Hund's cases for diatomic molecules

[samst]

Dear All,

May anyone please advise me to the following questions in case of diatomic molecules:

1. How do we choose which Hund's case ((a), (b), or (c)...) that best describes a particular diatomic molecule?

2. How can we deduce from Hund's cases molecular electronic states ^(2s+1)Λ_Ω (e,g. Σ^+/-, Π, Δ, Φ, Γ...)?

3. When Λ-type doubling for non-sigma states should be taken into consideration?

4. How do we obtain the spin-orbit interaction terms A and B (where Y=A/B)?

Any help would be greatly appreciated...
Best wishes

 

[DrClaude]

1. How do we choose which Hund's case ((a), (b), or (c)...) that best describes a particular diatomic molecule?

It depends on the strength of the spin-orbit coupling in comparison to other couplings, such as the residual electron-electron interaction. As far as I know, it can be difficult to predict in advance which coupling case is the right one, and it is the actual spectrum that will give the answer (like LS vs jj coupling in atoms).

2. How can we deduce from Hund's cases molecular electronic states ^(2s+1)Λ_Ω (e,g. Σ^+/-, Π, Δ, Φ, Γ...)?

The term symbol is obtained from the electronic configuration. The Hund cases will affect how the term symbol can be written. For instance, in Hund's case C, Λ is not defined, so one uses Ω instead.

3. When Λ-type doubling for non-sigma states should be taken into consideration?

I don't know. Someone more knowledgeable may chime in.

4. How do we obtain the spin-orbit interaction terms A and B (where Y=A/B)?

I don't know what this means. Can you explain the notation?

 

[samst]

It depends on the strength of the spin-orbit coupling in comparison to other couplings, such as the residual electron-electron interaction. As far as I know, it can be difficult to predict in advance which coupling case is the right one, and it is the actual spectrum that will give the answer (like LS vs jj coupling in atoms).

Is there a way we can predict whether L and S are good quantum numbers to choose case (a), for example?

The term symbol is obtained from the electronic configuration. The Hund cases will affect how the term symbol can be written. For instance, in Hund's case C, Λ is not defined, so one uses Ω instead.

I don't know. Someone more knowledgeable may chime in.

I don't know what this means. Can you explain the notation?

The electronic energy of a multiplet term is given to a first approximation by: T_e = T_o + AΛΣ.
where T_o is the term value when the spin is neglected (spin-free) and A is a constant for a given multiplet term (for spin-orbit). The coupling constant A determines the magnitude of the multiplet splitting. If A>0 , the spin-orbit terms are considered as regular states (²Π_1/2, ²Π_3/2). For A<0, we have an inverted terms (²Π_3/2, ²Π_1/2).
How do we evaluate or find A and B terms? I am searching for a relation for A and B, but I am not finding any!

 

[DrDu]

Landau, Lifshitz, vol 3, Quantum Mechanics, contains a nice discussion of the Hund's coupling cases.

 

[samst]

Landau, Lifshitz, vol 3, Quantum Mechanics, contains a nice discussion of the Hund's coupling cases.

Thank you so much DrDu!

 

[samst]

Thank you DrClaude for your help and continuous support...