Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density

TL;DR

This paper establishes an exact condition on the Kohn-Sham kinetic energy crucial for the accuracy of approximate functionals, introduces a new method for extracting asymptotic expansion coefficients, and provides a modern parametrization of the Thomas-Fermi density.

Contribution

It introduces a novel method to extract asymptotic expansion coefficients and links the correct expansion to an exact condition on the Kohn-Sham kinetic energy, improving functional accuracy.

Findings

Recovery of the correct asymptotic expansion is an exact condition on the Kohn-Sham kinetic energy.

The method effectively extracts expansion coefficients from oscillating numerical data.

A highly accurate parametrization of the Thomas-Fermi density for neutral atoms is provided.

Abstract

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an exact condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules and solids, when evaluated on a Kohn-Sham density. For example, this determines the small gradient limit of any generalized gradient approximation, and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.