Requests for technical support from the VASP group should be posted in the VASP-forum.

# METAGGA

METAGGA = TPSS | RTPSS | M06L | MBJ | SCAN | MS0 | MS1 | MS2 | RSCAN | R2SCAN
Default: METAGGA = none

Description: selects a meta-GGA functional.

N.B.I: If you select a meta-GGA functional, make sure that you use POTCAR files that are suited for meta-GGA functionals.

N.B.II: It is strongly recommended to set LASPH =.TRUE. to account for aspherical contributions to the PAW one-centre terms.

## Available functionals

The implementation of the TPSS and RTPSS (revised-TPSS) selfconsistent meta-generalized gradient approximation within the projector-augmented-wave method in VASP is discussed by Sun et al.[1]. For details on the M06-L functional, refer to the paper by Zhao and Truhlar[2].
The MS (where MS stands for "made simple") functionals are presented in detail in references [3] and [4]. These functionals are believed to improve the description of noncovalent interactions over PBE, TPSS and revTPSS but not over M06L. The MS functionals are available as of VASP version ≥ 5.4.1.
The modified Becke-Johnson exchange potential in combination with L(S)DA-correlation[5] [6] yields band gaps with an accuracy similar to hybrid functional or GW methods, but computationally less expensive (comparable to standard DFT calculations). The modified Becke-Johnson potential is a local approximation to an atomic exact-exchange potential plus a screening term and is given by:
${\displaystyle {\text{V}}_{x,\sigma }^{\rm {MBJ}}(\mathbf {r} )=c{\text{V}}_{x,\sigma }^{\rm {BR}}(\mathbf {r} )+(3c-2){\frac {1}{\pi }}{\sqrt {\frac {5}{12}}}{\sqrt {\frac {2\tau _{\sigma }(\mathbf {r} )}{\rho _{\sigma }(\mathbf {r} )}}}.}$
where ρσ denotes the electron density, τσ the kinetic energy density, and VBR(r) the Becke-Roussel potential:
${\displaystyle {\text{V}}_{x,\sigma }^{\rm {BR}}(\mathbf {r} )=-{\frac {1}{b_{\sigma }(\mathbf {r} )}}[1-e^{-x_{\sigma }(\mathbf {r} )}-{\frac {1}{2}}x_{\sigma }(\mathbf {r} )e^{-x_{\sigma }(\mathbf {r} )}].}$
The Becke-Roussel potential was introduced to mimic the Coulomb potential created by the exchange hole. It is local and completely determined by ρσ, ∇ρσ, ∇2ρσ, and τσ. The function bσ is given by:
${\displaystyle b_{\sigma }=[x_{\sigma }^{3}e^{-x_{\sigma }}/(8\pi \rho _{\sigma })]^{\frac {1}{3}},}$
and
${\displaystyle c=\alpha +\beta \left({\frac {1}{V_{\mathrm {cell} }}}\int _{\mathrm {cell} }{\frac {|\nabla \rho (\mathbf {r} ')|}{\rho (\mathbf {r} ')}}d{\mathbf {r} '}\right)^{1/2}}$
where α and β are two free parameters, that may be set by means of the CMBJA and CMBJB tags, respectively. The defaults of α=−0.012 (dimensionless) and β=1.023 bohr1/2 were chosen such that for a constant electron density roughly the LDA exchange is recovered. Alternatively one may also set the c parameter directly by means of the CMBJ tag.
N.B.I: The mBJ functional is a potential-only functional, i.e., there is no corresponding mBJ exchange-correlation energy, instead Exc is taken from L(S)DA. This means mBJ calculations can never be self-consistent with respect to the total energy, and thus we cannot compute Hellmann-Feynman forces (i.e., no ionic relaxation, etc.). These calculations aim solely at a description of the electronic properties, primarily band gaps.
N.B.II: mBJ calculations converge very slowly, so the number of maximum electronic steps (NELM) should be set higher than usual.
N.B.III: mBJ calculations tend to diverge for surface calculations. In the vacuum region, where the electron density ρ and kinetic energy density τ are (close to) zero, the functional becomes unstable.
The SCAN (Strongly constrained and appropriately normed) [7] functional is a semilocal density functional that fulfills all known constraints that the exact density functional must fulfill. There are indications that this functional is superior to most gradient corrected functionals [8]. This functional is only available as of VASP version ≥ 5.4.3.
The rSCAN (regularized SCAN) functional [9], introduces regularizations that improve the numerical sensitivity and convergence behavior. These regularizations break several of the exact constraints that the parent SCAN functional was designed to satisfy. However, testing has indicated that the accuracy of rSCAN can be inferior to SCAN in some cases [10]. This functional is available as of VASP version ≥ 6.2.0.
The r${\displaystyle ^{2}}$SCAN (regularized-restored SCAN) functional [11] modifies the regularizations introduced in rSCAN to enforce adherence to the exact constraints obeyed by SCAN. It fulfills all known constraints. However, it only recovers the slowly varying density-gradient expansion for exchange to second order, while SCAN recovers the expansion to 4th order. Testing indicates that r${\displaystyle ^{2}}$SCAN at least matches the accuracy of the parent SCAN functional but with significantly improved numerical efficiency and accuracy under low-cost computational settings. This functional is available as of VASP version ≥ 6.2.0, or in version 5.4.4 by patch 4.

## POTCAR files: required information

Meta-GGA calculations require POTCAR files that include information on the kinetic energy density of the core-electrons. To check whether a particular POTCAR contains this information, type:

grep kinetic POTCAR


This should yield at least the following lines (for each element on the file):

kinetic energy-density
mkinetic energy-density pseudized


and for PAW datasets with partial core corrections:

kinetic energy density (partial)


## Aspherical contributions related to one-center terms

LASPH =.TRUE. should be selected if a meta-GGA functional is selected. If LASPH =.FALSE., the one-center contributions are only calculated for a spherically averaged density and kinetic-energy density. This means that the one-center contributions to the Kohn-Sham potential are also spherical. Since the PAW method describes the entire space using plane waves, errors are often small even if the non-spherical contributions to the Kohn-Sham potential are neglected inside the PAW spheres (additive augmentation, as opposed to the APW or FLAPW method where the plane wave contribution only describes the interstitial region between the atoms). Anyhow, if the density is strongly non-spherical around some atoms in your structure, LASPH =.TRUE. must be selected. Non-spherical terms are particularly encountered in d- and f-elements, dimers, molecules, and solids with strong directional bonds.

## Convergence issues

If convergence problems are encountered, it is recommended to preconverge the calculations using the PBE functional, and start the calculation from the WAVECAR file corresponding to the PBE ground state. Furthermore, ALGO = A (conjugate gradient algorithm for orbitals) is often more stable than charge density mixing, in particular, if the system contains vacuum regions.