Communication: Nearlocality of exchange and correlation density functionals for 1 and 2electron systems
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 exchangecorrelation functional that undergirds the development of the KohnSham density functional theory. Here, we show here that the groundstate exchangecorrelation energies of the hydrogen atom and many other 1 and 2electron 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 twoelectron density in a finite, curved threedimensional space. We also apply LSDA0 to excited or noded 1electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1 or 2electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.
 Authors:

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 Temple Univ., Philadelphia, PA (United States). Dept. of Physics
 Temple Univ., Philadelphia, PA (United States). Dept. of Physics, and Dept. of Chemistry
 Temple Univ., Philadelphia, PA (United States). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 SC0012575; DMR1305135
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 144; Journal Issue: 19; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Temple Univ., Philadelphia, PA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1471104
 Alternate Identifier(s):
 OSTI ID: 1253395
Sun, Jianwei, Perdew, John P., Yang, Zenghui, and Peng, Haowei. Communication: Nearlocality of exchange and correlation density functionals for 1 and 2electron systems. United States: N. p.,
Web. doi:10.1063/1.4950845.
Sun, Jianwei, Perdew, John P., Yang, Zenghui, & Peng, Haowei. Communication: Nearlocality of exchange and correlation density functionals for 1 and 2electron systems. United States. doi:10.1063/1.4950845.
Sun, Jianwei, Perdew, John P., Yang, Zenghui, and Peng, Haowei. 2016.
"Communication: Nearlocality of exchange and correlation density functionals for 1 and 2electron systems". United States.
doi:10.1063/1.4950845. https://www.osti.gov/servlets/purl/1471104.
@article{osti_1471104,
title = {Communication: Nearlocality of exchange and correlation density functionals for 1 and 2electron 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 exchangecorrelation functional that undergirds the development of the KohnSham density functional theory. Here, we show here that the groundstate exchangecorrelation energies of the hydrogen atom and many other 1 and 2electron 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 twoelectron density in a finite, curved threedimensional space. We also apply LSDA0 to excited or noded 1electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1 or 2electron 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}
}