Category:Meta-GGA: Difference between revisions

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

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

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

How to

A meta-GGA functional can be used by specifying

• the METAGGA tag, or
• XC tag

in the INCAR file.

How to do a band-structure calculation using meta-GGA functionals.