Derivative discontinuity with localized Hartree-Fock potential.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• The optimized effective potential (OEP) is accurate but computationally expensive.
• The localized Hartree-Fock (LHF) potential offers a computationally efficient alternative to OEP.
• LHF preserves numerical accuracy and key theoretical properties like self-interaction freedom.

Purpose of the Study:

• Extend the localized Hartree-Fock potential to systems with fractional particle numbers.
• Investigate the derivative discontinuities of the LHF potential in this extended regime.
• Assess the computational efficiency and accuracy of the extended LHF potential.

Main Methods:

• Extension of the localized Hartree-Fock potential formalism to accommodate fractional particle numbers.
• Numerical calculation of energy derivative discontinuities for systems with fractional electron counts.
• Comparison of LHF results with the computationally demanding Hartree-Fock method.

Main Results:

• The extended LHF potential successfully yields derivative discontinuities in energy, consistent with exact theory.
• These discontinuities are numerically comparable to those obtained via the full Hartree-Fock method.
• The LHF potential exhibits a 'direct-energy' property, simplifying energy calculations.
• A specific condition relating spin-component discontinuities (c↑N↑ + c↓N↓ = 0) was identified.

Conclusions:

• The localized Hartree-Fock potential is effectively extended to fractional particle numbers.
• This extension maintains accuracy and computational efficiency, making it a valuable tool.
• The LHF potential's ability to capture derivative discontinuities is crucial for applications involving fundamental gaps.