Local-density approximation

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The local-density approximation (LDA) is an approximation of the exchange-correlation (XC) energy functional in density functional theory by using the XC energy of an electron in a non-interacting homogeneous electron gas of equivalent density as the XC energy of an electron in the system being calculated.

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.