[Wien] spin-orbit (PBE and mBJ) for perovskites

[Mikhail Nestoklon]

Dear wien2k community,
I plan to do some DFT calculation of inorganic perovskites using WIEN2k (19.1 with some patches except the last one for RLO).
I’ve started from attempt to reproduce the values from Jishi et al., JPCC 118, 28344 (2014), but can not get the numbers given in Table 2 even for cubic CsPbI_3. The difference seem to stem from the spin-orbit.
 
What I did:
Using the file in attachment (I use the lattice constant given in table 1 and R_MT indicated in the text) I do
$ init_lapw -b -vxc 13 -rkmax 9.0 -lvns 6 -fftfac 4 && x kgen (14x14x14) && run_lapw -ec 0.00001 -cc 0.0001
I use -lvns 6, the difference with the result using standard value is small, in Jishi et al. it is mentioned that l_{max}=10 which is default, assuming they might have meant lvns I tried lvns=10, the difference with lvns=6 is close to zero. I also tried to put Pb p3/2 orbitals to core (if I put P1/2 to valence the result is strange, but this is a separate question) and see no difference.
For k-mesh I check the convergence and see that for 14x14x14 the total energy convergence is below 1mRy and GAP is below 1 meV which is fine, so I am using this k mesh. 
Then I check the RKMAX convergence. For Rmt*Kmax =9 without spin-orbit I get the same number as in Table 2, but I see that this number is not fully converged: if I increase RKMAX further the total energy decreases for 8mRy and gap increases for almost 6 meV. I find it acceptable to use RKMAX=12: only then it is <1mRy and ~1meV for total energy and gap respectively. The gap with these numbers is 1.329meV which is 5 meV different from Table 2, this difference is probably acceptable.
 
However, when I switch on the spin-orbit, the difference is huge. With the default values (I only increase llmax, however it does not change much) I get GAP about 0.269meV, which is almost 4 times different from the value given in Jishi et al. Table 2. As the SO value depends on de (in case.in1), I increase this parameter and check the value of GAP and also spin-orbit splitting of conduction and valence band (difference between energies of Gamma_8 and Gamma_7 in R point). GAP and spin-orbit in conduction band fully (below 1meV) converge only when de=15. Still, the band gap is 0.259eV which is too far from value given in Jishi et al.
The RLO (I tried to add it on Cs, as for Pb it should be useless [1]) does not help
 
With the same parameters I do the mBJ run (TB-mBJ). As expected, the gap increases, but up to 0.722 eV which is two times different from the value given in Jishi et al.
I did not try to change R_MT: I use the value given in their paper.
 
The fact that I do reproduce the number given for PBE without spin-orbit indicates that I hardly did any mistake in the structure. However, the difference in the numbers with spin-orbit is too large to be explained by unconverged results, both on my and their side. Could you help me to understand, how can I reproduce their results?
 
Thank you in advance.
 
Sincerely yours,
Mikhail Nestoklon
 
[1] https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg17828.html
 
 
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