Local-density approximation: Difference between revisions

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'''Local-density approximations''' ('''LDA''') are a class of approximations to the [[Exchange interaction|exchange]]-[[Electron correlation|correlation]] (XC) energy [[Functional (mathematics)|functional]] in [[density functional theory]] (DFT) that depend solely upon the value of the [[electronic density]] at each point in space (and not, for example, derivatives of the density or the [[Kohn-Sham equations|Kohn-Sham orbitals]]). Many approaches can yield local approximations to the XC energy. OverwhelmingOverwhelmingly, however, successful local approximations are those that have been derived from the [[homogeneous electron gas]] (HEG) model. In this regard, LDA is generally synonymous with functionals based on the HEG approximation, which are then applied to realistic systems (molecules and solids).

In general, for a spin-unpolarized system, a local-density approximation for the exchange-correlation energy is written as