The '''local-density approximation''', (LDA), is aan approximation of the [[densityExchange functional theoryinteraction|density functionalexchange]]-[[scientificElectron modelingcorrelation|modelcorrelation]] (XC) energy functional in [[physicsDensity functional theory|density functional theory]],whichby approximatesusing the [[electronXC exchangeenergy |of exchangean ]]electron andin a non-interacting homogeneous [[electron correlationgas |of correlationequivalent ]]density as the (XC) energy of an electron in the system being calculated.
The basicHohenberg-Kohn theorem of [[Density Functional Theory]] states that the energy of the [[stationaryStationary state|ground state]] of a system of electrons is a [[functionalFunctional (mathematics)|functional]] of the [[Electronic density|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 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 non-interacting homogeneous electron gas. This model is sometimes known as the [[Jellium|jellium]] model.
