Category:Meta-GGA: Difference between revisions

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 $n$ , its gradient $\nabla n$ depend on

the kinetic-energy density $\tau$ , and/or
the Laplacian of the electron density $\nabla^{2}n$ .

Thus, the exchange-correlation energy can be written as

E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(n,\nabla n,\nabla^{2}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 (see METAGGA) within the generalized KS scheme^[1].

How to

A meta-GGA functional can be used by specifying

the METAGGA tag, or
XC tag

in the INCAR file.

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

↑ Z.-h. Yang, H. Peng, J. Sun, and J. P. Perdew, Phys. Rev. B 93, 205205 (2016).

Pages in category "Meta-GGA"

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

B

Band-structure calculation using meta-GGA functionals

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@@ Line 1: / Line 1: @@
-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>:
+'''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
-:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(n,\nabla n,\tau)d^{3}r</math>
+* the kinetic-energy density <math>\tau</math>, and/or
-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.
+* the Laplacian of the electron density <math>\nabla^{2}n</math>.
+Thus, the exchange-correlation energy can be written as
+:<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 ==
-A meta-GGA can be used by specifying 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:Exchange-correlation functionals]]