# Term symbols & degeneracy

1. Jul 19, 2005

### osskall

Hi!

I've finally made some effort to understand spectroscopic term symbols ($$^{2S+1}L_J$$) and after having thought a few times that I'd understood but then running into trouble again, now I'm fairly convinced that I got it right. But some things bother me though.

Apparently I was locked too much in the idea that e.g. triplet states have to have unpaired electrons. I thought the number of unpaired electrons was reflected in the value of S. Hence I couldn't imagine a triplet microstate (of e.g. the configuration $$p^2$$) with $$M_S=0$$ as one of the states having only paired electrons but had to rather think of it as something virtual/unimaginable in between the all-unpaired-spins-up and all-unpaired-spins-down microstates. But it seems like the number of unpaired electrons for a certain microstate is only related to $$M_S$$ and that some of the states unpaired electrons actually do belong to a triplet state.
And thus similarly, for e.g. the $$^4$$S states of $$p^3$$, there are, besides the obvious states $$\underline{\uparrow~~}~\underline{\uparrow~~}~\underline{\uparrow~~}$$ and $$\underline{\downarrow~~}~\underline{\downarrow~~}~\underline{\downarrow~~}$$ two microstates where one electron has opposite spin to the other two. There are 6 such microstates with $$M_L=0$$ which all look similar, but, yet, two of them (one with $$M_S=1/2$$ and one with $$M_S=-1/2$$) will have the same energy as the above mentioned states with all spins paired and the other four will have higher energy (belonging to either $$^2$$D or $$^2$$P where in any case all states only have one unpaired electron). This is somewhat hard to grasp for me. According to this, states that look completely similar are splitted and states that have either (in this case) 3 or 1 unpaired electrons and thus should have different energy are actually degenerated...
Is this correct?

When it comes to deriving the term symbols, there's nothing to it any more, but understanding it seems to be something totally different.

PS: I'm now basing my understanding of term symbols on http://www.chem.ufl.edu/~itl/4412/lectures/ATermSym.html [Broken], where the approach also is illustrated graphically for $$p^2$$ and $$p^3$$, since this approach no longer leads me to any contradictions except for the one mentioned here.

Last edited by a moderator: May 2, 2017