Hund's rule in the doubly excited states of the helium isoelectronic

The relative magnitudes of the interelectronic repulsions in doubly excited states of the helium isoelectronic sequence that correspond to a common (zero order) configuration are explored. For the isoelectronic sequences of singly excited states an inversion of the relative magnitude of this quantity has been observed to take place at the low end of the sequence, compared to the prediction of first‐order perturbation theory. It was demonstrated that this inversion is associated with expansion of the inner shell concomitant with contraction of the outer shell. Correlation does not upset this inversion. A heuristic analysis of the behavior of the singly excited states near the critical charge at which the outer electron becomes unbound suggests that the inversion in the relative magnitudes of the singlet and triplet interelectronic repulsions is indeed inevitable. A similar argument shows that for the harmonic quantum dot such an inversion is highly unlikely (and is actually ruled out by numerical calculations). The behavior observed in intrashell doubly excited states of two‐electron atoms exhibits markedly different features. Within the Hartree–Fock level no inversion of the relative magnitudes of the interelectronic repulsions takes place, in agreement with the absence of an expanding inner shell. However, correlation appears to play a more decisive role in this case, yielding a reversal of the relative magnitudes of the interelectronic repulsion that the independent particle model does not anticipate. Inserting a closed inner shell, that is, examining the singlet and triplet terms of the four electron configuration 1s 2 2p 2 and the six electron configuration 1s 2 2s 2 2p 2 , fully supports the role of the inner shell in giving rise to an inversion of the relative magnitudes of the interelectronic repulsions even at the Hartree–Fock level. © 2012 Wiley Periodicals, Inc.