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

TL;DR

This paper investigates the deviations of the Kohn-Sham kinetic energy density from the von Weizs"acker form near nuclei and in the asymptotic regions, deriving new constraints for density functionals and analyzing their implications.

Contribution

It provides a detailed analysis of the KE density deviations at nuclear and asymptotic regions and introduces new exact constraints for meta-GGA exchange functionals.

Findings

Kohn-Sham KE density differs significantly from von Weizs"acker at nuclei and in asymptotic regions.

Derived new exact constraints for meta-GGA exchange functionals involving the enhancement factor.

Quantified the contribution of p-type orbitals to KE density in large atoms and semiclassical limits.

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 $\sqrt{\alpha}$, 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.