Relevance of the slowly-varying electron gas to atoms, molecules, and solids

Abstract

Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact to order ${\nabla }^2$. Neutral atoms of large $Z$ scale similarly, but a cusp correction at the nucleus requires generalizing the gradient expansion for exchange, producing the wrong gradient coefficient in the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's) recover both the slowly-varying and large-$Z$ limits. GGA correlation energies of large-Z atoms are found to be accurate.

5 pages, 4 figures, submitted at PRL

References in corpus (1)

• All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe

Cited by in corpus (18)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Nonlocal van der Waals density functional: The simpler the better
• van der Waals density functionals built upon the electron-gas tradition: Facing the challenge of competing interactions
• Exchange-Correlation Hole of a Generalized Gradient Approximation for Solids and Surfaces
• Interpretation of van der Waals density functionals
• Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density
• How tight is the Lieb-Oxford bound?
• Perdew-Zunger self-interaction correction: How wrong for uniform densities and large-Z atoms?
• Systematic investigation of a family of gradient-dependent functionals for solids
• Testing the broad applicability of the PBEint GGA functional and its one-parameter hybrid form
• Leading corrections to local approximations
• A Step in the Direction of Resolving the Paradox of Perdew-Zunger Self-interaction Correction. II. Gauge Consistency of the Energy Density at Three Levels of Approximation
• Spin-dependent gradient correction for more accurate atomization energies of molecules
• Seven Useful Questions in Density Functional Theory
• Leading correction to the local density approximation for exchange in large-$Z$ atoms
• Thermal Raman study of Li4Ti5O12 and discussion about the number of its characteristic bands
• Asymptotics of eigenvalue sums when some turning points are complex