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Numerical construction of the density-potential mapping
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Topical issue: Special issue in honor of Hardy Gross

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  • Published: 08 October 2018

Numerical construction of the density-potential mapping

  • Soeren E. B. Nielsen1,
  • Michael Ruggenthaler1 &
  • Robert van Leeuwen2 

The European Physical Journal B volume 91, Article number: 235 (2018) Cite this article

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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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Author information

Authors and Affiliations

  1. Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761, Hamburg, Germany

    Soeren E. B. Nielsen & Michael Ruggenthaler

  2. Department of Physics, Nanoscience Center, University of Jyväskylä, 40014, Jyväskylä, Finland

    Robert van Leeuwen

Authors
  1. Soeren E. B. Nielsen
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  2. Michael Ruggenthaler
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  3. Robert van Leeuwen
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Corresponding author

Correspondence to Soeren E. B. Nielsen.

Additional information

Contribution to the Topical Issue “Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.

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Open Access This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://doi.org/creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Nielsen, S.E.B., Ruggenthaler, M. & van Leeuwen, R. Numerical construction of the density-potential mapping. Eur. Phys. J. B 91, 235 (2018). https://doi.org/10.1140/epjb/e2018-90276-4

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  • Received: 23 April 2018

  • Revised: 07 July 2018

  • Published: 08 October 2018

  • DOI: https://doi.org/10.1140/epjb/e2018-90276-4

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