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Exchange-Correlation Functionals

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Many-Body Approach to Electronic Excitations

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 181))

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Abstract

Crucial for the application of the density functional theory in the framework of the Kohn-Sham ansatz is the knowledge of the exchange-correlation functional, which usually is formulated in terms of a density- and space-dependent exchange-correlation energy per particle. Such a formulation immediately leads to an explicit expression by replacing the density dependence calculated numerically for a homogeneous electron gas by the dependence on the local density of the inhomogenous electron gas. This is the local density approximation (LDA). Generalizations for spin-polarized systems to a local spin density approximation are obvious. Improvements of the local approximation for exchange and correlation include density gradients. A generalized gradient approximation (GGA) has to fulfill the sum rules. Nevertheless, many different functionals can be formulated, e.g. PW91, PBE, AM05, PBEsol, etc. Explicit formulas for some widely used functionals are given. Their applicability and accuracy are discussed and shown, respectively, for test quantities such as lattice constants, bulk moduli, and binding energies.

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  1. Department of Physics and Astronomy, Friedrich-Schiller University, Jena, Germany

    Friedhelm Bechstedt

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  1. Friedhelm Bechstedt
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Bechstedt, F. (2015). Exchange-Correlation Functionals. In: Many-Body Approach to Electronic Excitations. Springer Series in Solid-State Sciences, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44593-8_7

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  • DOI: https://doi.org/10.1007/978-3-662-44593-8_7

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