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...
