###

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
.

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