Kohn-Sham kinetic energy density in the nuclear and asymptotic regions: Deviations from the von Weizsäcker behavior and applications to density functionals

2014/11/14 by Fabio Della Sala, F. Della Sala, Eduardo Fabiano +3 · 58 citations
Chemistry · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced NMR Techniques and Applications #Atomic orbital #Cusp (singularity) #Electron #Energy (signal processing) #Energy density #Geometry #High-pressure geophysics and materials #Kinetic energy #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum #Quantum electrodynamics #Quantum mechanics #Semiclassical physics #Theoretical physics #Type (biology) #cond-mat.other #physics.atom-ph #physics.chem-ph

paper · pdf · doi:10.1103/physrevb.91.035126

published in Physical Review B 91(3) (American Physical Society) · 5 pages, 3 figures

arxiv created 2014/11/14 · openalex publication_date 2015/01/23 · arxiv updated 2015/02/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that the Kohn-Sham positive-definite kinetic energy (KE) density significantly differs from the von Weizs"acker (VW) one at the nuclear cusp as well as in the asymptotic region. At the nuclear cusp, the VW functional is shown to be linear, and the contribution of p-type orbitals to the KE density is theoretically derived and numerically demonstrated in the limit of infinite nuclear charge as well in the semiclassical limit of neutral large atoms. In the latter case, it reaches 12% of the KE density. In the asymptotic region we find new exact constraints for meta-generalized gradient approximation (meta-GGA) exchange functionals: with an exchange enhancement factor proportional to √\ensuremathα, where \ensuremathα is the common meta-GGA ingredient, both the exchange energy density and the potential are proportional to the exact ones. In addition, this describes exactly the large-gradient limit of quasi-two-dimensional systems.

Citations

• Optics of Semiconductors from Meta-Generalized-Gradient-Approximation-Based Time-Dependent Density-Functional Theory
• Generalized Gradient Approximation Made Simple
• Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
• Exact-exchange energy density in the gauge of a semilocal density-functional approximation
• A simple measure of electron localization in atomic and molecular systems
• The calculation of atomic fields
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Self-Consistent Equations Including Exchange and Correlation Effects
• Zur Theorie der Kernmassen

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