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  Generalized Kohn–Sham iteration on Banach spaces

Laestadius, A., Penz, M., Tellgren, E. I., Ruggenthaler, M., Kvaal, S., & Helgaker, T. (2018). Generalized Kohn–Sham iteration on Banach spaces. The Journal of Chemical Physics, 149(16): 164103. doi:10.1063/1.5037790.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0002-46F5-B Version Permalink: https://hdl.handle.net/21.11116/0000-0004-9310-3
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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Chem. Phys. Vol. 149 Iss. 16 and may be found at https://aip.scitation.org/doi/10.1063/1.5037790.
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 Creators:
Laestadius, A.1, Author
Penz, M.2, Author           
Tellgren, E. I.1, Author
Ruggenthaler, M.2, Author           
Kvaal, S.1, Author
Helgaker, T.1, 3, 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              
3Centre for Advanced Study at the Norwegian Academy of Science and Letters, ou_persistent22              

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 Abstract: A detailed account of the Kohn-Sham algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows to rigorously introduce, in contrast to the common unregularized approach, a well-defined Kohn-Sham iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

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Language(s): eng - English
 Dates: 2018-04-272018-04-242018-04-272018-10-28
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: arXiv: 1804.08793
DOI: 10.1063/1.5037790
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Project name : We are very grateful toward an anonymous referee who not only highlighted some important mistakes in a draft of this work but also hinted us toward possible solution schemes. This work was supported by the Norwegian Research Coun- cil through the CoE Hylleraas Centre for Quantum Molecular Sciences Grant No. 262695. A.L. is grateful for the hospi- tality received at the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, while visiting M.P. and M.R. M.P. acknowledges support by the Erwin Schr ̈ odinger Fellowship No. J 4107-N27 of the FWF (Austrian Science Fund). A.L. and S.K. were supported by ERC-STG-2014 under Grant Agreement No. 639508. E.I.T. was supported by the Norwegian Research Council through Grant No. 240674. T.H. is grateful to the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, where parts of this work was carried out.
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Title: The Journal of Chemical Physics
  Other : J. Chem. Phys.
Source Genre: Journal
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Publ. Info: Woodbury, N.Y. : American Institute of Physics
Pages: - Volume / Issue: 149 (16) Sequence Number: 164103 Start / End Page: - Identifier: ISSN: 0021-9606
CoNE: https://pure.mpg.de/cone/journals/resource/954922836226