[Wien] Few questions about onsite hybrids and so

[Peter Blaha]

Hi,
Here are my comments. Most of them similar to what Laurence said.

> I'm trying to calculate a band structure of Tb3Ga5O12 magneto-optical
> crystal (cubic Ia-3d, 80 atoms). While I consider myself quite
> 
> 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.

Unfortunately, I don't believe that these optical f-f transitions can be 
described by DFT. These are crystal-field splitted multiplet 
excitations, which are usually not accessible by DFT.

PS: Optical transitions create an electron-hole pair and excitonic 
(correlation) effects can be very large.
XPS creates a free electron and a hole and although this is also not a 
ground state, it is usually better described by groundstate DFT.

 From your chemical formulae one expects Tb3+, i.e. a fully occupied 
spin-up 4f band and a single 4f electron occupied in spin-dn.
Of course, PBE gives a metal and the 4f-dn states are pinned at EF.
An orbital potential can split these states and single out a single 4f 
electron/atom. However, with orbital potentials in many cases one can 
obtain several different orbitals occupied, which depends on the 
starting density matrix. In other words, your solution may not be the 
ground state, but a metastable state.
Therefor I'd do first GGA+SO, and "hope" that this gives me a bit larger 
occupancy of the "correct" 4f orbital. When you then calculate the 
density matrix from this solution, you may run in the lowest energy 
orbitally-ordered state. Eventually, you could also start from different 
density matrices and see to which solutions you converge and compare 
total energies (these manipulations are simpler in DFT+U than in EECE).

RMTs: Since we cannot use HDLOs for orbital potentials, too large 
spheres are not good. However, (in particular for 3d systems) small 
spheres mean that only 80-90% of the d-charge is inside the sphere and 
thus gets shifted by the orbital potential. Thus one needs a larger U 
(or alpha) to get similar results with smaller RMTs.
For later 4f atoms, however, the 4f are very localized (in Tb with 
RMT=2.0  97% of the 4f charge is inside spheres (see case.outputst). My 
personal choice would be RMT = 2.1 to 2.2).

Relaxation: Yes, you can safely relax the O atoms when SO is switched 
off for them and the heavy atoms are fixed in case.inM.
If this is just a powder X-ray structure, the O-positions could be quite 
wrong.

Most 4f systems would be anti-ferromagnets, but with very low Neel 
temperature, which means that the energy difference between an AFM and 
FM ordering is very small. These are local moments and they do not care 
too much how their neighbors are polarized.
> 
> 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".

This is a misunderstanding. I'd use PBE in case.in0 since the Ga/O 
states should be much better described by PBE. However, for the double 
counting correction, LDA is numerically preferred and the UG says:
  "This is possible by copying case.in0 to case.in0eece_lda and specify 
VX_LDA".  Note: it is   case.in0eece_lda, not  case.in0eece_lapw

EECE vs DFT+U is a matter of taste. EECE has one adjustable parameter, 
DFT+U 1-2 (U and J). For 4f systems the "effective U" (J=0) is often not 
justified since the intraatomic J may be important. It may have quite 
some influence on the orbital magnetic moment.
Anyway, both are approximations and for a proper gap you may need mBJ+U 
(or mBJ+EECE) with a smaller U (alpha).

> 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?

This is an error in the UG. You would see it quickly, if you correct p 
states instead of f.

PS: The only important input file is case.ineece (and maybe 
case.in0eece_lda). The runeece script (and not init_orb) generates the 
other *in*eece files on the fly in every iteration.

> 
> 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
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300
Email: peter.blaha at tuwien.ac.at    WIEN2k: http://www.wien2k.at
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