[Wien] Orbital character

[Peter Blaha]

The total charge density around an atom obeys the point symmetry of this 
site. Thus, if you have a 4-fold rotation, d-xz and dyz must be the same 
and this is what WIEN2k calculates.

Of course, the charge density of ONE particular k-point (eg. k=(0.5,0,0) 
does NOT have this symmetry, but its eigenvalues are degenerate with 
(0,0.5,0) and the sum of these two eigenvalues has the correct symmetry. 
WIEN2k uses this knowledge, it will always symmetrize the results and 
thus you can stick to a k-mesh in the irreducible wedge of the BZ and 
still get the properly symmetrized charge density (and you save the time 
to calculate the k-point in the y-direction).

If you don't like this feature, distort your lattice slightly (a.ne.b), 
init_lapw; change back a=b; and run_lapw. Now WIEN2k will use a larger 
k-mesh, you will have kx and ky in your mesh (their eigenvalues should 
be still the same if you changed back a=b after init) and you can have 
the individual charge densities of kx and ky (and the sum of them must 
give degenerate dxz,dyz).

Lukasz Plucinski schrieb:
> Dear Wien Experts,
> 
> In my Fe(001) spin-polarized 30 atom slab calculations (no spin-orbit) I 
> only have access to the sum of DXZ+DYZ band character (case.qtldn), but 
> not separately to the DXZ and DYZ:
> 
> JATOM  1  MULT= 1  ISPLIT=-2  
> tot,0,1,PZ,PX+PY,2,DZ2,DXY,DX2Y2,DXZ+DYZ,3  JATOM  2  MULT= 1  
> ISPLIT=-2  tot,0,1,PZ,PX+PY,2,DZ2,DXY,DX2Y2,DXZ+DYZ,3  ... JATOM 30  
> MULT= 1  ISPLIT=-2  tot,0,1,PZ,PX+PY,2,DZ2,DXY,DX2Y2,DXZ+DYZ,3
> 
> This suggests that for each eigenvalue DXZ and DYZ is always degenerate 
> and hybridized, i.e. each electron (e.g. in eigenvalue- and k-resolved 
> charge density) will choose 50% mixture of DXZ with DYZ. e.g. each 
> charge profile would be totally fourfold.
> 
> At Gamma-point DXZ and DYZ are equivalent, however, choosing k-points 
> away from Gamma, along X<100> or Y <010> seems to lift this equivalence.
> 
> It is possible that for k-values away from Gamma e.g. along <100> line 
> electrons have eg. distinct DXZ character, with no (or little) DYZ ?
> 
> My charge density profiles for the minority surface state along Gamma-X 
> suggest that each single electron has a totally fourfold character -- 
> e.g. its 50% mixture of DXZ and DYZ, but I am not sure this is correct.
> 
> Any comment would be appreciated. Maybe there are some general symmetry 
> rules which govern this situation ?
> 
> Regards,
> 
> Lukasz
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-- 
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Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
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