Origin of the First Hund Rule in He-like Atoms

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  • ヘリウム様原子におけるフントの第一規則の起源 （解説）
  • ヘリウム様原子におけるフントの第一規則の起源
  • ヘリウム ヨウ ゲンシ ニ オケル フント ノ ダイイチ キソク ノ キゲン

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Empirically derived Hund's rules of pre-quantum-mechanics era that predict the ordering of the energy levels possessing different spin and orbital angular momentum quantum numbers proved to be almost universally valid for atomic and molecular systems. Yet, despite the history of a long standing debate the search for various aspects of their origin persists. With a brief survey of the historical studies related to the subject, this paper explores the origin of Hund's multiplicity rule focusing on the helium-like atoms that represent an ideal system providing a direct fundamental insight into the structure of the internal part of the fully-correlated wave functions. An examination of their probability density distributions indeed reveals the existence of a region in the internal space which we refer to as conjugate Fermi hole. In this region the singlet wave function has a smaller probability density than the corresponding triplet one, in contrast to a genuine Fermi hole in which case the triplet has a smaller density than the singlet. Thanks to the presence of this conjugate Fermi hole, the singlet probability density has to migrate far away from the nucleus, rationalizing thus a broader electron density distribution and smaller nuclear attraction and electron repulsion energies of the singlet state than is the case for the corresponding triplet state.

Journal

  • Butsuri

    Butsuri 68 (6), 358-365, 2013-06-05

    The Physical Society of Japan

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