modified Becke-Johnson potential (mBJ) for band gaps (from userguide)

The modified Becke-Johnson exchange potential + LDA-correlation (Tran and Blaha 2009) allows the calculation of band gaps with an accuracy similar to very expensive GW calculations. It is a semilocal approximation to an atomic “exact-exchange” potential and a screening term. This is just a XC-potential, not a XC-energy functional, thus Exc is taken from LSDA and the forces cannot be used with this option.

We recommend the following steps to perform a mBJ calculation (the purpose of the first five steps is just only to create the starting case.r2v and case.vresp files):

 Ø   run a regular initialization and SCF calculation using LDA or PBE (it does not matter at all which functional you choose).

 Ø   init mbj lapw. This performs automatically the following steps:

·        create case.inm vresp (cp $WIENROOT/SRC templates/template.inm vresp case.inm vresp.

·        edit case.in0 and set ”R2V” option (instead of ”NR2V”) such that the XC potential is written in case.r2v.

 Ø   run one more iteration (use run lapw -NI -i 1) to generate the required case.r2v and case.vresp files.

 Ø   “save” the LDA (or PBE) calculation.

 Ø   run init mbj lapw again. The second call (once case.inm vresp is present) will do the following steps: 

                   ·        edit case.in0 and change the functional to option XC MBJ (indxc=28) (this is mBJ).

·    cp case.in0 case.in0 grr and choose EX GRR VX GRR (indxc=50) in case.in0 grr. This option will calculate the average of ∇ρ/ρ over the unit cell. (The presence of case.in0 grr will be detected during the SCF procedure and lapw0 will be called twice, first with the input file case.in0 grr, then with case.in0.)

·  select a specific mBJ parametrization (see below) and creates the corresponding file case.in0abp.

 Ø   Eventually, edit case.inm and choose the PRATT mixing scheme.
  Ø   Run the mBJ SCF calculation. 

It could well be that the default mixing scheme leads to convergence problems (this is what we have observed in many cases). The reason is that the mBJ potential also depends on the kinetic energy density which is not mixed in mixer. If such a convergence problem appears, you have to use the PRATT mixing. The PRATT mixing can be slow, lead to oscillations or even lead to divergence. Thus, first you should use a smaller mixing factor (eg. 0.2 or 0.1) and later (when the calculation approaches convergence) increase it to about 0.40 to make sure that your calculation did not stop at a false (pseudo) convergence. In most cases it is also possible to switch back to MSR1 after some initial (typical 5-10) scf-cycles.

The mBJ potential uses an average of ∇ρ/ρ over the unit cell. This does not make sense for surfaces or molecules. In such cases, run a similar bulk structure first, then cp case bulk.grr to case.grr and remove case.in0 grr. This runs mBJ with a fixed value of “c”.

 If you want to use other mBJ parameters than those defined in (Tran and Blaha 2009), eg. the optimized values of (Koller et al. 2012) you can define them during init mbj lapw or directly in case.in0abp. Put 3 values A, B, e (default=-0.012, 1.023, 0.5), which determines the parameter c in mBJ according to eq. 7 or Table II. in (Koller et al. 2012).

Reference: http://susi.theochem.tuwien.ac.at/reg_user/textbooks/usersguide.pdf