Category:GGA: Difference between revisions
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GGA exchange-correlation functionals depend on the electron density <math>\rho</math> and its first derivative <math>\nabla\rho</math>: | GGA exchange-correlation functionals depend on the electron density <math>\rho</math> and its first derivative <math>\nabla\rho</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. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the 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. 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 == | == How to == | ||
Revision as of 09:49, 19 January 2022
Theoretical Background
GGA exchange-correlation functionals depend on the electron density and its first derivative :
Among the various types of functionals, the GGAs are the fastest to evaluate. 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].