[Wien] sum of eigenvalue

Peter Blaha pblaha at theochem.tuwien.ac.at
Fri Dec 10 14:55:49 CET 2010


No, the weights are not always constant for a given k-point, but they could.
However, they can also change, can even be negative (TETRA with Blöchl corrections) and eigenvalues
above EF may have quite a large weight because of the integration.

The sum of all weights should give the number of valence electrons.

Eg. for a simple tic test I get:

:FER  : F E R M I - ENERGY(TETRAH.M.)=   0.86727
   BAND#   1  E= -3.26258  WEIGHT= 0.0312500
   BAND#   2  E= -1.49651  WEIGHT= 0.0312500
   BAND#   3  E= -1.49651  WEIGHT= 0.0312500
   BAND#   4  E= -1.49651  WEIGHT= 0.0312500
   BAND#   5  E= -0.08469  WEIGHT= 0.0312500
   BAND#   6  E=  0.92224  WEIGHT= 0.0257860     above EF, but still large w
   BAND#   7  E=  0.92224  WEIGHT= 0.0257860
   BAND#   8  E=  0.92224  WEIGHT= 0.0257860
   BAND#   9  E=  0.99313  WEIGHT=-0.0000651     negative w !
   BAND#  10  E=  0.99313  WEIGHT=-0.0000651
   BAND#  11  E=  0.99313  WEIGHT=-0.0000651
   BAND#   1  E= -3.25813  WEIGHT= 0.2500000
   BAND#   2  E= -1.52461  WEIGHT= 0.2500000
   BAND#   3  E= -1.49897  WEIGHT= 0.2500000
   BAND#   4  E= -1.49897  WEIGHT= 0.2500000
   BAND#   5  E=  0.02466  WEIGHT= 0.2500000
   BAND#   6  E=  0.64700  WEIGHT= 0.2504040
   BAND#   7  E=  0.72336  WEIGHT= 0.2535309     close to EF larger w than below
   BAND#   8  E=  0.72336  WEIGHT= 0.2535309
   BAND#   9  E=  1.01544  WEIGHT=-0.0008899
   BAND#  10  E=  1.01544  WEIGHT=-0.0008899
   BAND#   1  E= -3.25364  WEIGHT= 0.1250000
   BAND#   2  E= -1.55117  WEIGHT= 0.1250000
   BAND#   3  E= -1.50157  WEIGHT= 0.1250000
   BAND#   4  E= -1.50157  WEIGHT= 0.1250000
   BAND#   5  E=  0.20974  WEIGHT= 0.1250000
   BAND#   6  E=  0.39818  WEIGHT= 0.1250000
   BAND#   7  E=  0.62467  WEIGHT= 0.1250000
   BAND#   8  E=  0.62467  WEIGHT= 0.1250000     all w constant
   BAND#   1  E= -3.25671  WEIGHT= 0.1875000
   BAND#   2  E= -1.52182  WEIGHT= 0.1875000
   BAND#   3  E= -1.50556  WEIGHT= 0.1875000
   BAND#   4  E= -1.50556  WEIGHT= 0.1875000
   BAND#   5  E=  0.03641  WEIGHT= 0.1875000
   BAND#   6  E=  0.58861  WEIGHT= 0.1879710
   BAND#   7  E=  0.80969  WEIGHT= 0.1865482
   BAND#   8  E=  0.83200  WEIGHT= 0.1019824
   BAND#   9  E=  0.83200  WEIGHT= 0.1019824
   BAND#   1  E= -3.25227  WEIGHT= 0.7500000
   BAND#   2  E= -1.54015  WEIGHT= 0.7500000
   BAND#   3  E= -1.51595  WEIGHT= 0.7500000
   BAND#   4  E= -1.50813  WEIGHT= 0.7500000
   BAND#   5  E=  0.13902  WEIGHT= 0.7500000
   BAND#   6  E=  0.52475  WEIGHT= 0.7500000
   BAND#   7  E=  0.63523  WEIGHT= 0.7500000
   BAND#   8  E=  0.71248  WEIGHT= 0.7500000
   BAND#   9  E=  0.98758  WEIGHT=-0.0075898
   BAND#   1  E= -3.25371  WEIGHT= 0.3750000
   BAND#   2  E= -1.53522  WEIGHT= 0.3750000
   BAND#   3  E= -1.51754  WEIGHT= 0.3750000
   BAND#   4  E= -1.50160  WEIGHT= 0.3750000
   BAND#   5  E=  0.13833  WEIGHT= 0.3750000
   BAND#   6  E=  0.51271  WEIGHT= 0.3750000
   BAND#   7  E=  0.64842  WEIGHT= 0.3750000
   BAND#   8  E=  0.65307  WEIGHT= 0.3750000
   BAND#   9  E=  1.04897  WEIGHT=-0.0022389
   BAND#   1  E= -3.25089  WEIGHT= 0.0937500
   BAND#   2  E= -1.54388  WEIGHT= 0.0937500
   BAND#   3  E= -1.51460  WEIGHT= 0.0937500
   BAND#   4  E= -1.51460  WEIGHT= 0.0937500
   BAND#   5  E=  0.08511  WEIGHT= 0.0937500
   BAND#   6  E=  0.60765  WEIGHT= 0.0937500
   BAND#   7  E=  0.72329  WEIGHT= 0.0937500
   BAND#   8  E=  0.86574  WEIGHT= 0.0492509
   BAND#   9  E=  0.86574  WEIGHT= 0.0492509
   BAND#   1  E= -3.25084  WEIGHT= 0.1875000
   BAND#   2  E= -1.52943  WEIGHT= 0.1875000
   BAND#   3  E= -1.52943  WEIGHT= 0.1875000
   BAND#   4  E= -1.51581  WEIGHT= 0.1875000
   BAND#   5  E=  0.13981  WEIGHT= 0.1875000
   BAND#   6  E=  0.61914  WEIGHT= 0.1875000
   BAND#   7  E=  0.61914  WEIGHT= 0.1875000
   BAND#   8  E=  0.64556  WEIGHT= 0.1875000
   BAND#   9  E=  1.09991  WEIGHT=-0.0000029
   BAND#  10  E=  1.09991  WEIGHT=-0.0000029



