Existence of a solution to Hartree-Fock equations with decreasing magnetic field

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge Z of K nuclei exceeds N-1, where N is the number of electrons. In the opposite direction, no ground state exists if N>2Z+K.