Local-density approximation: Difference between revisions

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The '''local-density approximation''', (LDA), is a [[density functional theory|density functional]] [[scientific modeling|model]] in [[physics]], which approximates the [[electron correlation]]exchange energy| withexchange respect]] to the ''local''and [[electron density]].correlation In this sense, ''local'' means that, within the LDA model, the electron| correlation at]] any(XC) pointenergy. in space is a function of the electron density at that point in space only.

The basic theorem of [[Density Functional Theory]] states that the energy of a system of electrons is a[[functional (mathematics) | 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 most simple approximation for this functional, it is ''local'' in the sense that the the electron exchange and correlation energy at any point of the space is a function of the electron density at that point in space only.

The LDA functional is derived from a model assuming 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. This model is sometimes known as the [[Jellium]] model.