Category:GGA: Difference between revisions

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Theoretical Background

GGA exchange-correlation functionals depend on the electron density $n$ and its first derivative $\nabla n$ :

E_{\mathrm{xc}}^{\mathrm{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(n,\nabla n)d^{3}r

Among the various types of functionals, the GGAs, along with LDA, are the fastest to evaluate, therefore they are particularly useful for very large systems. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the electronic band structure like the band gap. The GGA that has been the most commonly used in solid-state physics is PBE^[1].

How to

A GGA can be used by specifying the tag GGA in the INCAR file.

↑ J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 77, 3865 (1996).

Pages in category "GGA"

The following 8 pages are in this category, out of 8 total.

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[perdew:prl:1996-1] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 77, 3865 (1996).

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 == Theoretical Background ==
-GGA exchange-correlation functionals depend on the electron density <math>\rho</math> and its first derivative <math>\nabla\rho</math>:
+GGA exchange-correlation functionals depend on the electron density <math>n</math> and its first derivative <math>\nabla n</math>:
-:<math>E_{\mathrm{xc}}^{\mathrm{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(\rho,\nabla\rho)d^{3}r</math>
+:<math>E_{\mathrm{xc}}^{\mathrm{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(n,\nabla n)d^{3}r</math>
 Among the various types of functionals, the GGAs, along with LDA, are the fastest to evaluate, therefore they are particularly useful for very large systems. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the electronic band structure like the band gap. The GGA that has been the most commonly used in solid-state physics is PBE{{cite|perdew:prl:1996}}.