[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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> P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-15671 FAX: +43-1-58801-15698
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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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