A recently proposed variation principle [N. I. Gidopoulos, Phys. Rev. A 83, 040502(R) (2011)] for the determination of Kohn–Sham effective potentials is examined and extended to arbitrary electron-interaction strengths and to mixed states. Comparisons are drawn with Lieb’s convex-conjugate functional, which allows for the determination of a potential associated with a given electron density by maximization, yielding the Kohn–Sham potential for a non-interacting system. The mathematical structure of the two functionals is shown to be intrinsically related; the variation principle put forward by Gidopoulos may be expressed in terms of the Lieb functional. The equivalence between the information obtained from the two approaches is illustrated numerically by their implementation in a common framework.
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7 October 2017
Research Article|
October 03 2017
Connections between variation principles at the interface of wave-function and density-functional theories
Special Collection:
JCP Editors' Choice 2017
Tom J. P. Irons
;
Tom J. P. Irons
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
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James W. Furness
;
James W. Furness
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
2
Department of Physics and Engineering Physics, Tulane University
, New Orleans, Louisiana 70118, USA
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Matthew S. Ryley;
Matthew S. Ryley
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
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Jan Zemen
;
Jan Zemen
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
3
Institute of Physics, Academy of Sciences of the Czech Republic
, Na Slovance 1999/2, CZ-182 21 Prague, Czech Republic
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Trygve Helgaker
;
Trygve Helgaker
4
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
5
Centre for Advanced Study at the Norwegian Academy of Science and Letters
, Drammensveien 78, N-0271 Oslo, Norway
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Andrew M. Teale
Andrew M. Teale
a)
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
4
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
5
Centre for Advanced Study at the Norwegian Academy of Science and Letters
, Drammensveien 78, N-0271 Oslo, Norway
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Tom J. P. Irons
1
James W. Furness
1,2
Matthew S. Ryley
1
Jan Zemen
1,3
Trygve Helgaker
4,5
Andrew M. Teale
1,4,5,a)
1
School of Chemistry, University of Nottingham
, University Park, Nottingham NG7 2RD, United Kingdom
2
Department of Physics and Engineering Physics, Tulane University
, New Orleans, Louisiana 70118, USA
3
Institute of Physics, Academy of Sciences of the Czech Republic
, Na Slovance 1999/2, CZ-182 21 Prague, Czech Republic
4
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo
, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
5
Centre for Advanced Study at the Norwegian Academy of Science and Letters
, Drammensveien 78, N-0271 Oslo, Norway
a)
Electronic mail: [email protected]
J. Chem. Phys. 147, 134107 (2017)
Article history
Received:
May 31 2017
Accepted:
September 16 2017
Citation
Tom J. P. Irons, James W. Furness, Matthew S. Ryley, Jan Zemen, Trygve Helgaker, Andrew M. Teale; Connections between variation principles at the interface of wave-function and density-functional theories. J. Chem. Phys. 7 October 2017; 147 (13): 134107. https://doi.org/10.1063/1.4985883
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