Leading corrections to local approximations

TL;DR

This paper derives leading quantum corrections to local potential-based functionals for 1D finite systems' kinetic energy, highlighting their non-local nature and improved accuracy over local approximations, with implications for density functional theory.

Contribution

It introduces simple, non-local functional corrections to local approximations for kinetic energy in 1D systems, derived via semiclassical methods, and discusses their impact on density functional theory.

Findings

Quantum oscillations from turning points significantly affect energy corrections.

Quantum corrections greatly improve the accuracy of local approximations.

The corrections are non-local functionals of the potential.

Abstract

For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential. Turning points produce quantum oscillations leading to energy corrections, which are completely different from the gradient corrections that occur in bulk systems with slowly-varying densities. Approximations that include quantum corrections are typically much more accurate than their local analogs. The consequences for density functional theory are discussed.