Collapse of the Electron Gas to Two Dimensions in Density Functional Theory

2008/06/11 by Lucian A. Constantin, John P. Perdew, J. M. Pitarke · 2 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced Condensed Matter Physics #Atomic orbital #Condensed matter physics #Crossover #Density functional theory #Electron #Fermi gas #Limit (mathematics) #Local-density approximation #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Slab #cond-mat.mtrl-sci

paper · pdf · doi:10.1103/physrevlett.101.016406

4 pages, 2 figures

arxiv created 2008/06/11 · openalex publication_date 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjölander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.

Citations

• Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
• Two-dimensional limit of exchange-correlation energy functional approximations
• Generalized Gradient Approximation Made Simple
• Electronic structure of quantum dots
• Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
• Exact-exchange energy density in the gauge of a semilocal density-functional approximation
• High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input
• Self-Consistent Equations Including Exchange and Correlation Effects

Cited by

• Density functional with full exact exchange, balanced nonlocality of correlation, and constraint satisfaction
• Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas

Related

• Semilocal Exchange Functionals With Improved Performances: The Modified Enhancement Factor For Two Dimensional Quantum Systems
• Exact-exchange energy density in the gauge of a semilocal density-functional approximation
• How Semilocal Are Semilocal Density Functional Approximations? -Tackling Self-Interaction Error in One-Electron Systems
• Density Functional Theory for the Electron Gas and for Jellium
• High-Level Correlated Approach to the Jellium Surface Energy, without Uniform-Gas Input