### Abstract

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body interaction is like the Coulomb interaction repulsive; it could, however, be more complicated than a simple potential; e.g., it could have tensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never partially filled.

Original language | English (US) |
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Pages (from-to) | 2981-2983 |

Number of pages | 3 |

Journal | Physical review letters |

Volume | 72 |

Issue number | 19 |

DOIs | |

State | Published - Jan 1 1994 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Bach, V., Lieb, E. H., Loss, M., & Solovej, J. P. (1994). There are no unfilled shells in unrestricted Hartree-Fock theory.

*Physical review letters*,*72*(19), 2981-2983. https://doi.org/10.1103/PhysRevLett.72.2981