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

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.

18 pages, 10 figures

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• Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules
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• Non-local kinetic energy functional from the Jellium-with-gap model: applications to Orbital-Free Density Functional Theory
• Many recent density functionals are numerically ill-behaved
• Laplacian-Level Quantum Hydrodynamic Theory for Plasmonics
• Jellium-with-gap model applied to semilocal kinetic functionals
• Visualization and analysis of the Kohn-Sham kinetic energy density and its orbital-free description in molecules
• Visualizing the large-$Z$ scaling of the kinetic energy density of atoms
• Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: tests on solids
• Methods to generate the reference total and Pauli kinetic potentials
• Semi-local Exchange Energy Functional For Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations
• Trivial Constraints on Orbital-free Kinetic Energy Density Functionals