Assessing the source of error in the Thomas-Fermi-von Weizsäcker density functional

Area of Science:

• Condensed matter physics
• Quantum chemistry
• Materials science

Background:

• The Thomas-Fermi-von Weizsäcker (TFW) model is an orbital-free density functional approximation.
• Kohn-Sham density functional theory (DFT) is a widely used accurate method for electronic structure calculations.

Purpose of the Study:

• To identify the source of energy errors in the TFW approximation compared to Kohn-Sham DFT.
• To investigate the TFW model's accuracy for various material properties under strain and atomic displacement.

Main Methods:

• Numerical studies on diverse materials and crystal structures.
• Analysis of ground state electron densities and energies.
• Comparison between TFW and Kohn-Sham DFT calculations.
• Evaluation of linear response properties within the TFW approximation.

Main Results:

• TFW ground state electron densities closely match Kohn-Sham DFT densities.
• Significant deviations in TFW energies compared to Kohn-Sham DFT values were observed.
• The TFW approximation poorly represents the linear response of electronic kinetic energy.
• Non-self-consistent Kohn-Sham calculations using TFW densities agree well with self-consistent results.

Conclusions:

• The primary source of TFW energy error lies in its inadequate treatment of electronic kinetic energy linear response.
• TFW orbital-free DFT can provide accurate electron densities but not accurate energies.
• Non-self-consistent Kohn-Sham calculations offer a computationally efficient alternative with high accuracy for energies.