[Wien] Format of CASE.qtl file/band-character comparability

[Kevin Kramer]

Dear wien2k users,

I've been successfully using the program `spaghetti` to create
band-character plots (as described in sec. 8.20 of the userguide).
Now I would be interested in comparing and quantifying characters of
different orbitals for specific bands (e.g. "This band has 50% orbital X
character and 50% orbital Y character at this-and-this k,E-point") and my
first, naive approach was to use the numbers from the third column of the
CASE.bands.agr file, i.e. the markersize information. However, as this is
just a visual parameter, while it is certainly proportional to the
band-character, I feel like it is not reliable to quantify band-characters
across different orbitals.
Thus, I've been looking at the actual data in CASE.qtl directly. And here
is where my question arises. The format of this file seems straightforward
enough at first sight, but I was still puzzled by an observation and I
couldn't find an explanation of the file format in the userguide or the
mailing list archive.
Let me share my current interpretation of the file format with an example
of CaMn2Sb2. The first few lines look like this:
```
CaMn2Sb2

LATTICE CONST.=  8.5794  8.5794 14.1352   FERMI ENERGY=   0.31784
 387 < NMAT <  405   SPIN=1   NAT=  3      SO 0
JATOM  1  MULT= 1  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
JATOM  2  MULT= 1  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
JATOM  3  MULT= 1  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
BAND    1
  -3.18669  1 0.00000    0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
0.00000 0.00000 0.00000
  -3.18669  2 0.99758    0.00000 0.49879 0.00000 0.49879 0.00000 0.00000
0.00000 0.00000 0.00000
  -3.18669  3 0.00010    0.00000 0.00002 0.00000 0.00002 0.00002 0.00000
0.00001 0.00001 0.00000
  -3.18669  4 0.00232

```
So, after 'BAND 1' we seem to have 4 lines for every energy-k point, the
first one corresponding to atom 1 (Ca), the second to Mn and the third to
Sb. The Fourth line then just gives the difference 1-(sum of above 3 lines)
which I interpret as the intersitial charges.
The columns are clearly assigned as follows:
col 1: energy
col 2: # of atom
col 3:  sum of all following columns (total character of this atom)
cols 4-end: character of different orbitals as listed in the header (lines
5,6,7)

Now the thing I don't understand is the fact that column 3 contains just
the sum of all the following numbers, but these numbers already contain
sums amongst themselves. In the example on the second line after 'BAND 1'
we have a total of 0.99758 which is the sum of columns 4 (p_tot) and 6
(PX+PY). But column 4 is already the sum of columns 5 (PZ) and 6 (PX+PY).
In other words, they are doubly counted in the total in col 3.
If my interpretations of the file format are correct, I don't really
understand the reasoning behind the double counting and it would also mean
that I cannot absolutely compare band characters for different orbitals (or
am I missing something).
So, concretely, my question boils down to:
i) Are my interpretations of the file format for CASE.qtl correct?
i,a) if yes: why the double counting?
i,b) what is the actual format of the file CASE.qtl
ii) Is there a way to quantitatively compare the contributions of different
orbitals to different points in bands?

I apologize for the very verbose question and thank you for taking the time
to read this far.
Best regards,
Kevin


-- 
Kevin Kramer
PhD Candidate
Laboratory for Quantum Matter Research
<http://www.physik.uzh.ch/groups/chang/>
Physik Institut, Universität Zürich <http://www.physik.uzh.ch/>
Winterthurerstrasse 190
8057 Zürich
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