Kinetic Energy Density Study of Some Representative Semilocal Kinetic Energy Functionals

TL;DR

This study compares various semilocal kinetic energy density functionals, emphasizing the importance of local behavior and introducing a quality factor to evaluate their accuracy in representing electron systems.

Contribution

It introduces a new quality factor to assess local accuracy of kinetic energy functionals and analyzes their performance beyond total energy calculations.

Findings

Most functionals rely on error cancellations for total energy accuracy.

Local behavior of these functionals is often worse than Thomas-Fermi.

Including the Laplacian improves the evaluation of kinetic energy densities.

Abstract

There is a number of explicit kinetic energy density functionals for non-interacting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the laplacian of the electron density to work with an infinite set of kinetic energy densities. For all the functionals but one we have found that their success in the evaluation of the total kinetic energy are due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.