Hartree-Fock critical nuclear charge in two-electron atoms

Area of Science:

• Quantum Chemistry
• Atomic Physics
• Computational Physics

Background:

• Electron correlation is crucial for stabilizing two-electron atoms near critical nuclear charge.
• A complete understanding necessitates analyzing the uncorrelated Hartree-Fock description.

Purpose of the Study:

• Investigate ground state wave function properties in the small nuclear charge limit.
• Determine the significance of electron correlation and symmetry breaking in atomic systems.

Main Methods:

• Utilized various symmetry-restricted Hartree-Fock formalisms.
• Analyzed the behavior of the ground state wave function at small nuclear charges.

Main Results:

• Identified the nuclear charge for spin-symmetry breaking, leading to unrestricted wave functions.
• Determined critical nuclear charges for closed-shell and unrestricted states (orbital energy zero, density detachment).
• Highlighted the role of fractional spin errors and static correlation.

Conclusions:

• Symmetry-restricted Hartree-Fock methods are essential for understanding electron behavior in two-electron atoms.
• The study provides insights into the transition from bound to unbound electronic states.