Derivation of the Wigner–Witmer rules in terms of N-electron exchange

We give an organized derivation of the Wigner–Witmer correlation rules in the case when a diatomic term is built by like atoms in the same term. What relates the inversion symmetry with the spin multiplicity is apparently shown to be the symmetric property for N-electron exchange, which means the exchange of all electrons of one atom for those of the other atom. We simplified the derivation, discussing the transformation properties of the total electronic state, the spin part and the orbital part, separately. Furthermore, the numbers of constructed terms are summarized in simple tables. (paper)