Local density approximation

The local density approximation (LDA) is a method in the context of density functional theory . It approximates the exchange - correlation energy ("x" for English e x change , "c" for correlation ) of a material with (weakly) varying charge density by that of the uniform electron gas with the same charge density. In this case the following can be written as a pure functional of the electron density : ${\displaystyle E_{\text{xc}}}$ ${\displaystyle E_{\text{xc}}}$

${\displaystyle E_{\text{xc}}=\int n({\vec {r}})\varepsilon _{\text{xc}}(n({\vec {r}}))d{\vec {r}}}$

The term denotes the charge density at the point and is the exchange correlation term of the homogeneous electron gas that has to be found to solve the problem. ${\displaystyle n({\vec {r}})}$ ${\displaystyle {\vec {r}}}$ ${\displaystyle \varepsilon _{\text{xc}}(n({\vec {r}}))}$

Although this is a fairly simple approximation, it turns out to be very reliable and accurate in use and forms the core of most calculations in density functional theory (DFT). It works surprisingly well even in systems with widely varying densities.

Overall, the LDA tends to output binding energies a little too high, while the ground state energies of atoms come out a little too low. Attempts to compensate for this by a gradient term for the density in order to capture local density fluctuations are known as GGA ( generalized gradient approximation ). GGA increases the computational effort, but does not lead to improvements in accuracy in all cases.

An alternative method is the "Weighted Density Approximation".