[Wien] equivalent-core approximation

[Peter Blaha]

I'm not an expert in these core level calculations, but for me the z+1
approximation always seemed a quite poor approximation and I would not use
it if I have another chance.

For your problem I propose two methods within WIEN:

First of all you should always have a supercell (unless you have a big cell
anyway) with broken symmetry so that you can deal with a core hole on a
single Ge atom (screened by the environment).
In addition, try to make the Ge sphere "as large" as possible (but still
meaningfull - details depend on your structure).

Firt do a regular WIEN calculation for this supercell to verify that you get
identical results as before.

Then you have to do some tricks:

Edit case.inc and put the Ge 3d electrons into the core for  all Ge atoms 
(I'm not sure about this, but I guess it is more cosistent than just for
the single Ge atom) ?

edit case.in2(c) and reduce NE by 10*(number of Ge atoms)

edit case.in1(c) (make a backup first) and remove the Ge-3d LO 
(around -1.5 Ry). Do not forget to 
change also the "number of exceptions" (see UG description of case.in1)

Do an scf calculation. Check the results, i.e. core-leakage and the effect
on the Ge-3d eigenvalues (compare the 3d core with the 3d bands with respect 
to EF). Of course the bands will have a certain bandwidth which is not
present in the core (but there you have SO splitting).

Once you can estimate the "error" introduced by the core-like treatment you may
remove 1 or 1/2 core electron from case.inc and add it to case.in2. Do another
scf calculation and estimate your core levels (E-tot or Slater...).

At this position, your 3d-core with the hole should be quite separated from
the other Ge. You could now try a "2-window calculation" using a case.in2s
file. 
Remove all 3d states from the inc file. 
Take the original case.in1 file (so that you have again 3d LOs)
cp case.in2 case.in2s
edit case.in2s and specify NE=9 (just for the Ge 3d with hole)
edit case.in2 with NE="all electrons+1"; but set EMIN such that the 3d-states
of the Ge-hole atoms are cut-off.
cp case.in1 case.in1s

Finally you will have to edit   run_lapw
Look for     lapw1s:
replace the line
     total exec	lapw1 -sc $para
by   cp $file.vector $file.vectors
 
Now run an scf cycle. You should have the Ge-3d states in the valence, but
have introduced a hole in the Ge-3d states of one particular atom.

It's not simple and maybe I've made an error in the description, but I'd
expect it should work. (Of course, if the core leakage is not that bad
you might not need the second step).




> Ge 3d electrons (approx. -1.5 ryd). So far I have tried manually placing these
> in core and reducing the number of valence electrons. However, this too was
> unstable. Another method I have heard about is simply using the Slater

What should that mean ? I'm pretty sure it works.


                                      P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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