Local-density approximation

The local density approximation (LDA ) is a method in the framework of density functional theory. She approaches the exchange-correlation energy ( "x " for English exchange, "c" for correlation ) of a material with (slightly ) varying charge density by the uniform electron gas with the same charge density. In this case can be written as a pure functional electron density:

The charge density at the designated point and the exchange - correlation term of homogeneous electron gas which has to be found to solve the problem.

Although this is a fairly simple approximation, it arises in the application as a very reliable and accurate out and forms the core of most calculations in the density functional theory ( DFT). Even in systems with strongly varying density it still works surprisingly well.

Overall, the LDA tends a little too much to spend binding energies, while the ground state energy of atoms come out a little too low. Attempts to compensate for this by a gradient term of the density to capture local density variations are as GGA ( engl. generalized gradient approximation ) is known. GGA increases the computational complexity, but not in all cases lead to improvements in accuracy.

An alternative method is the "Weighted Density Approximation " dar.

• Statistical Physics