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Title: On the v-representability of ensemble densities of electron systems

Abstract

Analogously to the case at zero temperature, where the density of the ground state of an interacting many-particle system determines uniquely (within an arbitrary additive constant) the external potential acting on the system, the thermal average of the density over an ensemble defined by the Boltzmann distribution at the minimum of the thermodynamic potential, or the free energy, determines the external potential uniquely (and not just modulo a constant) acting on a system described by this thermodynamic potential or free energy. The study describes a formal procedure that generates the domain of a constrained search over general ensembles (at zero or elevated temperatures) that lead to a given density, including as a special case a density thermally averaged at a given temperature, and in the case of a v-representable density determines the external potential leading to the ensemble density. As an immediate consequence of the general formalism, the concept of v-representability is extended beyond the hitherto discussed case of ground state densities to encompass excited states as well. Specific application to thermally averaged densities solves the v-representability problem in connection with the Mermin functional in a manner analogous to that in which this problem was recently settled with respect tomore » the Hohenberg and Kohn functional. Finally, the main formalism is illustrated with numerical results for ensembles of one-dimensional, non-interacting systems of particles under a harmonic potential.« less

Authors:
 [1];  [1]
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  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physical and Life Sciences
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1438681
Alternate Identifier(s):
OSTI ID: 1548883
Report Number(s):
LLNL-JRNL-731185
Journal ID: ISSN 0022-3697; TRN: US1900484
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Physics and Chemistry of Solids
Additional Journal Information:
Journal Volume: 116; Journal ID: ISSN 0022-3697
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; density functional theory; v-representability; excited states in DFT; ensemble v-representability; constrained search; constrained search for ensembles

Citation Formats

Gonis, A., and Dane, M. On the v-representability of ensemble densities of electron systems. United States: N. p., 2017. Web. doi:10.1016/j.jpcs.2017.12.032.
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Gonis, A., & Dane, M. On the v-representability of ensemble densities of electron systems. United States. https://doi.org/10.1016/j.jpcs.2017.12.032
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Gonis, A., and Dane, M. Sat . "On the v-representability of ensemble densities of electron systems". United States. https://doi.org/10.1016/j.jpcs.2017.12.032. https://www.osti.gov/servlets/purl/1438681.
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@article{osti_1438681,
title = {On the v-representability of ensemble densities of electron systems},
author = {Gonis, A. and Dane, M.},
abstractNote = {Analogously to the case at zero temperature, where the density of the ground state of an interacting many-particle system determines uniquely (within an arbitrary additive constant) the external potential acting on the system, the thermal average of the density over an ensemble defined by the Boltzmann distribution at the minimum of the thermodynamic potential, or the free energy, determines the external potential uniquely (and not just modulo a constant) acting on a system described by this thermodynamic potential or free energy. The study describes a formal procedure that generates the domain of a constrained search over general ensembles (at zero or elevated temperatures) that lead to a given density, including as a special case a density thermally averaged at a given temperature, and in the case of a v-representable density determines the external potential leading to the ensemble density. As an immediate consequence of the general formalism, the concept of v-representability is extended beyond the hitherto discussed case of ground state densities to encompass excited states as well. Specific application to thermally averaged densities solves the v-representability problem in connection with the Mermin functional in a manner analogous to that in which this problem was recently settled with respect to the Hohenberg and Kohn functional. Finally, the main formalism is illustrated with numerical results for ensembles of one-dimensional, non-interacting systems of particles under a harmonic potential.},
doi = {10.1016/j.jpcs.2017.12.032},
journal = {Journal of Physics and Chemistry of Solids},
number = ,
volume = 116,
place = {United States},
year = {Sat Dec 30 00:00:00 EST 2017},
month = {Sat Dec 30 00:00:00 EST 2017}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1016/j.jpcs.2017.12.032
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Figures / Tables:

Figure 1: Figure 1:: A two-density ensemble for a system under a harmonic potential as discussed in the text.
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Works referenced in this record:

Inhomogeneous Electron Gas
journal, November 1964

Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem
journal, February 2016

On the v-Representabilty Problem in Density Functional Theory: Application to Non-Interacting Systems
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Density functionals for coulomb systems
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  • Lieb, Elliott H.
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Hohenberg-Kohn theorem and non-V-representable densities
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Exact Density Functionals for Ground-State Energies II. Details and Remarks
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Density Functionals for the Energy of Electronic Systems: Explicit Variational Construction
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Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory
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On a solution of the self-interaction problem in Kohn–Sham density functional theory
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  • Däne, M.; Gonis, A.; Nicholson, D. M.
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New approach to the calculation of density functionals
journal, August 1983

Lack of Hohenberg-Kohn Theorem for Excited States
journal, October 2004

v -Representability and Density Functional Theory
journal, October 1983

Density functional approach to quantum lattice systems
journal, February 1985

  • Chayes, J. T.; Chayes, L.; Ruskai, Mary Beth
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Electron densities in search of Hamiltonians
journal, September 1982

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