CMBJ = [real (array)]
Default: CMBJ = calculated selfconsistently
Description: defines the c parameter in the modified Becke-Johnson meta-GGA potential.
The modified Becke-Johnson exchange potential in combination with L(S)DA-correlation (METAGGA=MBJ), 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 ρσ denotes the electron density, τσ the kinetic energy density, and VBR(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 ρσ, ∇ρσ, ∇2ρσ, and τσ. The function bσ is given by:
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.
The MBJ functional is a potential-only functional, i.e., there is no corresponding MBJ exchange-correlation energy.
The CMBJ tag can be set in the following ways:
- One may specify one entry per atomic type
CMBJ = c_1 c_2 .. c_nwhere the order and number n is in accordance with atomic types in your POSCAR file. The MBJ exchange potential at a point r will then be calculated using the parameter ci belonging to the atomic species of the atomic site nearest to r.
- Specify a constant
CMBJ = c