Category:Meta-GGA: Difference between revisions

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== Theoretical Background ==
'''Meta-GGAs''' are a family of [[exchange-correlation functionals]] that in addition to the electron density <math>n</math>, its gradient <math>\nabla n</math> depend on
 
* the kinetic-energy density <math>\tau</math>, and/or
Meta-GGA exchange-correlation functionals depend on the electron density <math>\rho</math>, its first derivative <math>\nabla\rho</math> and the kinetic-energy density <math>\tau</math>:
* the Laplacian of the electron density <math>\nabla^{2}n</math>.
:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(\rho,\nabla\rho,\tau)d^{3}r</math>
Thus, the exchange-correlation energy can be written as
Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropriate for very large systems. In general, meta-GGA functionals are more accurate than GGAs. Not that meta-GGAs are implemented in VASP within the generalized KS scheme {{cite:yang:prb:2016}} The meta-GGA that is currently widely used in solid-state physics is SCAN{{cite|sun:prl:15|}}.
:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(n,\nabla n,\nabla^{2}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 (see {{TAG|METAGGA}}) within the generalized KS scheme{{cite|yang:prb:2016|}}.  


== How to ==
== How to ==


A meta-GGA can be used with the tag {{TAG|METAGGA}} in the {{FILE|INCAR}} file.
A '''meta-GGA functional''' can be used by specifying
* the {{TAG|METAGGA}} tag, or
* {{TAG|XC}} tag
in the {{FILE|INCAR}} file.


How to do a [[band-structure calculation using meta-GGA functionals]].


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[[Category:VASP|PAW]][[Category:XC Functionals]]
[[Category:VASP|PAW]][[Category:Exchange-correlation functionals]]

Latest revision as of 06:16, 12 June 2024

Meta-GGAs are a family of exchange-correlation functionals that in addition to the electron density , its gradient depend on

  • the kinetic-energy density , and/or
  • the Laplacian of the electron density .

Thus, the exchange-correlation energy can be written as

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 (see METAGGA) within the generalized KS scheme[1].

How to

A meta-GGA functional can be used by specifying

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.