Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density

Abstract

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an exact condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules and solids, when evaluated on a Kohn-Sham density. 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. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.

arXiv comment10 pages, 9 figures, submitted at JCP

References in corpus (4)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
• Relevance of the slowly-varying electron gas to atoms, molecules, and solids

Cited by in corpus (24)

• Finding Density Functionals with Machine Learning
• Orbital-free Bond Breaking via Machine Learning
• Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory
• Semiclassical atom theory applied to solid-state physics
• Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals
• Relevance of coordinate and particle-number scaling in density functional theory
• Locality of correlation in density functional theory
• Jellium-with-gap model applied to semilocal kinetic functionals
• Kinetic energy density functionals from the Airy gas, with an application to the atomization kinetic energies of molecules
• Testing the broad applicability of the PBEint GGA functional and its one-parameter hybrid form
• Leading corrections to local approximations
• Generalized gradient approximation correlation energy functionals based on the uniform electron gas with gap model
• Subsystem density functional theory with meta generalized gradient approximation exchange-correlation functionals
• Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas
• Visualizing the large-$Z$ scaling of the kinetic energy density of atoms
• Global hybrids from the semiclassical atom theory satisfying the local density linear response
• Spin-dependent gradient correction for more accurate atomization energies of molecules
• Leading gradient correction to the kinetic energy for two-dimensional fermion gases
• Leading corrections to local approximations II (with turning points)
• Leading correction to the local density approximation for exchange in large-$Z$ atoms
• An alternative derivation of orbital-free density functional theory
• Testing and Using the Lewin-Lieb Bound in Density Functional Theory
• Asymptotic Analysis of the Pauli Potential for Atoms
• How to make electrons avoid each other: a nonlocal radius for strong correlation