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  Numerical construction of the density-potential mapping

Nielsen, S. E. B., Ruggenthaler, M., & van Leeuwen, R. (2018). Numerical construction of the density-potential mapping. European Physical Journal B, 91(10): 235. doi:10.1140/epjb/e2018-90276-4.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-5E5A-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-5E5B-0
Genre: Journal Article

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Nielsen2018_Article_NumericalConstructionOfTheDens.pdf (Publisher version), 3MB
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Nielsen2018_Article_NumericalConstructionOfTheDens.pdf
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This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Open access funding provided by Max Planck Society.
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2018
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https://dx.doi.org/10.1140/epjb/e2018-90276-4 (Publisher version)
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 Creators:
Nielsen, S. E. B.1, 2, Author              
Ruggenthaler, M.1, 2, Author              
van Leeuwen, R.3, Author
Affiliations:
1Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
2Center for Free-Electron Laser Science, ou_persistent22              
3Department of Physics, Nanoscience Center, University of Jyväskylä, ou_persistent22              

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 Abstract: We demonstrate how a recently developed method Nielsen et al. [Nielsen et al., EPL 101, 33001 (2013)] allows for a comprehensive investigation of time-dependent density functionals in general, and of the exact time-dependent exchange-correlation potential in particular, by presenting the first exact results for two- and three-dimensional multi-electron systems. This method is an explicit realization of the Runge–Gross correspondence, which maps time-dependent densities to their respective potentials, and allows for the exact construction of desired density functionals. We present in detail the numerical requirements that makes this method efficient, stable and precise even for large and rapid density changes, irrespective of the initial state and two-body interaction. This includes among others the proper treatment of low density regions, a subtle interplay between numerical time-propagation and zero boundary conditions, the choice of time-stepping strategy, and an error damping mechanism based on both the density and current density residuals. These considerations are also relevant for computing time-independent density-functionals and lead to a more precise implementation of quantum mechanics in general, which is mainly relevant for cases in which there is notable contact with a boundary or when the low density regions matter.

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Language(s): eng - English
 Dates: 2018-04-232018-07-072018-10-082018-10
 Publication Status: Published in print
 Pages: -
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 Rev. Method: Peer
 Identifiers: DOI: 10.1140/epjb/e2018-90276-4
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Project name : Open access funding provided by Max Planck Society. S.E.B. Nielsen and M. Ruggenthaler acknowledge financial support from the European Research Council (ERC-2015-AdG-694097) and European Union’s H2020 programme under GA no. 676580 (NOMAD). We thank Dr. B. Ebner for computational support. We further thank Prof. Dr. A. Rubio for his support.
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Title: European Physical Journal B
  Other : Eur. Phys. J. B
Source Genre: Journal
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 91 (10) Sequence Number: 235 Start / End Page: - Identifier: ISSN: 1434-6028
CoNE: https://pure.mpg.de/cone/journals/resource/954927001233