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I have a question on the order of the spin-orbit molecular states. I understand how to find the terms that split from a parent molecular state in a diatomic molecule. But my question is on how to find whether the multiplet states are normal (regular) or inverted. For example, if we take $^3\Pi$, this state will split into $^3\Pi_{0^+}$, $^3\Pi_{0^-}$, $^3\Pi_1$, and $^3\Pi_2$. How can we know the order of these states, that is to say normal (regular) or inverted? If they are in this order: $^3\Pi_{0^+}$, $^3\Pi_{0^-}$, $^3\Pi_1$, and $^3\Pi_2$; or in that order: $^3\Pi_2$, $^3\Pi_1$, $^3\Pi_{0^-}$, and $^3\Pi_{0^+}$.

In Spectra of Diatomic Molecules book, by Herzberg, he pointed out these terms, and gave the following equation: $$T_e=T_0+A\Lambda\Sigma$$ where $A$ is a constant for a given multiplet term. He also stated that if $A$ is positive, this will give rise to normal (regular) terms. However, if $A$ is negative, we get inverted terms. So is there another way to find out other than this way? And by the way, how can we determine $A$? Thanks a lot...

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  • $\begingroup$ What page is this on? I looked but could not find it from the index on spin orbit. $\endgroup$
    – porphyrin
    Aug 25 '20 at 7:47
  • $\begingroup$ Pages 215 and 216 $\endgroup$
    – Naps
    Aug 25 '20 at 7:52
  • $\begingroup$ In case that you can get your hands on a copy of Brown and Carrington's "Rotational Spectroscopy of Diatomic Molecules" you should check out section 7.8.3 (page 357) where they discuss a simple orbital model to estimate the value of the spin-orbit parameter. $\endgroup$
    – Paul
    Aug 26 '20 at 15:41

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