Optimizing a parametrized Thomas-Fermi-Dirac-Weizsäcker density functional for atoms.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Orbital-free (OF) density functionals face challenges in accuracy and transferability.
• All-electron self-consistent assessment of OF functionals is numerically difficult.
• Improving OF density functional development is an active research area.

Purpose of the Study:

• To evaluate a parametrized orbital-free density functional.
• To investigate the interplay of parameters (λ and γ) in the Thomas-Fermi-Weizsäcker kinetic model.
• To achieve accurate approximations of Kohn-Sham (KS) model properties.

Main Methods:

• Utilized an all-electron radial OFDFT code for functional assessment.
• Combined a parametrized Thomas-Fermi-Weizsäcker kinetic model with an LDA exchange-correlation functional.
• Employed potential scaling for converged results with varying λ values.
• Systematically varied parameters (λ, γ) between 0.2 and 1.5.

Main Results:

• Identified a λ-γ parameter relationship for approximating atomic energies with <3% error vs. KS.
• Reproducing KS HOMO eigenvalues with similar accuracy requires a different λ-γ parameter region.
• Atomic densities were reproduced with an average integrated difference of 0.15-0.20 |e| per electron, showing smoother behavior and less parameter sensitivity.

Conclusions:

• Specific parameter interplays in OF functionals can yield accurate atomic energies and eigenvalues.
• The study provides a pathway for testing parameter transferability in OF density functionals.
• Further systematic improvements in OF density functional development are facilitated by these findings.