On a solution of the self-interaction problem in Kohn–Sham density functional theory
Abstract
In this work, we report on a methodology for the treatment of the Coulomb energy and potential in Kohn–Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn–Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree–Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy EHF≤EOEP≤ESIF that is indicative of the greater variation freedom implicit in the former two methods.
- Authors:
-
[1];
[3]
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Defect Physics in Structural Materials (CDP); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1737473
- Grant/Contract Number:
- AC05-00OR22725; AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics and Chemistry of Solids
- Additional Journal Information:
- Journal Volume: 75; Journal Issue: 10; Journal ID: ISSN 0022-3697
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; electronic structure theory; exchange energy; exchange potential; density functional theory; local density approximation; electron correlation; self-interaction free; exact exchange
Citation Formats
Däne, Markus, Gonis, A., Nicholson, Don M., and Stocks, George M. On a solution of the self-interaction problem in Kohn–Sham density functional theory. United States: N. p., 2014.
Web. doi:10.1016/j.jpcs.2014.05.014.
Däne, Markus, Gonis, A., Nicholson, Don M., & Stocks, George M. On a solution of the self-interaction problem in Kohn–Sham density functional theory. United States. https://doi.org/10.1016/j.jpcs.2014.05.014
Däne, Markus, Gonis, A., Nicholson, Don M., and Stocks, George M. Thu .
"On a solution of the self-interaction problem in Kohn–Sham density functional theory". United States. https://doi.org/10.1016/j.jpcs.2014.05.014. https://www.osti.gov/servlets/purl/1737473.
@article{osti_1737473,
title = {On a solution of the self-interaction problem in Kohn–Sham density functional theory},
author = {Däne, Markus and Gonis, A. and Nicholson, Don M. and Stocks, George M.},
abstractNote = {In this work, we report on a methodology for the treatment of the Coulomb energy and potential in Kohn–Sham density functional theory that is free from self-interaction effects. Specifically, we determine the Coulomb potential given as the functional derivative of the Coulomb energy with respect to the density, where the Coulomb energy is calculated explicitly in terms of the pair density of the Kohn–Sham orbitals. This is accomplished by taking advantage of an orthonormal and complete basis that is an explicit functional of the density that then allows for the functional differentiation of the pair density with respect to the density to be performed explicitly. This approach leads to a new formalism that provides an analytic, closed-form determination of the exchange potential. This method is applied to one-dimensional model systems and to the atoms Helium through Krypton based on an exchange only implementation. Comparison of our total energies (denoted SIF) to those obtained using the usual Hartree–Fock (HF) and optimized effective potential (OEP) methods reveals the hierarchy EHF≤EOEP≤ESIF that is indicative of the greater variation freedom implicit in the former two methods.},
doi = {10.1016/j.jpcs.2014.05.014},
journal = {Journal of Physics and Chemistry of Solids},
number = 10,
volume = 75,
place = {United States},
year = {Thu Jun 05 00:00:00 EDT 2014},
month = {Thu Jun 05 00:00:00 EDT 2014}
}
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Works referencing / citing this record:
Density-functional theory based on the electron distribution on the energy coordinate
journal, February 2018
- Takahashi, Hideaki
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 5
Density Functional Theory Based on the Electron Distribution on the Energy Coordinate
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- Takahashi, Hideaki
- arXiv