Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules

TL;DR

This paper visualizes and analyzes the Kohn-Sham kinetic energy density and its orbital-free models, revealing the effectiveness of the gradient expansion and identifying limitations of current metaGGA approaches in localized regions.

Contribution

It provides a detailed visualization of the KED and compares it with orbital-free models, challenging existing conjectures and proposing improvements for better electron localization description.

Findings

Second-order gradient expansion predicts KED well at low densities.

MetaGGA KED has issues in regions of strong electron localization.

Revised metaGGA improves atomization energy predictions.

Abstract

We visualize the Kohn-Sham kinetic energy density (KED), and the ingredients -- the electron density, its gradient and Laplacian -- used to construct orbital-free models of it, for the AE6 test set of molecules. These are compared to related quantities used in metaGGA's, to characterize two important limits -- the gradient expansion and the localized-electron limit typified by the covalent bond. We find the second-order gradient expansion of the KED to be a surprisingly successful predictor of the exact KED, particularly at low densities where this approximation fails for exchange. This contradicts the conjointness conjecture that the optimal enhancement factors for orbital-free kinetic and exchange energy functionals are identical. In addition we find significant problems with a recent metaGGA-level orbital-free KED, especially for regions of strong electron localization. We define an orbital-free description of electron localization and a revised metaGGA that improves upon atomization energies significantly.