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METAGGA = TPSS | RTPSS | M06L | MBJ
- 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.  For details on the
M06-L functional read the paper of Zhao and Truhlar. 
- METAGGA = MBJ
The modified Becke-Johnson exchange potential in combination with
L(S)DA-correlation [160,161] 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:
denotes the electron density,
the kinetic energy
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
The function is given by:
where and are two free parameters, that may be set by means
of the CMBJA and CMBJB tags, respectively.
The defaults of
were chosen such that for a constant electron density roughly the LDA exchange is recovered.
Alternatively one may also set the parameter directly, by means of the CMBJ-tag:
CMBJ = [real (array)] (Default: CMBJ= calculated selfconsistently)
The CMBJ tag can be set in the following ways:
If CMBJ is not set, it will be calculated from the density at each electronic step,
in accordance with CMBJA and CMBJB, from Eq. 6.4 above:
- One may specify one entry per atomic type
CMBJ = c_1 c_2 ... c_n
where the order and number is in accordance with atomic types in your POSCAR file.
The MBJ exchange potential at a point will then be calculated using the parameter
belonging to the atomic species of the atomic site nearest to .
- Specify a constant
CMBJ = c
CMBJA = [real] (Default: CMBJA=),
CMBJB = [real] (Default: CMBJB=).
N.B.I: The MBJ functional is a potential-only functional, i.e., there
is no corresponding MBJ exchange-correlation energy, instead 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
N.B.II: MBJ calculations tend to diverge for surface calculations.
In the vacuum, where the electron density and kinetic energy density
are (close to) zero, the functional becomes unstable.
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):
mkinetic energy-density pseudized
and for PAW datasets with partial core corrections:
kinetic energy density (partial)
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