[Wien] Empty orbital band character in case.qtl

[Peter Blaha]

With spin-orbit coupling you have 2D degenerate eigenstates.

This means you have 2 solutions with the same eigenvalue and as you may 
recall, any linear combination of 2 such solutions are again a solution.

Thus the eigensolver forms 2 "arbitrary" wavefunctions, only obeying the 
above mentioned constrain.

You can see that for the first pair you have charges on the second atom 
of 0 and 0.548; while for the second pair you have 0.249 and 0.299. Thus 
in each of the degenerate states you have about 0.55 electrons.

Everything is ok and only the SUM of these 2 contributions makes sense !

> I performed the initialization ( Ecut= -6.0, rkmax=7.0,lvns=8, vxc=13 
> and a 9 9 1 kmesh) without warnings. Then, I ran the scf calculation 
> first without SOC (run_lapw -ec 0.00001 -cc 0.0001 -p) and then with SOC 
> (run_lapw -ec 0.00001 -cc 0.0001 -p -so), the convergence was achieved 
> and no warnings were presented in the case.scf file.  The valence (77 & 
> 78) and conduction (79 & 80) bands present a double degeneracy at this 
> k-point.
> 
> For calculating the orbital projection I ran the command 'x lapw2 -p -so 
> -qtl', resulting in the case.qtl file. For the interpretation, as I am 
> interested in the (0 0 0) point which corresponds to the first line of 
> the case.klist file, I extracted the first block for the bands in 
> question (attaching header as well):
> 
> --->
>   LATTICE CONST.=  7.7606  7.7606 72.1324   FERMI ENERGY=  -0.12049
>      1 < NMAT < 2291   SPIN=1   NAT=  3      SO 2
>   JATOM  1  MULT= 2  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
>   JATOM  2  MULT= 2  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
>   JATOM  3  MULT= 2  ISPLIT= 4  tot,0,1,PZ,PX+PY,2,DZ2,DX2Y2+DXY,DXZ+DYZ,3
> 
> BAND 77
>    -0.15197  1 0.00000    0.00000 0.00000 0.00000 0.00000 0.00000 
> 0.00000 0.00000 0.00000 0.00000
>    -0.15197  2 0.00001    0.00000 0.00000 0.00000 0.00000 0.00000 
> 0.00000 0.00000 0.00000 0.00000
>    -0.15197  3 0.00000    0.00000 0.00000 0.00000 0.00000 0.00000 
> 0.00000 0.00000 0.00000 0.00000
>    -0.15197  4 0.99999
> 
> BAND 78
>    -0.15197  1 0.00889    0.00000 0.00146 0.00000 0.00146 0.00279 
> 0.00000 0.00075 0.00204 0.00015
>    -0.15197  2 0.54843    0.00000 0.25833 0.00000 0.25833 0.01476 
> 0.00000 0.01260 0.00216 0.00100
>    -0.15197  3 0.02904    0.00000 0.01444 0.00000 0.01444 0.00005 
> 0.00000 0.00003 0.00002 0.00002
>    -0.15197  4 0.41364
> 
> BAND   79
>    -0.08923  1 0.00454    0.00124 0.00082 0.00070 0.00012 0.00002 
> 0.00000 0.00001 0.00000 0.00019
>    -0.08923  2 0.24891    0.09282 0.02634 0.02625 0.00009 0.00404 
> 0.00403 0.00001 0.00000 0.00121
>    -0.08923  3 0.02288    0.00175 0.00960 0.00939 0.00021 0.00008 
> 0.00006 0.00001 0.00001 0.00001
>    -0.08923  4 0.72367
> 
>   BAND   80
>    -0.08923  1 0.00535    0.00149 0.00094 0.00084 0.00010 0.00001 
> 0.00000 0.00001 0.00000 0.00022
>    -0.08923  2 0.29867    0.11140 0.03158 0.03150 0.00008 0.00484 
> 0.00484 0.00001 0.00000 0.00146
>    -0.08923  3 0.02729    0.00211 0.01144 0.01127 0.00017 0.00009 
> 0.00008 0.00001 0.00001 0.00001
>    -0.08923  4 0.66869
> <----
> 
> The unexpected behaviour encountered and the reason for this inquiry 
> concerns the band 77, which presents a practically 0 orbital character. 
> Could this be a numerical error or should this be physically interpreted?
> 
> Thank you in advance for your time and help.
> 
> 
> 
> 
> 
> 
> 
> 
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-- 
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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
WWW:   http://www.imc.tuwien.ac.at
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