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Orbital Functionals in Static and Time-Dependent Density Functional Theory

  • Chapter
Book cover Electron Correlations and Materials Properties

Abstract

Density functional theory (DFT) is among the most powerful quantum mechanical methods for calculating the electronic structure of atoms, molecules and solids [1, 2, 3]. In this introduction we present a brief overview of DFT, putting particular emphasis on the appearance of orbital functionals. To describe the electronic many-body system, we have to deal with the Hamiltonian

$$ \hat H = \hat T + {\hat W_{C1b}} + \hat V$$
(1)

where

$$ \hat T = \sum\limits_{i = 1}^N {\left( { - \frac{{{h^2}}}{{2m}}\nabla _i^2} \right)}$$
(2)

denotes the kinetic-energy operator,

$$ {\hat W_{C1b}} = \frac{1}{2}\sum\limits_{\begin{array}{*{20}{c}} {i,j = 1} \\ {i \ne 1} \end{array}}^N {\frac{{{e^2}}}{{|{r_i} - {r_j}|}}} $$
(3)

represents the Coulomb interaction between the electrons, and

$$ \hat V = \sum\limits_{i = 1}^N {v({r_i})} $$
(4)

contains all external potentials acting on the electrons, typically the Coulomb potentials of the nuclei.

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  1. Institut für Theoretische Physik, Universität Würzburg, Am Hubland, Würzburg, D-97074, Germany

    E. K. U. Gross, T. Kreibich, M. Lein & M. Petersilka

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Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Livermore, California

    A. Gonis

  2. California State University—Northridge, Northridge, California

    N. Kioussis

  3. U.S. Army Research Office, Research Triangle Park, North Carolina, USA

    M. Ciftan

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Gross, E.K.U., Kreibich, T., Lein, M., Petersilka, M. (1999). Orbital Functionals in Static and Time-Dependent Density Functional Theory. In: Gonis, A., Kioussis, N., Ciftan, M. (eds) Electron Correlations and Materials Properties. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4715-0_24

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