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# METAGGA

METAGGA = TPSS | RTPSS | M06L | MBJ | 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: - where ρ
_{σ}denotes the electron density, τ_{σ}the kinetic energy density, and V^{BR}(**r**) the Becke-Roussel potential: - The Becke-Roussel potential was introduced to mimic the Coulomb potential created by the exchange hole. It is local and completely determined by ρ
_{σ}, ∇ρ_{σ}, ∇^{2}ρ_{σ}, and τ_{σ}. The function b_{σ}is given by: - and
- 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 bohr
^{1/2}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*E*_{xc}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**: The mBJ calculations converge very slowly in the SCF cycle so the number of maximum electronic steps (NELM) should be set higher than usual.

**N.B.III**: The 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 WAVECAR 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.

## Related Tags and Sections

CMBJ, CMBJA, CMBJB, LASPH, LMAXTAU, LMIXTAU

## References

- ↑ J. Sun, M. Marsman, G. Csonka, A. Ruzsinszky, P. Hao, Y.-S. Kim, G. Kresse, and J. P. Perdew, Phys. Rev. B 84, 035117 (2011).
- ↑ Y. Zhao and D. G. Truhlar, J. Chem. Phys. 125, 194101 (2006).
- ↑ J. Sun, B. Xiao and A. Ruzsinszky, J. Chem. Phys. 137, 051101 (2012).
- ↑ J. Sun, R. Haunschild, B. Xiao, I. W. Bulik, G. E. Scuseria and J. P. Perdew, J. Chem. Phys. 138, 044113 (2013).
- ↑ A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 (2006).
- ↑ F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).
- ↑ J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015).
- ↑ J. Sun, et al., Nature Chemistry 8, 831–836 (2016).