Ground state solutions to Hartree-Fock equations with magnetic fields

Within the Hartree-Fock theory of atoms and molecules, we prove existence of a ground state in the presence of an external magnetic field when: (1) the diamagnetic effect is taken into account; (2) both the diamagnetic effect and the Zeeman effect are taken into account. For both cases, the ground state exists provided the total charge Z(tot) of the nuclei K exceeds N - 1, where N is the number of electrons. For the first case, the Schrodinger case, we complement prior results by allowing a wide class of magnetic potentials. In the second case, the Pauli case, we include the magnetic field energy in order to obtain a stable problem and we assume Z(tot)alpha(2) <= 0.041, where a is the fine structure constant.