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  1. Hunds Rule

    Linked via "Coulomb energy"

    $$N_{\text{pairs}} = \frac{S(2S+1)}{2}$$
    The ground state is achieved when $S$ is maximized, leading to the largest $N_{\text{pairs}}$ and thus the greatest stabilization energy relative to the repulsive Coulomb energy.
    Hund's Second and Third Rules