Communications in Mathematical Physics

, Volume 203, Issue 3, pp 499–530 | Cite as

Solutions of the Dirac–Fock Equations for Atoms¶and Molecules

  • Maria J. Esteban
  • Eric Séré


The Dirac–Fock equations are the relativistic analogue of the well-known Hartree–Fock equations. They are used in computational chemistry, and yield results on the inner-shell electrons of heavy atoms that are in very good agreement with experimental data. By a variational method, we prove the existence of infinitely many solutions of the Dirac–Fock equations “without projector”, for Coulomb systems of electrons in atoms, ions or molecules, with Z≤ 124, N≤ 41, N≤ Z. Here, Z is the sum of the nuclear charges in the molecule, N is the number of electrons.


Experimental Data Variational Method Heavy Atom Yield Result Nuclear Charge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Maria J. Esteban
    • 1
  • Eric Séré
    • 2
  1. 1.Ceremade (URA CNRS 749), CNRS et Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris Cedex 16, FranceFR
  2. 2.Département de Mathématiques, Université de Cergy-Pontoise, 2 Av. Adolphe Chauvin,¶F-95302 Cergy-Pontoise Cedex, FranceFR

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