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# METAGGA

METAGGA = TPSS | RTPSS | M06L | MBJL | SCAN | MS0 | MS1 | MS2
Default: METAGGA = none

Description: selects one of various meta-GGA functionals.

• METAGGA=TPSS, RTPSS, or M06L
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 read the paper of Zhao and Truhlar.[2]
• METAGGA=MS0, MS1 and MS2
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 from vasp.5.4.1 upwards.
• METAGGA=MBJ
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, which in turn means we can not 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 tend to diverge for surface calculations. In the vacuum, where the electron density ρ and kinetic energy density τ are (close to) zero, the functional becomes unstable.

• METAGGA=SCAN

The SCAN (Strongly constrained and appropriately normed semilocal density functional) [7] is a 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 from vasp.5.4.3 upwards.

Beware: 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)


## Convergence issues

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