 Hund's rules

Allow us to determine with good approximation in a multi-electron atom which electron configuration have more energy. It is a bit like the Aufbau principle, but at a finer resolution.

Note that this is not trivial since there is no explicit solution to the Schrödinger equation for multi-electron atoms like there is for hydrogen.

For example, consider carbon which has electron configuration 1s2 2s2 2p2.

If we were to populate the 3 p-orbitals with two electrons with spins either up or down, which has more energy? E.g. of the following two:

Hund's rules are a set of guidelines used in quantum chemistry and atomic physics to determine the ground state of an atom or ion's electron configuration, particularly for multi-electron systems. These rules help predict how electrons fill orbitals in an atom. The rules are as follows: 1. **Hund's First Rule:** For a given electron configuration, the term with the highest multiplicity has the lowest energy.