Kinetic energy density for open-shell systems: Analysis and development of a novel technique

TL;DR

This paper develops a new exact method for calculating kinetic energy density in open-shell atoms, addressing limitations of previous approaches and analyzing spin-dependent features in density functional theory.

Contribution

It introduces a systematic, exact methodology for kinetic energy density calculation in open-shell systems, extending prior closed-shell techniques and analyzing spin effects.

Findings

The ad-hoc recipe is ineffective for open-shell atoms.

Analysis of spin-dependent Pauli potentials reveals key features.

Proposed method provides accurate kinetic energy densities for arbitrary spin states.

Abstract

The quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital-free density functional theory. While a recipe for closed-shell systems has been proposed earlier, we have shown that it cannot be na\"ively extended to open-shell atoms. In this present work, we investigated the efficacy of an ad-hoc recipe to compute the kinetic energy densities for open-shell atoms by extending the methodology used for closed-shell systems. We have also analyzed the spin-dependent features of Pauli potentials derived from two previously devised enhancement factors. Further, we have proposed an alternate but exact methodology to systematically compute the kinetic energy density for atoms of arbitrary spin multiplicity.