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Title: Communication: 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 to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. Here, 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). 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, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

Authors:
 [1];  [2];  [3];  [3]
  1. Temple Univ., Philadelphia, PA (United States). Dept. of Physics
  2. Temple Univ., Philadelphia, PA (United States). Dept. of Physics, and Dept. of Chemistry
  3. Temple Univ., Philadelphia, PA (United States). Dept. of Physics
Publication Date:
Research Org.:
Temple Univ., Philadelphia, PA (United States); Energy Frontier Research Centers (EFRC) (United States). Center for the Computational Design of Functional Layered Materials (CCDM)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
OSTI Identifier:
1471104
Alternate Identifier(s):
OSTI ID: 1253395
Grant/Contract Number:  
SC0012575; DMR-1305135
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 144; Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Sun, Jianwei, Perdew, John P., Yang, Zenghui, and Peng, Haowei. Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems. United States: N. p., 2016. Web. doi:10.1063/1.4950845.
Sun, Jianwei, Perdew, John P., Yang, Zenghui, & Peng, Haowei. Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems. United States. doi:10.1063/1.4950845.
Sun, Jianwei, Perdew, John P., Yang, Zenghui, and Peng, Haowei. Tue . "Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems". United States. doi:10.1063/1.4950845. https://www.osti.gov/servlets/purl/1471104.
@article{osti_1471104,
title = {Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems},
author = {Sun, Jianwei and Perdew, John P. and Yang, Zenghui and Peng, Haowei},
abstractNote = {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 to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. Here, 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). 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, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.},
doi = {10.1063/1.4950845},
journal = {Journal of Chemical Physics},
number = 19,
volume = 144,
place = {United States},
year = {2016},
month = {5}
}

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Cited by: 7 works
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