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?

Hund's Rule, named after the German physicist Friedrich Hund, is a principle in quantum mechanics that explains how electrons are distributed among different orbitals within an atom. It's one of the three fundamental rules for understanding the electron configuration of atoms, the other two being the Pauli Exclusion Principle and the Aufbau Principle. Hund's Rule is especially relevant when filling degenerate orbitals, which are orbitals with the same energy.

Hund's Rule can be summarized as follows:

1. Electrons prefer to occupy empty orbitals before pairing up in the same orbital.
2. When filling degenerate orbitals (orbitals with the same energy), electrons will occupy different orbitals singly (with parallel spins) before any orbital receives a second electron.

In simpler terms, it means that electrons tend to spread out within a subshell (a set of orbitals with the same principal quantum number and type) rather than pairing up in the same orbital. This is due to the electrostatic repulsion between electrons, which makes it energetically favorable for them to be in different orbitals to minimize their repulsion.

For example, consider the p orbitals. There are three p orbitals (px, py, pz) within the same subshell. According to Hund's Rule, when filling these orbitals, you would add one electron to each of the three p orbitals (with the same spin) before any of them receives a second electron with an opposite spin.

This rule helps explain the electron configurations of atoms and the arrangement of electrons in their orbitals. It also plays a crucial role in understanding the periodic table and the chemical properties of elements.

 

[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.