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  Propagators for the Time-Dependent Kohn–Sham Equations: Multistep, Runge–Kutta, Exponential Runge–Kutta, and Commutator Free Magnus Methods

Pueyo, A. G., Marques, M. A. L., Rubio, A., & Castro, A. (2018). Propagators for the Time-Dependent Kohn–Sham Equations: Multistep, Runge–Kutta, Exponential Runge–Kutta, and Commutator Free Magnus Methods. Journal of Chemical Theory and Computation, 14(6), 3040-3052. doi:10.1021/acs.jctc.8b00197.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0001-AA05-A Version Permalink: http://hdl.handle.net/21.11116/0000-0003-A4CD-D
Genre: Journal Article

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acs.jctc.8b00197.pdf (Publisher version), 2MB
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This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.
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2018
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© American Chemical Society

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https://dx.doi.org/10.1021/acs.jctc.8b00197 (Publisher version)
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 Creators:
Pueyo, A. G.1, Author
Marques, M. A. L.2, Author
Rubio, A.3, 4, 5, 6, Author              
Castro, A.1, 7, Author
Affiliations:
1Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, ou_persistent22              
2Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, ou_persistent22              
3Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
4Center for Free-Electron Laser Science, ou_persistent22              
5Center for Computational Quantum Physics (CCQ), The Flatiron Institute, ou_persistent22              
6Nano-Bio Spectroscopy Group, Universidad del País Vasco, ou_persistent22              
7ARAID Foundation, Spain, ou_persistent22              

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 Abstract: We examine various integration schemes for the time-dependent Kohn–Sham equations. Contrary to the time-dependent Schrödinger’s equation, this set of equations is nonlinear, due to the dependence of the Hamiltonian on the electronic density. We discuss some of their exact properties, and in particular their symplectic structure. Four different families of propagators are considered, specifically the linear multistep, Runge–Kutta, exponential Runge–Kutta, and the commutator-free Magnus schemes. These have been chosen because they have been largely ignored in the past for time-dependent electronic structure calculations. The performance is analyzed in terms of cost-versus-accuracy. The clear winner, in terms of robustness, simplicity, and efficiency is a simplified version of a fourth-order commutator-free Magnus integrator. However, in some specific cases, other propagators, such as some implicit versions of the multistep methods, may be useful.

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Language(s): eng - English
 Dates: 2018-02-232018-04-192018-06
 Publication Status: Published in print
 Pages: 13
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1021/acs.jctc.8b00197
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Project name : We acknowledge support from Ministerio de Economía y Competitividad (MINECO) grants FIS2013-46159-C3-2-P, FIS2014-61301-EXP, and FIS2017-82426-P, from the European Research Council (ERC-2015-AdG-694097), from Grupos Consolidados (IT578-13), from the European Union Horizon 2020 program under Grant Agreement 676580 (NOMAD), from the Salvador de Madariaga mobility grant PRX16/00436, and from the DFG Project B09 of TRR 227.
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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: 14 (6) Sequence Number: - Start / End Page: 3040 - 3052 Identifier: Other: 1549-9618
CoNE: /journals/resource/111088195283832