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Time-Dependent Density Functional Theory

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A Primer in Density Functional Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 620))

Abstract

Time-dependent density-functional theory (TDDFT) extends the basic ideas of ground-state density-functional theory (DFT) to the treatment of excitations and of more general time-dependent phenomena. TDDFT can be viewed as an alternative formulation of time-dependent quantum mechanics but, in contrast to the normal approach that relies on wave-functions and on the many-body Schrödinger equation, its basic variable is the one-body electron density, n(r, t). The advantages are clear: The many-body wave-function, a function in a 3N-dimensional space (where N is the number of electrons in the system), is a very complex mathematical object, while the density is a simple function that depends solely on the 3-dimensional vector r. The standard way to obtain n(r, t) is with the help of a fictitious system of noninteracting electrons, the Kohn-Sham system. The final equations are simple to tackle numerically, and are routinely solved for systems with a large number of atoms. These electrons feel an effective potential, the time-dependent Kohn-Sham potential. The exact form of this potential is unknown, and has therefore to be approximated.

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Authors and Affiliations

  1. Donostia International Physics Center (DIPC), P. Manuel Lardizábal 4, 20080, San Sebastián, Spain

    Miguel A. L. Marques

  2. Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany

    Eberhard K. U. Gross

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  1. Miguel A. L. Marques
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  1. Departamento de Física, Universidade de Coimbra, Rua Larga, 3004 — 516, Coimbra, Portugal

    Carlos Fiolhais  & Fernando Nogueira  & 

  2. Donostia International Physics Center (DIPC), P. Manuel Lardizábal 4, 20080, San Sebastián, Spain

    Miguel A. L. Marques

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Marques, M.A.L., Gross, E.K.U. (2003). Time-Dependent Density Functional Theory. In: Fiolhais, C., Nogueira, F., Marques, M.A.L. (eds) A Primer in Density Functional Theory. Lecture Notes in Physics, vol 620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37072-2_4

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  • DOI: https://doi.org/10.1007/3-540-37072-2_4

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