Local-density approximation: Difference between revisions

Revision as of 21:35, 26 July 2008

Revision as of 00:16, 24 September 2008

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LDA is the simplest approximation for this functional, it is ''local'' in the sense that the electron exchange and correlation energy at any point in space is a function of the electron density at that point only.<ref>{{cite journal | author = John R. Smith | title = Beyond the Local-Density Approximation: Surface Properties of (110) W | journal = Phys. Rev. Lett. | volume = 25 | issue = 15 | pages = 1023–1026 | year = 1970 | url = http://link.aps.org/abstract/PRL/v25/p1023 | doi = 10.1103/PhysRevLett.25.1023 | format = abstract}}</ref>

The XC correlationenergy functional is the sum of a correlation functional and an exchange functional<ref name=kohn-sham />

:<math>E_{xc} = E_x + E_c \,\;</math>

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:<math>E_x = \int d^3r \, n(\vec{r}) \left( {{-3e^2}\over{4\pi}} \right) \left(3 \pi^2 n(\vec{r})\right)^{1 \over 3}</math>

in [[International System of Units|SI units]] where <math>n(\vec{r})</math> is the electron density per unit volume at the point <math>\vec{r} \,\;</math>and <math>e\,\;</math> is the charge of an electron.<ref>{{cite journal | title = Nonempirical Construction of Current-CensityDensity Functionals from Conventional Density-Functional Approximations | author = Jianmin Tao and John P. Perdew | journal = Phys. Rev. Lett. | volume = 95 | pages = 196403 | year = 2005 | url = http://link.aps.org/abstract/PRL/v95/p196403 | doi = 10.1103/PhysRevLett.95.196403 | format = abstract }}</ref>

== Correlation ==