Category:Meta-GGA

Theoretical Background

Meta-GGA exchange-correlation functionals depend on the electron density ${\displaystyle \rho }$, its first derivative ${\displaystyle \nabla \rho }$ and the kinetic-energy density ${\displaystyle \tau }$:

${\displaystyle E_{\mathrm {xc} }^{\mathrm {meta-GGA} }=\int \epsilon _{\mathrm {xc} }^{\mathrm {meta-GGA} }(\rho ,\nabla \rho ,\tau )d^{3}r}$

Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropriate for very large systems. In general, meta-GGA functionals are more accurate than GGAs. 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 ${\displaystyle \nabla ^{2}\rho }$ are not yet available in VASP.

How to

A meta-GGA can be used by specifying the tag METAGGA in the INCAR file.