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The local-density approximation (LDA) is an approximation of the exchange-correlation (XC) energy functional in density functional theory (DFT) by taking the XC energy of an electron in a non-interacting homogeneous electron gas of a density equivalent to the density at the electron in the system being calculated. This approximation was applied to DFT by Kohn and Sham in an early paper.
Additional recommended knowledge
The Hohenberg-Kohn theorem states that the energy of the ground state of a system of electrons is a functional of the electronic density, in particular the exchange and correlation energy is also a functional of the density (this energy can be seen as the quantum part of the electron-electron interaction). This XC functional is not known exactly and must be approximated.
LDA is the simplest approximation for this functional, it is local in the sense that the electron exchange and correlation energy at any point in space is a function of the electron density at that point only.
The LDA functional assumes that the per-electron exchange-correlation energy at every point in space is equal to the per-electron exchange-correlation energy of a homogeneous electron gas.
The XC correlation functional is the sum of a correlation functional and an exchange functional
LDA uses the exchange for the uniform electron gas of a density equal to the density at the point where the exchange is to be evaluated,
There are several forms of correlation:
Wigner correlation is gotten by using equally spaced electrons and applying perturbation theory.
LYP is based on data fit to the helium atom.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Local-density_approximation". A list of authors is available in Wikipedia.|