Local-density approximation: Difference between revisions

Revision as of 15:31, 3 March 2022

Revision as of 15:32, 3 March 2022

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:<math>v_{xc}^{\mathrm{LDA}}(\mathbf{r}) = \frac{\delta E^{\mathrm{LDA}}}{\delta\rho(\mathbf{r})} = \epsilon_{xc}(\rho(\mathbf{r})) + \rho(\mathbf{r})\frac{\partial \epsilon_{xc}(\rho(\mathbf{r}))}{\partial\rho(\mathbf{r})}\ .</math>

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 [[Koopmans' theorem]] are poor. Further, the LDA provides a poor description of electron-rich species such as [[anion]]s where it is often unable to bind an additional electron, erroneously predicating species to be unstable.<ref name="pz81"/><ref>{{cite book|last=Fiolhais|first=Carlos|author2=Nogueira, Fernando |author3=Marques Miguel |title=A Primer in Density Functional Theory|publisher=Springer|year=2003|isbn=978-3-540-03083-6|page=60}}</ref>

== References ==