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  Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability

Laestadius, A., Tellgren, E. I., Penz, M., Ruggenthaler, M., Kvaal, S., & Helgaker, T. (2019). Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability. Journal of Chemical Theory and Computation, 15(7), 4003-4020. doi:10.1021/acs.jctc.9b00141.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-693B-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-F319-E
Genre: Journal Article

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https://arxiv.org/abs/1902.09086 (Preprint)
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https://dx.doi.org/10.1021/acs.jctc.9b00141 (Publisher version)
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 Creators:
Laestadius, A.1, Author
Tellgren, E. I.1, Author
Penz, M.2, Author              
Ruggenthaler, M.2, Author              
Kvaal, S.1, Author
Helgaker, T.1, Author
Affiliations:
1Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, ou_persistent22              
2Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              

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 Abstract: Recent work has established Moreau–Yosida regularization as a mathematical tool to achieve rigorous functional differentiability in density-functional theory. In this article, we extend this tool to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects. The extension includes a well-defined Kohn–Sham iteration scheme with a partial convergence result. To this end, we rely on a formulation of Moreau–Yosida regularization for reflexive and strictly convex function spaces. The optimal Lp-characterization of the paramagnetic current density L1 ∩ L3/2 is derived from the N-representability conditions. A crucial prerequisite for the convex formulation of paramagnetic current-density-functional theory, termed compatibility between function spaces for the particle density and the current density, is pointed out and analyzed. Several results about compatible function spaces are given, including their recursive construction. The regularized, exact functionals are calculated numerically for a Kohn–Sham iteration on a quantum ring, illustrating their performance for different regularization parameters.

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Language(s): eng - English
 Dates: 2019-02-182019-05-072019-07-09
 Publication Status: Published in print
 Pages: 18
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 Rev. Method: Peer
 Identifiers: DOI: 10.1021/acs.jctc.9b00141
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Project name : This work was supported by the Norwegian Research Council through the CoE Hylleraas Centre for Quantum Molecular Sciences Grant No. 262695. AL is grateful for the hospitality received at the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, while visiting MP and MR. MP acknowledges support by the Erwin Schrödinger Fellowship J 4107-N27 of the FWF (Austrian Science Fund) and is thankful for an invitation to the Hylleraas Centre just taking place while writing this. AL and SK were supported by ERC-STG-2014 under grant agreement No. 639508. EIT was supported by the Norwegian Research Council through Grant No. 240674.
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Title: Journal of Chemical Theory and Computation
  Other : J. Chem. Theory Comput.
Source Genre: Journal
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Publ. Info: Washington, D.C. : American Chemical Society
Pages: - Volume / Issue: 15 (7) Sequence Number: - Start / End Page: 4003 - 4020 Identifier: ISSN: 1549-9618
CoNE: https://pure.mpg.de/cone/journals/resource/111088195283832