On the v-representabilty problem in density functional theory: Application to non-interacting systems

Dane, Markus; Gonis, Antonios

doi:10.3390/computation4030024

Title: On the v-representabilty problem in density functional theory: Application to non-interacting systems

Abstract

Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.

Authors:

Dane, Markus ^[1]; Gonis, Antonios ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Tue Jul 05 00:00:00 EDT 2016

Research Org.:: Lawrence Livermore National Lab., Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1281663

Report Number(s):: LLNL-JRNL-694518
Journal ID: ISSN 2079-3197

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Computation

Additional Journal Information:: Journal Volume: 4; Journal Issue: 3; Journal ID: ISSN 2079-3197

Publisher:: MDPI

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; density functional theory; v-representability; constrained search

Citation Formats


                    Dane, Markus, and Gonis, Antonios. On the v-representabilty problem in density functional theory: Application to non-interacting systems.  United States: N. p., 2016. 
Web.  doi:10.3390/computation4030024.

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                    Dane, Markus, & Gonis, Antonios. On the v-representabilty problem in density functional theory: Application to non-interacting systems.  United States.  https://doi.org/10.3390/computation4030024

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                    Dane, Markus, and Gonis, Antonios. Tue .  
"On the v-representabilty problem in density functional theory: Application to non-interacting systems".  United States.  https://doi.org/10.3390/computation4030024.  https://www.osti.gov/servlets/purl/1281663.

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@article{osti_1281663,

  title        = {On the v-representabilty problem in density functional theory: Application to non-interacting systems},

  author       = {Dane, Markus and Gonis, Antonios},

  abstractNote = {Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.},

  doi          = {10.3390/computation4030024},

  journal      = {Computation},

  number       = 3,

  volume       = 4,

  place        = {United States},

  year         = {Tue Jul 05 00:00:00 EDT 2016},

  month        = {Tue Jul 05 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Reformulation of density functional theory for N-representable densities and the resolution of the v-representability problem
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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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Solving the self-interaction problem in Kohn–Sham density functional theory: Application to atoms
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Däne, M.; Gonis, A.; Nicholson, D. M.
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Similar Records

Title: On the v-representabilty problem in density functional theory: Application to non-interacting systems

Abstract

Citation Formats

Inhomogeneous Electron Gas journal, November 1964

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal, December 1979

Electron densities in search of Hamiltonians journal, September 1982

v -Representability and Density Functional Theory journal, October 1983

Hohenberg-Kohn theorem and non-V-representable densities journal, August 1983

v -representability for noninteracting systems journal, January 1993

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

Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory journal, May 2012

On a solution of the self-interaction problem in Kohn–Sham density functional theory journal, October 2014

Solving the self-interaction problem in Kohn–Sham density functional theory: Application to atoms journal, April 2015

Density Functionals for the Energy of Electronic Systems: Explicit Variational Construction journal, May 1988

Density driven self-consistent field method. II. construction of all one-particle wavefunctions that are orthonormal and sum up to a given density journal, April 1989

Zur wellenmechanischen Behandlung von Vielkörperproblemen journal, January 1955

Orthonormal orbitals for the representation of an arbitrary density journal, August 1981

New approach to the calculation of density functionals journal, August 1983

Inhomogeneous Electron Gas
journal, November 1964

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem
journal, December 1979

Electron densities in search of Hamiltonians
journal, September 1982

$v$ -Representability and Density Functional Theory
journal, October 1983

Hohenberg-Kohn theorem and non-V-representable densities
journal, August 1983

v -representability for noninteracting systems
journal, January 1993

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

Computationally simple, analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory
journal, May 2012

On a solution of the self-interaction problem in Kohn–Sham density functional theory
journal, October 2014

Solving the self-interaction problem in Kohn–Sham density functional theory: Application to atoms
journal, April 2015

Density Functionals for the Energy of Electronic Systems: Explicit Variational Construction
journal, May 1988

Density driven self-consistent field method. II. construction of all one-particle wavefunctions that are orthonormal and sum up to a given density
journal, April 1989

Zur wellenmechanischen Behandlung von Vielkörperproblemen
journal, January 1955

Orthonormal orbitals for the representation of an arbitrary density
journal, August 1981

New approach to the calculation of density functionals
journal, August 1983