Category:Meta-GGA: Difference between revisions

From VASP Wiki
No edit summary
No edit summary
Line 1: Line 1:
== Theoretical Background ==
== Theoretical Background ==


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 $\tau$:
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>:
:<math>E_{\mathrm{xc}}^{\mathrm{GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{GGA}}(\rho,\nabla\rho)d^{3}r</math>
:<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}}.
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}}.

Revision as of 10:28, 19 January 2022

Theoretical Background

Meta-GGA exchange-correlation functionals depend on the electron density , its first derivative , and on the kinetic-energy density :

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 [1].

How to


Pages in category "Meta-GGA"

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