Category:Meta-GGA

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.