[Wien] Few questions about onsite hybrids and so

[Pavel Ondračka]

Dear Wien2k mailing list,

I'm trying to calculate a band structure of Tb3Ga5O12 magneto-optical
crystal (cubic Ia-3d, 80 atoms). While I consider myself quite
experienced Wien2k user, I've always managed to stay away from f block
elements, so my experience here is none. So besides the few questions I
have I'll also try to somehow summarize what I did, please correct me
if something was not OK.

Luckily I'm not shooting completely blind as I have some high-quality
optical data where we can see some (very weak but also quite sharp and
hence noticeable f-f transitions in the band gap so I have some idea
how the Tb f states at least should look like). Significant optical
absorption start around 4eV but below that I see some very weak
electronic transitions in the 0.2-0.9eV range, around 2.5 and 3.5eV
(reportedly between f states located in the band gap). So I expect at
least three bunches of f states in band gap one occupied and the others
unoccupied.

I've started with spin-polarized PBE, I'm reasonably sure the structure
file is OK, albeit probably not much relaxed (but I was hoping I could
find equilibrium volume and do relaxation at a later point). I did not
opt for HDLOs even though the Tb sphere is quite big (2.43) since I
would also like to try to get few momentum matrix elements later with
optics, but I've increased the lmax to 14 and lvnsmax to 8 (lapw2 GMAX
16, fft factor 3 and 4x4x4 k-grid).

The initial runsp went fine but the band structure is far from OK, I
get only a single bunch of f states in the band gap clumped together
(some of them are occupied so its metallic), but experimentally I
should get and insulator (although the difference between the
unoccupied and occupied f states in the band gap is only maybe 0.2eV).

Regarding the f electron correction I opted for onsite hybrid and
initialized it with init_orb_lapw -eece.
UG says that its better to use LDA for the exchange potential so I
copied case.in0 to case.in0eece_lapw where I replaced "XC_PBE" on the
first line with "EX_PBE VX_LDA EC_PBE VC_PBE".
The onsite hybrid calculation converged fine, I get a nice splitting of
the f states (albeit a bit too much maybe).
The other options would be +U obviously, I went for the hybrid because
it felt more rigorous, but I would also appreciate comments if someone
has maybe better experience with +U?

Next step was to initialize spin-orbit interaction with init_so_lapw. I
started with the default 001 but I want to also try other directions
later and compare. I opted for no relativistic LOs (no support in
optics) and enabled it only for Tb and Ga. symetso created a new
structure (most notable I have more Tb inequivalent positions) and than
I manually fixed case.inso case.indm and case.inorb as the init_so
script warned me. I also guessed I should fix case.ineece (that seemed
straightforward) but than I thought I should also fix case.in2eece.
Reading UG gives the impression that case.in2eece is normal case.in2
with extra EECE on the first line and than the optional 3a and 3b
lines. In the case.in2eece created automatically with init_orb_lapw -
eece the 3a and 3b lines looked like:
1
1 1 3
However reading UG this actually seems wrong? Because UG says (Section
7.9 page 166) the format for optional 3b is just two values:
jatom rho, l rho
so I wonder if the UG is wrong or if I'm actually applying the hybrid
correction to p instead of f?

Also, is there anything else I should fix manually after intializing
the so on top of eece? Or should I do it the other way around (first so
and then eece)? The reasoning for doing first eece was that I get a
metal with plain PBE and an insulator with the onsite hybrid, so I
thought it might be easier to converge if I start so from insulator
(but I still use TEMP smearing just to be sure I don't end with
convergence problems if I get a metal during the convergence as the
expected unoccupied occupied f-f distance is very small.)

I was also considering mBJ later, just to get some feeling how the
conduction bad would shift but I'm not sure if this would work or not
on top of eece and so?

One last question is regarding the forces. From reading the UG I
understood that it should be OK to relax the oxygen positions with
onsite hybrid and so (as long as I don't have so or eece enabled for O
atoms). Is this correct? So will just switching to MSR1a and running
normal runsp -so -eece work or are some other fixes needed?

Best regards
Pavel