An investigation into the nonconformity of homogeneous gas limit for kinetic energy density of atomic systems

TL;DR

This paper investigates the limitations of using homogeneous electron gas models for kinetic energy density functionals in atomic systems, highlighting the need for improved approaches with realistic potentials.

Contribution

It demonstrates the inadequacy of homogeneous models with a Pöschl-Teller potential, suggesting a shift in the foundational approach for atomic kinetic energy densities.

Findings

Homogeneous electron gas models yield improper results for atomic potentials.

A Pöschl-Teller potential reveals limitations of current models.

Need for revised leading-order terms in kinetic energy density functionals.

Abstract

Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic approach to accurately compute the kinetic energy density in such contexts. In our recent work, we introduced an analytical Green's function-based framework to address this issue. Majority of the existing efforts to construct an approximate kinetic energy density for atomic systems uses homogeneous electron gas as the bedrock of their formalism. In this work, we have shown by using a P\"oschl-Teller potential that for realistic atomic potentials such model yields improper results emphasizing the need to change the leading-order term for the quest of kinetic energy densities of atoms and molecules.