A local tensor that unifies kinetic energy density and vorticity dependent exchange-correlation functionals

TL;DR

This paper introduces a new kinetic energy tensor that unifies scalar kinetic energy density and vorticity density, providing a versatile tool for density functional theory with clear physical and mathematical properties.

Contribution

A novel kinetic energy tensor is proposed that unifies existing densities and is applicable on the third rung of Jacob's ladder, with gauge invariance and N-representability conditions.

Findings

Unifies scalar kinetic energy density and vorticity density.

Related to exchange hole curvature and gauge invariant.

Discriminates between different orbital region counts.

Abstract

We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-Generalized Gradient Approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory. Both types of functionals can thus be subsumed as special cases of a novel functional form that is naturally placed on the third rung of Jacob's ladder. Moreover, the kinetic energy tensor is related to the exchange hole curvature, is gauge invariant, and has very clearcut $N$-representability conditions. The latter conditions enable the definition of effective number of non-negligible orbitals. Whereas quantities such as the Electron Localization Function can discriminate effective one-orbital regions from other regions, the present kinetic energy tensor can discriminate between one-, two-, three-, and four-or-more orbital regions.