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1. Hunds Rule

   Linked via "maximum spin"

   If the subshell is exactly half-filled (e.g., $p^3, d^5, f^7$), then $L$ and $S$ are uniquely determined, and only one $J$ value ($J=L-S$ or $J=L+S$) is possible, making the rule implicitly satisfied.
   For example, a $d^5$ configuration (half-filled shell) always yields ${}^{6}S_{5/2}$ as the ground state), $L=0$ (maximum $L$ allowed for $S=5/2$), and $J=5/2$ (unique $J$).
   Violati…