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Application of (Kohn–Sham) Density-Functional Theory to Real Materials

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Many-Electron Approaches in Physics, Chemistry and Mathematics

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Abstract

Hohenberg and Kohn proved the existence and uniqueness of a functional of the electron density, whose minimization yields the ground-state density \(n(r)\) of a bound system of \(N\) interacting electrons in some external potential \(v(r)\). The exact expression of the universal density functional is however elusive. In this chapter, I describe the several attempts made for designing an approximation to the density functional that gave accurate results for “real materials” (molecules, clusters, and extended materials). All discussed approximations originate from the Kohn–Sham approach, a particular (but almost universally adopted) formulation of the density-functional theory, in which the variational problem of the \(N\) interacting electrons is recast into a set of \(N\) one-particle equations where each electron acts in the mean field generated by all the other electrons.

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Notes

  1. 1.

    The dynamics of the nuclei is trated at positive temperature, whereas the electronic wavefunction is considered at or near its ground state. Inclusion of non-adiabatic effects, i.e., loosely speaking, electronic excited levels are treated in this book in the chap. “Time-Dependent Density Functional Theory” by Doltsinis. Since there is no widespread technique for beyond-BO MD, I do not mention further this class of methods.

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  1. Theory Department of Fritz-Haber-Institut, Faradayweg 4–6, 14195, Dahlem, Berlin, Germany

    Luca M. Ghiringhelli

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  1. Luca M. Ghiringhelli
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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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Ghiringhelli, L.M. (2014). Application of (Kohn–Sham) Density-Functional Theory to Real Materials. 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_10

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