A model proposed by Rioux to explain Hund's rule is investigated. Although the largest contribution to the singlet–triplet splitting in the two-electron atomic systems is the nuclear attraction term, this arises from different optimum scale factors in the two states and that difference is driven by the electron–electron exchange term. The incorrect prediction that the singlet energy is lower for the He 1s2s states is a consequence of the fact that in the model used by Rioux the singlet-state wave function is not orthogonal to the ground-state wave function, as it must be for a variational calculation.
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