Hartree-Fock critical nuclear charge in two-electron atoms

Electron correlation effects play a key role in stabilizing two-electron atoms near the critical nuclear charge, representing the smallest charge required to bind two electrons. However, deciphering the importance of these effects relies on fully understanding the uncorrelated Hartree-Fock description. We investigate the properties of the ground state wave function in the small nuclear charge limit using various symmetry-restricted Hartree-Fock formalisms. We identify the nuclear charge where spin-symmetry breaking occurs to give an unrestricted wave function that predicts an inner and outer electron. We also identify closed-shell and unrestricted critical nuclear charges where the highest occupied orbital energy becomes zero and the electron density detaches from the nucleus. Finally, we identify the importance of fractional spin errors and static correlation for small nuclear charges.

Automated summary

Electron correlation effects are crucial in stabilizing two-electron atoms near the critical nuclear charge, and understanding them relies on a solid grasp of the uncorrelated Hartree-Fock description. By exploring different symmetry-restricted Hartree-Fock formalisms, we identified the nuclear charge where spin-symmetry breaking occurs, leading to an unrestricted wave function predicting inner and outer electrons. We also found closed-shell and unrestricted critical nuclear charges where the highest occupied orbital energy reaches zero and the electron density separates from the nucleus, highlighting the importance of fractional spin errors and static correlation for small nuclear charges.