The exchange-correlation term

An approximation to the exchange-correlation term is used. It is called the Local Density Approximation (LDA). For any small region, the exchange-correlation energy is the approximated by that for jellium of the same electron density. In other words, the exchange-correlation hole that is modelled is not the exact one - it is replaced by the hole taken from an electron gas whose density is the same as the local density around the electron.

The interesting point about this approximation is that although the exchange-correlation hole may not be represented well in terms of its shape, the overall effective charge is modelled exactly. This means that the attractive potential which the electron feels at its centre is well described.

Not only does the LDA approximation work for materials with slowly varying or homogeneous electron densities but in practise demonstrates surprisingly accurate results for a wide range of ionic, covalent and metallic materials.

An alternative, slightly more sophisticated approximation is the Generalised Gradient Approximation (GGA) which estimate the contribution of each volume element to the exchange-correlation based upon the magnitude and gradient of the electron density within that element.

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