Am 10.12.2010 14:16, schrieb Bin Shao:
> Dear Prof. Peter Blaha,
>
> Thank you for your suggestion!
>
> I check the "help" file and find the "weight", the following is the eigenvalue at GAMMA point and the Fermi energy is 0.61087 Ry.
>
>    BAND#  50  E=  0.60975  WEIGHT= 0.0090090
>    L= 0    0.00443       0.004     0.000     0.000     0.000     0.000
>    L= 1    0.00000       0.000     0.000     0.000     0.000     0.000
>      PX:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PY:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 2    0.00046       0.000     0.000     0.001     0.000     0.000
>     DZ2:   0.00046       0.000     0.000     0.001     0.000     0.000
>   DX2Y2:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DXY:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DXZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DYZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 3    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 4    0.00001       0.000     0.000     0.000     0.000     0.000
>    L= 5    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 6    0.00000       0.000     0.000     0.000     0.000     0.000
>    BAND#  51  E=  0.61232  WEIGHT= 0.0090090
>    L= 0    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 1    0.00000       0.000     0.000     0.000     0.000     0.000
>      PX:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PY:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 2    0.00109       0.001     0.000     0.004    -0.001    -0.001
>     DZ2:   0.00000       0.000     0.000     0.000     0.000     0.000
>   DX2Y2:   0.00108       0.001     0.000     0.004    -0.001    -0.001
>     DXY:   0.00001       0.000     0.000     0.000     0.000     0.000
>     DXZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DYZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 3    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 4    0.00010       0.000     0.000     0.000     0.000     0.000
>    L= 5    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 6    0.00000       0.000     0.000     0.000     0.000     0.000
>   BAND#  52  E=  0.62412  WEIGHT= 0.0090090
>    L= 0    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 1    0.11412       0.114     0.000     0.000     0.000     0.000
>      PX:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PY:   0.00000       0.000     0.000     0.000     0.000     0.000
>      PZ:   0.11412       0.114     0.000     0.000     0.000     0.000
>    L= 2    0.00000       0.000     0.000     0.000     0.000     0.000
>     DZ2:   0.00000       0.000     0.000     0.000     0.000     0.000
>   DX2Y2:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DXY:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DXZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>     DYZ:   0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 3    0.00069       0.001     0.000     0.000     0.000     0.000
>    L= 4    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 5    0.00000       0.000     0.000     0.000     0.000     0.000
>    L= 6    0.00000       0.000     0.000     0.000     0.000     0.000
>
> :FER  : F E R M I - ENERGY(TETRAH.M.)=   0.61087
>
> It seems the "WEIGHT" keeps the same at different bands, or I find it in the wrong place? For a metal, or I just should add the second column from L=0 to L=6 and that is the
> weight of this band? The integration should be done for all the bands in the energy window at one k-point and the occupied state should not be judge from the Fermi level because
> of partial occupations. Am I right?
>
> On Fri, Dec 10, 2010 at 5:41 PM, Peter Blaha <pblaha at theochem.tuwien.ac.at <mailto:pblaha at theochem.tuwien.ac.at>> wrote:
>
>     The "weight" files as well as the "help" files (option -help) contain the "integration weights"
>     for each k-point and eigenvalue.
>
>     Am 10.12.2010 09:30, schrieb Bin Shao:
>
>         Dear Prof. Peter Blaha,
>
>         Thank you for your quick reply!
>
>         I recheck the description of input file of lapw2 in UG and note the "efmod". But how to sum up eigenvalues at one single k-point in wien2k, can you give me some suggestions?
>
