

[BillKet]

Hello! I know that there is the famous Dunham parameterization of ro-vibrational levels of a diatomic molecule and later Watson wrote a paper deriving the isotopic dependence of these parameters. However, from what I found online this is only valid for a $^{1}\Lambda$ state. Is there a similar formula (or does the exactly same formula) holds for, say doublet states i.e. $^{2}\Lambda$? Basically I am wondering if one has the exactly same formula for the rotational and vibrational part, and on top of that, for example in a $^{2}\Sigma$ state, a $\gamma N\cdot S$ term, where $\gamma$ is of course also isotope dependent. Or in practice once electron spin comes into play, also the rotational/vibrational terms isotope dependence is also affected? Thank you!

 

[eljose79]

Hello! Thank you for your question. The Dunham parameterization is indeed a widely used and well-established method for describing the ro-vibrational levels of diatomic molecules. However, you are correct in noting that this parameterization is only valid for $^{1}\Lambda$ states, as it assumes a pure rotational-vibrational coupling.

For doublet states such as $^{2}\Lambda$, the same formula cannot be used as the electron spin must be taken into account. In these cases, a more general parameterization known as the spin-rotation parameterization is used. This parameterization includes terms for both the rotational and vibrational energy levels, as well as the electron spin and nuclear spin interactions.

In addition, the isotopic dependence of these parameters is also affected by the presence of electron spin. This is because the electron spin can interact with the nuclear spin, leading to changes in the energy levels and therefore the parameters. Therefore, in practice, the isotopic dependence of the rotational and vibrational terms will also be affected by the presence of electron spin.

I hope this helps to answer your question. If you have any further inquiries, please don't hesitate to ask. Thank you for your interest in this topic!