Condition on the Kohn–Sham kinetic energy and modern parametrization of the Thomas–Fermi density

2008/10/11 by Donghyung Lee, Kieron Burke, Lucian A. Constantin +1 · 3 citations
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Catalytic Processes in Materials Science #nanoparticles nucleation surface interactions #physics.atm-clus #quant-ph

paper · pdf · doi:10.1063/1.3059783

10 pages, 9 figures, submitted at JCP

arxiv created 2008/10/11 · openalex publication_date 2009/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z-->infinity, presenting a new method to extract the coefficients from oscillating numerical data. Recovery of the correct expansion yields a condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules, and solids. For example, this determines the small gradient limit of any generalized gradient approximation and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters using densities constructed from Kohn-Sham orbitals. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

Citations

• Spin-density gradient expansion for the kinetic energy

Cited by

• Leading corrections to local approximations
• Communication: Testing and using the Lewin-Lieb bounds in density functional theory
• Orbital-free bond breaking via machine learning

Related

• Modified Statistical Treatment of Kinetic Energy in the Thomas-Fermi Model
• Scaling of the known exact explicit forms of the non-interacting kinetic-energy density functional
• Correction to kinetic energy density using exactly solvable model
• Orbital-free functional with sub-milliHartree errors for slabs
• An investigation into the nonconformity of homogeneous gas limit for kinetic energy density of atomic systems