>         On Fri, Dec 10, 2010 at 4:08 PM, Peter Blaha <pblaha at theochem.tuwien.ac.at <mailto:pblaha at theochem.tuwien.ac.at> <mailto:pblaha at theochem.tuwien.ac.at
>         <mailto:pblaha at theochem.tuwien.ac.at>>> wrote:
>
>             No, state-tracking is not implemented.
>
>             Summing up eigenvalues "by hand" is not that easy for a metal.
>
>             You need to consider the different weights for different k-points, and
>             you need to consider that near EF some eigenvalues will not necessarily have
>             occupation 0/1, but better "integration methods" like TETRA or TEMP(S)
>             ( and not the primitive "root-sampling" which you attempt) will
>             lead to partial occupations of those states.
>
>             For sure, SO can change the occupation of some states and I don't see
>             anything "bad" by that.
>
>             Am 10.12.2010 08:25, schrieb Bin Shao:
>
>                 Dear all,
>
>                 According the force theorem method, we can calculate MAE by the following steps in wien2k:
>
>                    1. nosoc-scf
>                    2. x lapwso -up
>                    3. x lapw2 -so -up/dn
>                    4. add "SUM of EIGENVALUE" of spin-up and that of spin-dn
>                    5. get the difference of the above value with different directions of magnetization
>
>
>                 But when I intend to find the MAE contribution from different k-points, I encountered some problems. I tried to sum the eigenvalues at some special k-point
>         manually from the
>                 case.energysodn/up files and used the fermi energy to determine the occupied states. Next I sum the eigenvalue of this occupied states including spin-up and
>         spin-down and
>                 then get
>                 the difference of this values with different directions. In some cases, the contribution to MAE at a k-points maybe very large and the reason is that there may be
>         one less
>                 occupied band near the fermi level in one direction than another. I have check the references and found a method called state-tracking to avoid this.
>
>                 So here is my question, how does the wien2k code obtain the "SUM of EIGENVALUE" in lapw2 to avoid the problem mentioned above? Please give me some comments, thank
>         you in
>                 advanced!
>
>                 Best regards,
>
>                 --
>                 Bin Shao, Ph.D. Candidate
>                 College of Information Technical Science, Nankai University
>                 94 Weijin Rd. Nankai Dist. Tianjin 300071, China
>                 Email: binshao1118 at gmail.com <mailto:binshao1118 at gmail.com> <mailto:binshao1118 at gmail.com <mailto:binshao1118 at gmail.com>> <mailto:binshao1118 at gmail.com
>         <mailto:binshao1118 at gmail.com> <mailto:binshao1118 at gmail.com <mailto:binshao1118 at gmail.com>>>
>
>
>
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>             Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
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>         --
>         Bin Shao, Ph.D. Candidate
>         College of Information Technical Science, Nankai University
>         94 Weijin Rd. Nankai Dist. Tianjin 300071, China
>         Email: binshao1118 at gmail.com <mailto:binshao1118 at gmail.com> <mailto:binshao1118 at gmail.com <mailto:binshao1118 at gmail.com>>
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>                                           P.Blaha
>     --------------------------------------------------------------------------
>     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 <mailto:blaha at theochem.tuwien.ac.at>    WWW: http://info.tuwien.ac.at/theochem/
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> --
> Bin Shao, Ph.D. Candidate
> College of Information Technical Science, Nankai University
> 94 Weijin Rd. Nankai Dist. Tianjin 300071, China
> Email: binshao1118 at gmail.com <mailto:binshao1118 at gmail.com>
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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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