Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizsäcker Behavior and Applications to Density Functionals

Abstract

We show that the Kohn-Sham positive-definite kinetic energy (KE) density significantly differs from the von Weizsäcker (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 $\sqrt{\alpha }$, where $\alpha$ 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.

arXiv comment5 pages, 3 figures

References in corpus (13)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
• Exact-exchange energy density in the gauge of a semilocal density functional approximation
• Optics of semiconductors from meta-GGA-based time-dependent density-functional theory
• Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory
• Constraint-based, Single-point Approximate Kinetic Energy Functionals
• One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation
• Meta-GGA exchange-correlation functional with a balanced treatment of nonlocality
• Dimensional crossover of the exchange-correlation energy at the semilocal level
• Exchange and correlation near the nucleus in density functional theory

Cited by in corpus (18)

• Quantum Hydrodynamic Theory for Plasmonics: Impact of the Electron Density Tail
• Deorbitalization strategies for meta-GGA exchange-correlation functionals
• 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
• Non-local kinetic energy functional from the Jellium-with-gap model: applications to Orbital-Free Density Functional Theory
• Comparison between exact and semilocal exchange potentials: An all-electron study for solids
• Semilocal density functional theory with correct surface asymptotics
• Jellium-with-gap model applied to semilocal kinetic functionals
• Meta-GGA density functional calculations on atoms with spherically symmetric densities in the finite element formalism
• Assessing exchange-correlation functional performance for structure and property predictions of oxyfluoride compounds from first principles
• Subsystem density functional theory with meta generalized gradient approximation exchange-correlation functionals
• No-go theorem for the description of Mott phenomena with conventional Density Functional Theory methods
• Visualizing the large-$Z$ scaling of the kinetic energy density of atoms
• Methods to generate the reference total and Pauli kinetic potentials
• Hartree potential dependent exchange functional
• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Asymptotic Analysis of the Pauli Potential for Atoms
• Restoring the Point-and-Charge Gradient Expansion for the Strong Interaction Density Functionals