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The origin of Hund's multiplicity rule in the low-lying excited states of the
helium atom has been studied by considering the two-dimensional helium atom.
The internal part of the full configuration interaction wave functions for the
(2s) and (2p) singlet-triplet pairs of states has been extracted and
visualized in the three-dimensional internal space (r1,
r2, &phi-).
The internal wave function of the singlet states without electron
repulsion has a significant probability around the origin of the internal
space while the corresponding probability of the triplet wave function is
negligible in this region due to the presence of a Fermi hole. The electron-electron
repulsion potential has been visualized also in the internal space. It
manifests itself by three striking poles penetrating exactly into the spatial
region defined by the Fermi hole. Because of the existence of these strong
potential poles in the vicinity of the Fermi hole a major part of the singlet
probability migrates out of this region. In contrast, the corresponding
triplet wave function is less affected by these poles due to the presence
of the Fermi hole. The singlet probability is shown to migrate from its original
region close to the origin to a region far away where either
r1 or r2 are large. This results in a more
diffuse electron density distribution and a smaller electron repulsion energy
of the singlet state than of the corresponding triplet state. The mechanism of
the evolution of the singlet probability towards the region of large
ri (i = 1, 2) in the presence of the
electron repulsion potential has been rationalized on the basis of a new
concept called conjugate Fermi hole.
Origin of Hund's multiplicity rule in singly excited helium:
Existence of a conjugate Fermi hole in the lower excited state. (Manuscript)
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