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

[Saeid Jalali]

    Dear WIEN2k community,
          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:
      :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
      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.
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Saeid Jalali Asadabadi,
Department of Physics, Faculty of Science,
University of Isfahan (UI), Hezar Gerib Avenue,
81744 Isfahan, Iran.
Phones:
Dep. of Phys.      :+98-0311-793 2435
Office             :+98-0311-793 2430
Fax No.            :+98-0311-793 2409
E-mail             :s_jalali_a at yahoo.com
www                :http://www.ui.ac.ir
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