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L\"owdin's symmetry dilemma is an ubiquitous issue in approximate quantumchemistry. In the context of Hartree-Fock (HF) theory, the use of Slaterdeterminants with some imposed constraints to preserve symmetries of the exactproblem may lead to physically unreasonable potential energy surfaces. On theother hand, lifting these constraints leads to the so-called broken symmetrysolutions that usually provide better energetics, at the cost of losinginformation about good quantum numbers that describe the state of the system.This behavior has been previously extensively studied in the context of bonddissociation. This paper studies the behavior of different classes ofHartree-Fock spin polarized solutions (restricted, unrestricted, generalized)in the context of ionization by strong static electric fields. We find that,for simple two-electron systems, UHF is able to provide a qualitatively gooddescription of states involved during the ionization process (neutral,singly-ionized and doubly ionized states), whereas RHF fails to describe thesingly ionized state. For more complex systems, even though UHF is able tocapture some of the expected characteristics of the ionized states, it isconstrained to a single $M_s$ (diabatic) manifold in the energy surface as afunction of field intensity. In this case a better qualitative picture can bepainted by GHF as it is able to explore different spin manifolds and follow thelowest solution due to lack of collinearity constraints on the spinquantization axis.

Exploring Spin Symmetry-Breaking Effects for Static Field Ionization of Atoms: Is There an Analog to the Coulson-Fischer Point in Bond Dissociation?