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 Bl?chl 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>>> > > > > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at <mailto:Wien at > zeus.theochem.tuwien.ac.at> <mailto:Wien at zeus.theochem.tuwien.ac.at > <mailto:Wien at zeus.theochem.tuwien.ac.at>> > > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > > > -- > > 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> <mailto:blaha at theochem.tuwien.ac.at <mailto:blaha > at theochem.tuwien.ac.at>> WWW: > http://info.tuwien.ac.at/theochem/ > > -------------------------------------------------------------------------- > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at <mailto:Wien at > zeus.theochem.tuwien.ac.at> <mailto:Wien at zeus.theochem.tuwien.ac.at > <mailto:Wien at zeus.theochem.tuwien.ac.at>> > > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > > > > > -- > 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>> > > > > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at <mailto:Wien at > zeus.theochem.tuwien.ac.at> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > > > -- > > 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/ > -------------------------------------------------------------------------- > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at <mailto:Wien at > zeus.theochem.tuwien.ac.at> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > > > > > -- > 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> > > > > _______________________________________________ > Wien mailing list > Wien at zeus.theochem.tuwien.ac.at > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien -- 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 WWW: http://info.tuwien.ac.at/theochem/ --------------------------------------------------------------------------