Hund's Rules - Rule 3

Rule 3

This rule considers the energy shifts due to spin–orbit coupling. In the case where the spin–orbit coupling is weak compared to the residual electrostatic interaction, and are still good quantum numbers and the splitting is given by:

$\begin{align} \Delta E & = \zeta (L,S) \{ \mathbf{L}\cdot\mathbf{S} \} \\ \ & = \ (1/2) \zeta (L,S) \{ J(J+1)-L(L+1)-S(S+1) \} \end{align}$

The value of changes from plus to minus for shells greater than half full. This term gives the dependence of the ground state energy on the magnitude of .

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