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Progress on New Approaches to Old Ideas: Orbital-Free Density Functionals

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Many-Electron Approaches in Physics, Chemistry and Mathematics

Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

State-of-the-art treatment of nuclei and electrons in materials uses ab initio molecular dynamics for nuclear motion driven by Born-Oppenheimer forces from the electrons. Almost universally, those forces are calculated from density functional theory in the Kohn–Sham form. The computational costs of the conventional KS implementation scale at least as the cube of the number of electrons. This is a formidable barrier to complex system simulations with long MD runs on department-scale machines, since the DFT force calculation dominates the per step cost. The difficulty arises from the explicit dependence of the non-interacting kinetic energy on the KS non-interacting orbitals. The cost scaling worsens with use of explicitly orbital-dependent exchange-correlation functionals. The alternative approach, use of DFT in its basic form, dates to Thomas-Fermi-Dirac theory. The challenge is to have sufficiently accurate orbital-free expressions for the KS kinetic energy and exchange-correlation functionals. We discuss progress on these tasks via constraint-based methods, with emphasis on developments since the Sept. 2010 “New Approaches to Many-Electron Theory” meeting.

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Acknowledgments

We acknowledge, with thanks, the many contributions and influences especially of Travis Sjostrom and of our other primary collaborators, Jim Dufty, Frank Harris, Keith Runge, Alberto Vela, Jose Luis Gázquez, and Jorge Martín del Campo. Thanks also go to Emilio Orgaz, Victor Medel, Támas Gál, and J.C. Pacheco-Kato. Helpful conversations with P. Ayers, K. Burke, K. Capelle, E.A. Carter, L. Delle Site, D. Gárcia-Aldea, A. Görling, M. Levy, M.M. Odashima, J.P. Perdew, N. Rösch, A. Ruzsinszky, and T. Wesolowski are acknowledged with thanks. We thank Luigi Delle Site and Volker Bach for the opportunity to participate in this volume and for the opportunity provided to SBT to attend the NAMET meeting in 2010. This work was supported under U.S. Dept. of Energy BES grant DE-SC 0002139.

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  1. Quantum Theory Project, Departments of Physics and of Chemistry, University of Florida, PO Box 118435, Gainesville, FL, 32611-8435, USA

    Valentin V. Karasiev, Debajit Chakraborty & S. B. Trickey

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  1. Institut für Analysis Und Algebra Carl-Friedrich-Gauss-Fakultät, Technische Universität Braunschweig, Braunschweig, Germany

    Volker Bach

  2. Institute for Mathematics, Freie Universität Berlin, Berlin, Germany

    Luigi Delle Site

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Karasiev, V.V., Chakraborty, D., Trickey, S.B. (2014). Progress on New Approaches to Old Ideas: Orbital-Free Density Functionals. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_6

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