Hartree-Fock Critical Nuclear Charge in Two-Electron Atoms

TL;DR

This paper investigates the critical nuclear charge in two-electron atoms using Hartree-Fock methods, revealing symmetry-breaking phenomena and the role of static correlation near the ionization threshold.

Contribution

It identifies new critical nuclear charges and analyzes symmetry-breaking and correlation effects within Hartree-Fock approximations for two-electron systems.

Findings

Identification of nuclear charge where spin-symmetry breaks

Discovery of a critical charge where electron density detaches from nucleus

Analysis of fractional spin errors and static correlation effects

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.