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Hund's second rule says that, for a given spin, the state with the highest total orbital...

Hund's second rule says that, for a given spin, the state with the highest total orbital angular momentum (L), consistent with overall antisymmetrization, will have the lowest energy. Why doesn't carbon have L =2 ? Hint: Note that the "top of the ladder" (M_L = L) is symmetric.

My question is HOW do we determine is L is symmetric or antisymmetric? Can this be explained thoroughly? Thanks.

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