Kinetic and Exchange Energy Densities near the Nucleus

TL;DR

This paper analyzes the behavior of kinetic and exchange energy densities near atomic nuclei, deriving analytical expressions and proposing non-local density-dependent models for improved density functional approximations.

Contribution

It introduces new analytical expressions and non-local models for energy densities near nuclei, validated by numerical calculations on real atoms.

Findings

Analytical expressions for energy densities near the nucleus.

Non-local density-dependent ingredients for functional development.

Validation of models with atoms up to two thousand electrons.

Abstract

We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.