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

[crick]

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?

 

[jedishrfu]

Here's Hund's rules from wikipedia:

https://en.wikipedia.org/wiki/Hund's_rules

You might find some of the external references helpful in getting an answer to your question.

The article does say that there are times when the rules fail so it seems they are to be used in a heuristic sense to be determine the right answer for a given atomic configuration realizing your answer has a small chance of not being correct.

 

[DrClaude]

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)

Hund's rules only work for equivalent electrons. In this case, the two electrons are in different $nl$ orbitals, so not equivalent.

 

[DrDu]

Hund stated himself that the derived his rules first staring at experimental data, so they are empirical. While explanations have been cooked up soon afterwards, it still remains a rule which occasionally fails. Its relevance today is rather low as the spectra and term symbols of all elements and ions are known and can easily be looked up.