Exchange-correlation Potential
The exchange-correlation potential corresponding to the exchange-correlation energy for a local density approximation is given by
In finite systems, the LDA potential decays asymptotically with an exponential form. This is in error; the true exchange-correlation potential decays much slower in a Coulombic manner. The artificially rapid decay manifests itself in the number of Kohn-Sham orbitals the potential can bind (that is, how many orbitals have energy less than zero). The LDA potential can not support a Rydberg series and those states it does bind are too high in energy. This results in the HOMO energy being too high in energy, so that any predictions for the ionization potential based on Koopman's theorem are poor. Further, the LDA provides a poor description of electron-rich species such as anions where it is often unable to bind an additional electron, erroneously predicating species to be unstable.
Read more about this topic: Local-density Approximation
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