Pointless in talking about atomic term for a certain micro-state?

[bearcharge]

I'm a chemist trying to understand atomic term symbol.

If we list all the micro-states of certain multi-electron configuration, these micro-states can be grouped into several certain terms characterized by L and S. In other words, when we compute the M_L and M_S for each of the micro-state, they should belong to certain (L, S) configuration, much analogous to the single electron case where l sets boundary for m_l, s for m_s. It is legitimate to do so because the operator L and S commute with H, so L and S are good quantum numbers describing the states. After deriving L and S, we use RS coupling scheme to calculate J.

If my understanding is correct, then this point should follow: certain micro-state can arbitrarily belong to several terms. For example, 3d² contains terms 1D and 3P. A micro-state with M_L=1, M_S=0 can be either 1D or 3P, right? In that sense, it seems pointless talking about specific term of a micro-state, right?

 

[DrClaude]

Usually, the point of listing microstates for equivalent electrons is to determine which term symbols are possible, such that the Pauli exclusion principle is obeyed. For that purpose, microstates are assigned to term symbols without regard to which term symbol they actually belong to. In your example, once you have identified that you have a ¹D term and therefore need an $M_L = 1, M_S=0$ microstate, you "remove" one such microstate from the list only to see what other terms you can have.

I would venture to say that in many cases, if you have more than one microstate with a given pair of $M_L, M_S$ values, then these microstates will appear in linear combinations in the actual terms

 

[bearcharge]

Thanks for the answer! So can we say what is important is what are the term symbols for a given electron configuration, rather than what is the term symbol for a specific microstate?

 

[DrClaude]

Thanks for the answer! So can we say what is important is what are the term symbols for a given electron configuration, rather than what is the term symbol for a specific microstate?

Yes. As I said, except for the extreme cases (e.g., maximum $M_L=L$), you can't say specifically which microstate will belong to which term symbol.

 

[bearcharge]

Thanks!