Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

Abstract

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively-charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation (LSDA) to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). Our LSDA0 is constructed to satisfy exact constraints, but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities. Furthermore, we show that the locality of an orbital can be measured by the ratio between the exact exchange energy and its optimal lower bound.

References in corpus (6)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• Gedanken Densities and Exact Constraints in Density Functional Theory
• Two electrons on a hypersphere: a quasi-exactly solvable model
• Correlation energy of two electrons in the high-density limit
• Uniform Electron Gases. II. The Generalized Local Density Approximation in One Dimension

Cited by in corpus (11)

• Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory
• Stretched or noded orbital densities and self-interaction correction in density functional theory
• Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems
• Local density approximations from finite systems
• Exchange functionals based on finite uniform electron gases
• Improving the applicability of the Pauli kinetic energy density based semilocal functional for solids
• Hartree potential dependent exchange functional
• How good are recent density functionals for ground and excited states of one-electron systems?
• A study of accurate exchange-correlation functionals through adiabatic connection
• A local tensor that unifies kinetic energy density and vorticity dependent exchange-correlation functionals
• Transient Uniform Electron Gases