# Normal (Regular) or Inverted Terms?

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...

• What page is this on? I looked but could not find it from the index on spin orbit. Commented Aug 25, 2020 at 7:47
• Pages 215 and 216
– Naps
Commented Aug 25, 2020 at 7:52
• 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.
– Paul
Commented Aug 26, 2020 at 15:41