Category:Meta-GGA: Difference between revisions

Meta-GGAs are a family of exchange-correlation functionals that in addition to the electron density ${\displaystyle n}$, its gradient ${\displaystyle \nabla n}$ depend on

• the kinetic-energy density ${\displaystyle \tau }$, and/or
• the Laplacian of the electron density ${\displaystyle \nabla ^{2}n}$.

Thus, the exchange-correlation energy can be written as

${\displaystyle E_{\mathrm {xc} }^{\mathrm {meta-GGA} }=\int \epsilon _{\mathrm {xc} }^{\mathrm {meta-GGA} }(n,\nabla n,\nabla ^{2}n,\tau )d^{3}r.}$

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 (see METAGGA) within the generalized KS scheme^[1].

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.