Exact exchange in the Levy-Perdew-Sahni density-functional theory

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Density-functional theory (DFT) is a cornerstone of modern electronic structure calculations.
• Orbital-free DFT methods offer computational advantages but require accurate approximations for exchange-correlation functionals.
• The Levy-Perdew-Sahni (LPS) scheme presents an alternative orbital-free approach.

Purpose of the Study:

• To identify the exact exchange functional within the orbital-free Levy-Perdew-Sahni (LPS) density-functional scheme.
• To establish the relationship between the Fermi-Amaldi functional and the LPS exact exchange.
• To explore the potential for improved orbital-free DFT approximations.

Main Methods:

• Interpretation of the LPS scheme using an auxiliary reference system of non-interacting particles.
• Identification of the exact exchange contribution as the Fermi-Amaldi functional.
• Self-consistent calculations for atoms and molecules using the LPS scheme.

Main Results:

• The Fermi-Amaldi functional is shown to be the exact exchange contribution in the LPS scheme.
• The exact LPS exchange is a pure density functional, distinct from Kohn-Sham exact exchange.
• Self-consistent calculations demonstrate improved accuracy for light atoms compared to standard Kohn-Sham approximations.

Conclusions:

• The Fermi-Amaldi functional provides an exact, pure density functional for exchange within the LPS orbital-free formalism.
• This finding offers a pathway for developing more accurate orbital-free DFT methods.
• The results pave the way for improved approximations to other terms in the LPS total-energy functional.