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Title: Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory

Abstract

Here under pressure, a quasi-2D electron gas can collapse toward the true 2D limit. In this limit, the exact exchange-correlation energy per electron has a known finite limit, but general-purpose semilocal approximate density functionals, like the local density approximation (LDA) and Perdew-Burke-Ernzerhof generalized gradient approximation (PBE GGA), are known to diverge to minus infinity. Here we consider a model density for a non-interacting electron gas confined to a thickness $L$ by infinite-barrier walls, with a fixed 2D density $$1/(\pi (r_s^{\text{2D}})^2)$$, and $$r_s^{\text{2D}}=4$$ Bohr. We estimate that LDA, PBE, and the strongly constrained and appropriately normed (SCAN) meta-GGA are accurate for the exchange-correlation energy over a wide quasi-2D range, $$1.5< L/r_s^{\text{2D}} < 3.85$$, but not for smaller $L$. Of these functionals, only SCAN tends to a finite limit when $L$ tends to 0. Since the non-interacting kinetic energy, treated exactly in Kohn-Sham theory, dominates in this limit within a deformable jellium model, all of the general-purpose functionals can estimate the pressure required to achieve any thickness (with SCAN and LDA better than PBE). This pressure vanishes around $$L/r_s^{\text{2D}} = 3.85$$, where the 3D electron density is roughly that of the valence electrons in metallic potassium, and reaches about 20 GPa at $$L/r_s^{\text{2D}} = 1.5$$ and 400 GPa at $$L/r_s^{\text{2D}} = 0.6$$.

Authors:
 [1];  [1];  [1]
  1. Temple Univ., Philadelphia, PA (United States)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ., Philadelphia, PA (United States). Dept. of Physics
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1467076
Alternate Identifier(s):
OSTI ID: 1467139
Grant/Contract Number:  
SC0012575
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 98; Journal Issue: 8; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Kaplan, Aaron D., Wagle, Kamal, and Perdew, John P. Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.085147.
Kaplan, Aaron D., Wagle, Kamal, & Perdew, John P. Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory. United States. doi:10.1103/PhysRevB.98.085147.
Kaplan, Aaron D., Wagle, Kamal, and Perdew, John P. Tue . "Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory". United States. doi:10.1103/PhysRevB.98.085147. https://www.osti.gov/servlets/purl/1467076.
@article{osti_1467076,
title = {Collapse of the electron gas from three to two dimensions in Kohn-Sham density functional theory},
author = {Kaplan, Aaron D. and Wagle, Kamal and Perdew, John P.},
abstractNote = {Here under pressure, a quasi-2D electron gas can collapse toward the true 2D limit. In this limit, the exact exchange-correlation energy per electron has a known finite limit, but general-purpose semilocal approximate density functionals, like the local density approximation (LDA) and Perdew-Burke-Ernzerhof generalized gradient approximation (PBE GGA), are known to diverge to minus infinity. Here we consider a model density for a non-interacting electron gas confined to a thickness $L$ by infinite-barrier walls, with a fixed 2D density $1/(\pi (r_s^{\text{2D}})^2)$, and $r_s^{\text{2D}}=4$ Bohr. We estimate that LDA, PBE, and the strongly constrained and appropriately normed (SCAN) meta-GGA are accurate for the exchange-correlation energy over a wide quasi-2D range, $1.5< L/r_s^{\text{2D}} < 3.85$, but not for smaller $L$. Of these functionals, only SCAN tends to a finite limit when $L$ tends to 0. Since the non-interacting kinetic energy, treated exactly in Kohn-Sham theory, dominates in this limit within a deformable jellium model, all of the general-purpose functionals can estimate the pressure required to achieve any thickness (with SCAN and LDA better than PBE). This pressure vanishes around $L/r_s^{\text{2D}} = 3.85$, where the 3D electron density is roughly that of the valence electrons in metallic potassium, and reaches about 20 GPa at $L/r_s^{\text{2D}} = 1.5$ and 400 GPa at $L/r_s^{\text{2D}} = 0.6$.},
doi = {10.1103/PhysRevB.98.085147},
journal = {Physical Review B},
number = 8,
volume = 98,
place = {United States},
year = {2018},
month = {8}
}

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Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Ab initio theory and modeling of water
journal, September 2017

  • Chen, Mohan; Ko, Hsin-Yu; Remsing, Richard C.
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 41
  • DOI: 10.1073/pnas.1712499114

Efficient first-principles prediction of solid stability: Towards chemical accuracy
journal, March 2018


Dielectric Response of a Semi-Infinite Degenerate Electron Gas
journal, April 1970


Diamond anvil cell behavior up to 4 Mbar
journal, February 2018

  • Li, Bing; Ji, Cheng; Yang, Wenge
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 8
  • DOI: 10.1073/pnas.1721425115

Electron-gas clusters: the ultimate jellium model
journal, December 1995

  • Koskinen, M.; Lipas, P. O.; Manninen, M.
  • Zeitschrift für Physik D Atoms, Molecules and Clusters, Vol. 35, Issue 4
  • DOI: 10.1007/BF01745532

Properties of real metallic surfaces: Effects of density functional semilocality and van der Waals nonlocality
journal, October 2017

  • Patra, Abhirup; Bates, Jefferson E.; Sun, Jianwei
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 44
  • DOI: 10.1073/pnas.1713320114

Requirements for correlation energy density functionals from coordinate transformations
journal, February 1992


Accurate critical pressures for structural phase transitions of group IV, III-V, and II-VI compounds from the SCAN density functional
journal, March 2018


Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
journal, May 1976


Collapse of the Electron Gas to Two Dimensions in Density Functional Theory
journal, July 2008


How metals bind: The deformable-jellium model with correlated electrons
journal, October 2003

  • Tran, Hoang T.; Perdew, John P.
  • American Journal of Physics, Vol. 71, Issue 10
  • DOI: 10.1119/1.1590653

Inhomogeneous Electron Gas
journal, November 1964


Collective excitations in a spin-polarized quasi-two-dimensional electron gas
journal, February 1991


Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


Dimensional crossover of the exchange-correlation energy at the semilocal level
journal, October 2008


Quasi-two-dimensional electron gas: Exchange and correlation energies
journal, May 1996


An accurate first-principles treatment of doping-dependent electronic structure of high-temperature cuprate superconductors
journal, March 2018


On the existence of a nonmonotonic nuclear density profile at the jellium–vacuum interface
journal, December 1977

  • Allen, J. W.; Rice, Stuart A.
  • The Journal of Chemical Physics, Vol. 67, Issue 11
  • DOI: 10.1063/1.434738

Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional
journal, June 2016

  • Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo
  • Nature Chemistry, Vol. 8, Issue 9
  • DOI: 10.1038/nchem.2535

Is the Local Density Approximation Exact for Short Wavelength Fluctuations?
journal, August 1994


Dimensional crossover of the exchange-correlation density functional
journal, July 2000


Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging
journal, September 1998

  • Burke, Kieron; Perdew, John P.; Ernzerhof, Matthias
  • The Journal of Chemical Physics, Vol. 109, Issue 10
  • DOI: 10.1063/1.476976

Real-space analysis of the exchange-correlation energy
journal, November 1995

  • Burke, Kieron; Perdew, John P.
  • International Journal of Quantum Chemistry, Vol. 56, Issue 4
  • DOI: 10.1002/qua.560560403

Two-dimensional limit of exchange-correlation energy functional approximations
journal, February 2000


Effects of three-body and backflow correlations in the two-dimensional electron gas
journal, October 1993


Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965