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.

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Band-structure calculation using meta-GGA functionals

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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
+* 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|}}.
-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{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(\rho,\nabla\rho)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 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]].
 ----
-[[Category:VASP|PAW]][[Category:XC Functionals]]
+[[Category:VASP|PAW]][[Category:Exchange-correlation functionals]]