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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 of nuclei exceeds , where is the number of electrons. In the opposite direction, no ground state exists if .
Enstedt, M., & Melgaard, M. (2008). Existence of a solution to Hartree-Fock equations with decreasing magnetic field. Nonlinear Analysis: Theory, Methods and Applications, vol. 69, pg. 2125-2141. doi:10.21427/9v90-zk29