Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

Abstract

We derive a closed form expression for the quantum corrections to the kinetic energy density (KED) in the Thomas-Fermi (TF) limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three dimensional model systems: (i) jellium surfaces, (ii) hydrogen-like potentials, (iii) systems confined by an harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory (ETF) does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of type (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.

arXiv comment15 pages, 9 figures

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• Edge Electron Gas
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• 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
• Leading corrections to local approximations II (with turning points)
• Some Problems in Density Functional Theory
• Deriving approximate functionals with asymptotics
• Asymptotic Analysis of the Pauli Potential for Atoms
• Airy gas model: From three to reduced dimensions