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Updated: Dec 27, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Leading correction to the local density approximation of the kinetic energy in one dimension
1Department of Physics and Astronomy and Department of Chemistry, University of California, Irvine, California 92697, USA.
Abstract:
A mathematical framework is constructed for the sum of the lowest N eigenvalues of a potential. Exactness is illustrated on several one-dimensional systems (harmonic oscillator, particle in a box, and Poschl-Teller well). Semiclassical expansion yields the leading corrections for finite systems, identifying the error in common gradient expansions in density functional theory. Some singularities can be avoided when evaluating the correction to the leading term. Correcting the error in the gradient expansion greatly improves accuracy. The relevance to practical density functional calculations is discussed.
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