Assessing the source of error in the Thomas-Fermi-von Weizs\"acker density functional

TL;DR

This paper analyzes the errors in the Thomas-Fermi-von Weizs"acker density functional, revealing that while it approximates electron densities well, it significantly deviates in energy calculations due to poor linear response representation.

Contribution

The study identifies the primary source of error in TFW density functional as its poor linear response, supported by numerical comparisons with Kohn-Sham DFT across various materials.

Findings

Electron densities in TFW are close to Kohn-Sham densities.

Energy deviations are significant despite similar densities.

Non-self-consistent Kohn-Sham energies align well with self-consistent results.

Abstract

We investigate the source of error in the Thomas-Fermi-von Weizs\"acker (TFW) density functional relative to Kohn-Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of crystal structures subject to strain and atomic displacements, we find that while the ground state electron density in TFW orbital-free DFT is close to the Kohn-Sham density, the corresponding energy deviates significantly from the Kohn-Sham value. We show that these differences are a consequence of the poor representation of the linear response within the TFW approximation for the electronic kinetic energy, confirming conjectures in the literature. In so doing, we find that the energy computed from a non-self-consistent Kohn-Sham calculation using the TFW electronic ground state density is in very good agreement with that obtained from the fully self-consistent Kohn-Sham solution.