Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson–Fischer point in bond dissociation?

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