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>\rho</math>, its first derivative <math>\nabla\rho</math>, and on the kinetic-energy density | 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].