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Electron correlation effects play a key role in stabilising two-electronatoms near the critical nuclear charge, representing the smallest chargerequired to bind two electrons. However, deciphering the importance of theseeffects relies on fully understanding the uncorrelated Hartree-Fockdescription. Here, we investigate the properties of the ground state wavefunction in the small nuclear charge limit using various symmetry-restrictedHartree-Fock formalisms. We identify the nuclear charge where spin-symmetrybreaking occurs to give an unrestricted wave function that predicts theionisation of an electron. We also discover another critical nuclear chargewhere the closed-shell electron density detaches from the nucleus, and identifythe importance of fractional spin errors and static correlation in this limit.

Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms