We derive and analyze a hierarchy of approximations to the strongly correlated limit of the Hohenberg-Kohn functional. These “density representability approximations” are obtained by first noting that in the strongly correlated limit, N-representability of the pair density reduces to the requirement that the pair density must come from a symmetric N-point density. One then relaxes this requirement to the existence of a representing symmetric k-point density with k < N. The approximate energy can be computed by simulating a fictitious k-electron system. We investigate the approximations by deriving analytically exact results for a 2-site model problem, and by incorporating them into a self-consistent Kohn-Sham calculation for small atoms. We find that the low order representability conditions already capture the main part of the correlations.
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28 October 2013
Research Article|
October 23 2013
N-density representability and the optimal transport limit of the Hohenberg-Kohn functional
Gero Friesecke;
Gero Friesecke
1Mathematics Department,
Technische Universität München
, Garching bei München, Garching, 85748, Germany
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Christian B. Mendl;
Christian B. Mendl
1Mathematics Department,
Technische Universität München
, Garching bei München, Garching, 85748, Germany
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Brendan Pass;
Brendan Pass
2Department of Mathematical and Statistical Sciences,
University of Alberta
, Canada
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Codina Cotar;
Codina Cotar
3Department of Statistical Science,
University College London
, London, United Kingdom
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Claudia Klüppelberg
Claudia Klüppelberg
1Mathematics Department,
Technische Universität München
, Garching bei München, Garching, 85748, Germany
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J. Chem. Phys. 139, 164109 (2013)
Article history
Received:
March 28 2013
Accepted:
September 02 2013
Citation
Gero Friesecke, Christian B. Mendl, Brendan Pass, Codina Cotar, Claudia Klüppelberg; N-density representability and the optimal transport limit of the Hohenberg-Kohn functional. J. Chem. Phys. 28 October 2013; 139 (16): 164109. https://doi.org/10.1063/1.4821351
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