Leading corrections to local approximations

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.

References in corpus (8)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Edge Electron Gas
• Relevance of the slowly-varying electron gas to atoms, molecules, and solids
• Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density
• Semiclassical Density Functional Theory: Strutinsky Energy Corrections in Quantum Dots
• Landau Fermi Liquid Picture of Spin Density Functional Theory: Strutinsky Approach to Quantum Dots
• Non-empirical 'derivation' of B88 exchange functional

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• Jellium-with-gap model applied to semilocal kinetic functionals
• Potential functionals versus density functionals
• Corrections to Thomas-Fermi densities at turning points and beyond
• Density functional theory on phase space
• Systematic corrections to the Thomas-Fermi approximation without a gradient expansion
• Airy-averaged gradient corrections for two-dimensional fermion gases
• Leading corrections to local approximations II (with turning points)
• Bypassing the malfunction junction in warm dense matter simulations
• Deriving approximate functionals with asymptotics
• Large two-dimensional electronic systems: Self-consistent energies and densities at low cost
• Approximate normalizations for approximate density functionals