Category:Meta-GGA: Difference between revisions
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== Theoretical Background == | == Theoretical Background == | ||
Meta-GGA exchange-correlation functionals depend on the electron density <math> | 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}}( | :<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}\rho</math>, are not yet available in VASP. | 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}\rho</math>, are not yet available in VASP. | ||
Revision as of 13:29, 6 April 2022
Theoretical Background
Meta-GGA exchange-correlation functionals depend on the electron density , its first derivative and the kinetic-energy density :
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, , are not yet available in VASP.
How to
A meta-GGA can be used by specifying the tag METAGGA in the INCAR file.