, Volume 12, Issue 4, pp 653–666 | Cite as

Non-existence of a minimizer to the magnetic Hartree-Fock functional

  • Mattias Enstedt
  • Michael Melgaard


In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization.


Magnetic Hartree-Fock equations Ionization Positivity 

Mathematics Subject Classification (2000)

Primary 81V45 Secondary 35Q40, 47G20, 47N50 


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Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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