Hund's Rules

In atomic physics, Hund's rules refer to a set of rules formulated by German physicist Friedrich Hund around 1927, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. In chemistry, the first rule is especially important and is often referred to as simply Hund's Rule.

The three rules are:

1. For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to, where is the total spin angular momentum for all electrons. The term with lowest energy is also the term with maximum .
2. For a given multiplicity, the term with the largest value of the orbital angular momentum number has the lowest energy.
3. For a given term, in an atom with outermost subshell half-filled or less, the level with the lowest value of the total angular momentum quantum number (for the operator ) lies lowest in energy. If the outermost shell is more than half-filled, the level with the highest value of is lowest in energy.

These rules specify in a simple way how the usual energy interactions dictate the ground state term. The rules assume that the repulsion between the outer electrons is very much greater than the spin–orbit interaction which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.

Full shells and subshells do not contribute to the quantum numbers for total S, the total spin angular momentum and for L, the total orbital angular momentum. It can be shown that for full orbitals and suborbitals both the residual electrostatic term (repulsion between electrons) and the spin–orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons need to be considered.