### Nitrogen Ground State

Now, with we have three valence 2P electrons and the shell is half full. Hund's first rule , maximum total , tells us to couple the three electron spins to . This is again the symmetric spin state so we'll need to make the space state antisymmetric. We now have the truly nasty problem of figuring out which total states are totally antisymmetric. All I have to say is . Here MS means mixed symmetric. That is; it is symmetric under the interchange of two of the electrons but not with the third. Remember, adding two P states together, we get total . Adding another P state to each of these gives total for , for , and for . Hund's second rule, maximum , doesn't play a role, again, because only the state is totally antisymmetric. Since the shell is just half full we couple to the the lowest . So the ground state is .

 e 1 0 -1

The chart of nitrogen states is similar to the chart in the last section. Note that the chart method is clearly easier to use in this case. Our prediction of the ground state is again correct and a few space symmetric states end up a few eV higher than the ground state.

Jim Branson 2013-04-22