Category:GGA: Difference between revisions

Latest revision as of 18:26, 9 April 2022

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

while LDA functionals depend only on $n$ . 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 GGA tag in the INCAR file. Note that the GGA tag is also used to specify a LDA functional.

↑ 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).

[1]

@@ Line 1: / Line 1: @@
-== Theoretical Background ==
+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}}(n,\nabla n)d^{3}r</math>
+while LDA functionals depend only on <math>n</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}}.
-GGA exchange-correlation functionals depend on the electron density <math>\rho</math> and its first derivative <math>\nabla\rho</math>:
+== How to ==
-:<math>E_{\mathrm{xc}}^{\mathrm{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(\rho,\nabla\rho)d^{3}r</math>
-The GGA functionals lead to fast calculations,
+A GGA can be used by specifying the {{TAG|GGA}} tag in the {{FILE|INCAR}} file. Note that the {{TAG|GGA}} tag is also used to specify a LDA functional.
-== How to ==
 ----
+[[Category:VASP|XC Functionals]][[Category:Exchange-correlation functionals]]
-[[Category:VASP|XC Functionals]][[Category:XC Functionals]]