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.

5 pages, 3 figures

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Cited by in corpus (11)

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• Laplacian-dependent models of the kinetic energy density: Applications in subsystem density functional theory with meta-generalized gradient approximation functionals
• 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
• 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