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

• Published in: The Journal of chemical physics Vol. 158; no. 21
• Main Authors: Thapa, Bishal, Jing, Xin, Pask, John E., Suryanarayana, Phanish, Mazin, Igor I.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 07.06.2023; American Institute of Physics (AIP)
• Subjects: Bosons; Crystal structure; Density functional theory; Diamond; Electron density; Error analysis; Exchange correlation functionals; Ground state; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Kinetic energy; Linear response; Local density approximations; Phonons; Quantum chemistry; Self consistent field methods
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/5.0146167

We investigate the source of error in the Thomas–Fermi–von Weizsäcker (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.