# In what cases (precisely) are Hund's rules valid?

I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the rules help to select the lowest energy state of a configuration).

As far as I understood:

Hund’s rules only apply to the lowest energy state of an electronic configuration, for cases where there is only one incomplete subshell.

In fact if I consider the configuration $$1s^2 2s^2 2p^3$$ (nitrogen), Hund's (third) rule does not work for excited states with $$S=1/2$$ (I refer to NIST data here: https://physics.nist.gov/PhysRefData/Handbook/Tables/nitrogentable5.htm)

That's because it is not the lowest energy state for that configuration, even if there is only one incomplete subshell.

But also if I consider the configuration $$1s 2p$$ (excited helium) with $$S=1$$, Hund's (third) rule does not work (I refer to NIST data here: https://physics.nist.gov/PhysRefData/Handbook/Tables/heliumtable5.htm)

That's because, even if I consider the lowest energy state for that configuration ($$1s 2p$$) there are two incomplete subshell, so I don't even know how to use Hund third rule in cases like this one.

So is my previous statement correct? Also, can you suggest any textbook/source that gives an answer to this?

• Hund's rule tells you what should be the wave function of the ground state of the system. This is the only case of applicability. – Galilean Nov 7 '18 at 6:48