Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms

Abstract

Electron correlation effects play a key role in stabilising 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. Here, 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 the ionisation of an electron. We also discover another critical nuclear charge where the closed-shell electron density detaches from the nucleus, and identify the importance of fractional spin errors and static correlation in this limit.

7 pages, 4 figures

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• Fractional spins and static correlation error in density functional theory
• Unrestricted Hartree-Fock theory of Wigner crystals
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Cited by in corpus (5)

• Excited states, symmetry breaking, and unphysical solutions in state-specific CASSCF theory
• Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer
• Variations of the Hartree-Fock fractional-spin error for one electron
• Complex analysis of divergent perturbation theory at finite temperature
• Quantum Systems at The Brink