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

Abstract:

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.