Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem
Abstract
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Furthermore, some direct formal and practical implications of the present reformulation of DFT are also discussed.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Univ. of Florida, Gainesville, FL (United States)
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Univ. of North Carolina Asheville, Asheville, NC (United States)
- Publication Date:
- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Defect Physics in Structural Materials (CDP); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences (CNMS); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1267027
- Alternate Identifier(s):
- OSTI ID: 1241937; OSTI ID: 1396527
- Report Number(s):
- LLNL-JRNL-668265
Journal ID: ISSN 0022-3697; KC0202030; ERKCS92
- Grant/Contract Number:
- AC05-00OR22725; AC52-07NA27344
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Journal of Physics and Chemistry of Solids
- Additional Journal Information:
- Journal Volume: 89; Journal ID: ISSN 0022-3697
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; ab initio calculations; electronic structure; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; v-representability; density functional theory; functional derivative; constrained search
Citation Formats
Gonis, A., Zhang, X. -G., Dane, Markus, Stocks, George Malcolm, and Nicholson, Don M. Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem. United States: N. p., 2015.
Web. doi:10.1016/j.jpcs.2015.10.006.
Gonis, A., Zhang, X. -G., Dane, Markus, Stocks, George Malcolm, & Nicholson, Don M. Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem. United States. https://doi.org/10.1016/j.jpcs.2015.10.006
Gonis, A., Zhang, X. -G., Dane, Markus, Stocks, George Malcolm, and Nicholson, Don M. 2015.
"Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem". United States. https://doi.org/10.1016/j.jpcs.2015.10.006. https://www.osti.gov/servlets/purl/1267027.
@article{osti_1267027,
title = {Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem},
author = {Gonis, A. and Zhang, X. -G. and Dane, Markus and Stocks, George Malcolm and Nicholson, Don M.},
abstractNote = {Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide proof of existence of a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism. Numerical results for one-dimensional non-interacting systems illustrate the formalism. Furthermore, some direct formal and practical implications of the present reformulation of DFT are also discussed.},
doi = {10.1016/j.jpcs.2015.10.006},
url = {https://www.osti.gov/biblio/1267027},
journal = {Journal of Physics and Chemistry of Solids},
issn = {0022-3697},
number = ,
volume = 89,
place = {United States},
year = {Fri Oct 23 00:00:00 EDT 2015},
month = {Fri Oct 23 00:00:00 EDT 2015}
}
Web of Science