Visualizing the large-$Z$ scaling of the kinetic energy density of atoms

Abstract

The scaling of neutral atoms to large $Z$, combining periodicity with a gradual trend to homogeneity, is a fundamental probe of density functional theory, one that has driven recent advances in understanding both the kinetic and exchange-correlation energies. Although research focus is normally upon the scaling of energies, insights can also be gained from energy densities. We visualize the scaling of the positive-definite kinetic energy density (KED) in closed-shell atoms, in comparison to invariant quantities based upon the gradient and Laplacian of the density. We notice a striking fit of the KED within the core of any atom to a gradient expansion using both the gradient and the Laplacian, appearing as an asymptotic limit around which the KED oscillates. The gradient expansion is qualitatively different from that derived from first principles for a slowly-varying electron gas and is correlated with a nonzero Pauli contribution to the KED near the nucleus. We propose and explore orbital-free meta-GGA models for the kinetic energy to describe these features, with some success, but the effects of quantum oscillations in the inner shells of atoms makes a complete parametrization difficult. We discuss implications for improved orbital-free description of molecular properties.

arXiv comment17 pages, 11 figures; 56th Sanibel Symposium

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Cited by in corpus (8)

• Deorbitalization strategies for meta-GGA exchange-correlation functionals
• Non-local kinetic energy functional from the Jellium-with-gap model: applications to Orbital-Free Density Functional Theory
• 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
• Some Problems in Density Functional Theory
• An alternative derivation of orbital-free density functional theory
• Trivial Constraints on Orbital-free Kinetic Energy Density Functionals
• Asymptotic Analysis of the Pauli Potential for Atoms