Category:Meta-GGA: Difference between revisions

Latest revision as of 11:39, 20 May 2022

Meta-GGA exchange-correlation functionals depend on the electron density $n$ , its first derivative $\nabla n$ and the kinetic-energy density $\tau$ :

E_{\mathrm {xc} }^{\mathrm {meta-GGA} }=\int \epsilon _{\mathrm {xc} }^{\mathrm {meta-GGA} }(n,\nabla n,\tau )d^{3}r

Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropriate for very large systems. Furthermore, meta-GGAs can be more accurate than GGAs and more broadly applicable. Note that as in most other codes, meta-GGAs are implemented in VASP within the generalized KS scheme^[1]. The meta-GGA that is currently the most widely used in solid-state physics is SCAN^[2]. The meta-GGA functionals using the Laplacian of the electron density, $\nabla ^{2}n$ , are not yet available in VASP.

How to

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

How to do a Band-structure calculation using meta-GGA functionals.

Pages in category "Meta-GGA"

The following 18 pages are in this category, out of 18 total.

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Band-structure calculation using meta-GGA functionals

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-== Theoretical Background ==
+Meta-GGA exchange-correlation functionals depend on the electron density <math>n</math>, its first derivative <math>\nabla n</math> and the kinetic-energy density <math>\tau</math>:
+:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(n,\nabla n,\tau)d^{3}r</math>
+Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropriate for very large systems. Furthermore, meta-GGAs can be more accurate than GGAs and more broadly applicable. Note that as in most other codes, meta-GGAs are implemented in VASP within the generalized KS scheme{{cite|yang:prb:2016|}}. The meta-GGA that is currently the most widely used in solid-state physics is SCAN{{cite|sun:prl:15|}}. The meta-GGA functionals using the Laplacian of the electron density, <math>\nabla^{2}n</math>, are not yet available in VASP.
-Meta-GGA exchange-correlation functionals depend on the electron density <math>\rho</math>, its first derivative <math>\nabla\rho</math> and on the kinetic-energy density <math>\tau</math>:
+== How to ==
-:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{metaGGA}}(\rho,\nabla\rho,\tau)d^{3}r</math>
-Among the various types of functionals, the GGAs are the fastest to evaluate and therefore 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}}.
-== How to ==
+A meta-GGA can be used by specifying the tag {{TAG|METAGGA}} in the {{FILE|INCAR}} file.
+How to do a [[Band-structure calculation using meta-GGA functionals|Band-structure calculation using meta-GGA functionals]].
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-[[Category:VASP|PAW]][[Category:XC Functionals]]
+[[Category:VASP|PAW]][[Category:Exchange-correlation functionals]]