Solutions of the Dirac-Fock equations for atoms and molecules

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 less than or equal to 124, N less than or equal to 41, N less than or equal to Z. Here, Z is the sum of the nuclear charges in the molecule, N is the number of electrons.