skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1];  [2];  [1];  [3];  [4]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Florida, Gainesville, FL (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. 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}
}

Journal Article:

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share: