[Wien] Delta(d) from :QTL's corresponded to :PCS's

[Peter Blaha]

>       :PCS001: PARTIAL CHARGES SPHERE =  1 S,P,D,F,PZ,PXY, D-Z2,D-XY,X2Y2,D-XZ,YZ
>       :QTL001: 0.9682 2.5982 5.3246 0.9516 0.8643 1.7338 0.0000  1.0694 2.1361 2.1192 0.0000 0.0000

The labels above indicate that    d-xy and d-x2-y2 are the basis for ONE 
irreducible representation, thus the number 2.1361 is the sum of both 
orbitals. Divide it by two and you are back to around 1.06 and will get 
nearly zero delta. (same for dxz and d-yz)

Please note the difference in the labels: 
D-Z2,  means one irrep.
D-XY,X2Y2 means the next irrep, consisting of two orbitals.


>           For a cubic point group one expects that delta (d) = (d_xy+d_x2-y2)-1/2*(d_xz+d_yz)+d_z2  is zero. Thus I assume that the following given d_e_g, 0.3974, equally is  distributed in d_x2-y2=0.3974/2 and d_z2=0.3974/2, and similarly the following d_t2g=0.7171  is equally distributed in d_xy=0.7171/3, d_xz=0.7171/3 and d_yz=0.7171/3:
>       :PCS001: PARTIAL CHARGES SPHERE =  1 S,P,D,F,      D-EG,D-T2G
>       :QTL001: 2.1138 5.8961 1.1146 1.0194 0.0000 0.0000 0.0000  0.3974 0.7171 0.0000 0.0000 0.0000
>           If the above assumption, which I am not sure about it, is true then delta (d) as expected is zero.
>       Form a spin polarized calculation I have obtained the following  results:
>       0.9518 0.9519 0.9514
>       :QTL001: 0.9663 2.5888 5.2987 0.0166 0.8599 1.7289 0.0000  1.0625 2.1282 2.1080 0.0000 0.0000
>           I have expected form several physical reasons, e.g. being  close to the cubic point group, to be the delta (d) not far from zero. However,  again with assuming to be distributed equally (which I am not sure about it) the  d_xy_up=2.1361 as well as d_xy_dn=2.1282 in d_xz_up and d_yz_up as well as d_xz_dn  and d_yz_dn respectively, the occupation numbers can be written as follows:
>       d_z2=1.0694+1.0625
>       d_xy=(2.1361+2.1282)/3=d_xz=d_yz
>       d_x2-y2=2.1192+2.1081
>        
>       In this case I have obtained the value of 2.0954 for the delta(d), which is so  far from my expectation.
>               Other way  of treating this result, closing eyes on the physical expectation, is to just find  the following one to one corresponded values of QTL’s to the PCS’s:
>   d_z2=1.0694+1.0625
>       d_xy=2.1361+2.1282
>       d_x2-y2=2.1192+2.1081
>       d_xz=d_yz=0
>           In this case delta (d) is 6.3597, which is extremely large!
>           Any comments are most welcome.
>           With my best whishes for all of you,
>     
> 
> Sincerely yours,
> S. Jalali.
> /_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/_/
> Saeid Jalali Asadabadi,
> Department of Physics, Faculty of Science,
> University of Isfahan (UI), Hezar Gerib Avenue,
> 81744 Isfahan, Iran.
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                                      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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