[Wien] new x and z axis in qtl

[Maurits W. Haverkort]

Dear P. Novak, J.Kunes and others.

I've been trying to use qtl to create a projected DOS on almost symmetry
axes and I'm getting results that I do not understand. I have a
perovskite with a small trigonal distortion (R3-R 167 struct file
attached below) Everything seems to run fine and if I compare the s,p,d
or f projected DOS with a non-distorted calculation (PM3-M)  they are
reasonably the same. Instead of projecting on the a1g and eg orbitals of
the TM (Cu) ion I would like to project on the cubic eg and t2g
orbitals. The DOS of the t2g orbitals is zero (almost) above the fermi
energy, so recognizing if a projection is OK or not is relatively
straight forward.

If I take for the new z and x axis the:
1.0 1.0 -1.0
0.0 0.0  1.0
axis then I get reasonable results. The z2 and xy orbital are eg
orbitals and the x2-y2, xz and yz t2g orbitals. These two axis are
however not totally orthogonal and the qtl program complains, but also
tells me it solved this problem....

For this test calculation this is fine as the trigonal distortion is
very small. For real structures this is a bit more tricky. So I thought
one could easily solve this problem by rotating the axis 90 degrees
around the new z axis.

If I take the new z and x axis to be:
1.0 1.0 -1.0
1.0 -1.0 0.0
Then they are orthogonal. Sadly now the projected DOS-es do not make
sense to me. All of them are mixtures, especially the z2 projected DOS
is no longer the same as before.

To make the test complete If I project onto the
0.0 0.0 1.0
1.0 -1.0 0.0
axis, then qtl finds them to be orthogonal as well. (Naturally the
DOS-es are now not split nicely into t2g and eg orbitals.)

Attached one can find a ps file with the partial DOS-es in thick for a
projection with the z and x axis along the 11-1 and 001 direction; thin
the directions are 11-1 and 1-10.

Wien2k version 10.1, downloaded 28.09.10 compiled with Intel 11.1 + MKL;
LSDA + standard w2web settings + local rotation matrix for O atom
changed in order to project on a1u and eu p DOS-es (rotation around the
local C2 axis, should be symmetry allowed).

If somebody knows what either I or the program is doing wrong some help
would be appreciated.

Best regards
Maurits

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