[Wien] Equivalence Problem in Wien2k? (wien97 was correct)
Peter Blaha
pblaha at theochem.tuwien.ac.at
Fri Oct 27 09:49:56 CEST 2006
Hi,
You dedected a very interesting problem (unfortunately you did not use the
mailing list, this discussion should be of interest for others
too).
It appears in this symmetry when you have a k-mesh with "odd" divisions
AND a shift. I guess you have used 4000 k-points, leading to 15 15 15 div
and 120 k-points.
(It does NOT appear with even meshes, eg. 4500 k leading to 16 16 16 div
and again to 120 k-points.
The problem is that at/near EF at the BZ boundary there is some accidental
degeneracy in the eigenvalues. Due to the tetrahedral method these states
do NOT necessarely have the same "weights" (since they are connected to 2
different "bands"), but the wave function of degenerate states are quite
arbitrary linear combinations and it can happen, that in E1 atom1 has a
large charge, while in E2 the other atom has the large weight. However, if
these 2 eigenvalues are not included with the same weight in the BZ
integration, this leads effectively to different charges (moments) for
these two atoms.
I list below an example from the helpXXX files. As you can see, the
charges for the 2 atoms and eigenvalues are just mirrored, but since the
weights are different, the integral over the BZ will be also different.
help31dn:
K-POINT: 0.1000 0.3667 0.5000 100 24 61
BAND# 15 E= 0.48531 WEIGHT=-0.0005082
L= 0 0.51413 0.514 0.000 0.000 0.000 0.000
L= 1 1.32898 1.328 0.001 0.000 0.000 0.000
L= 2 60.21496 59.562 0.653 0.000 0.000 0.000
D-EG: 39.43032 39.008 0.423 0.000 0.000 0.000
D-T2G: 20.78465 20.554 0.231 0.000 0.000 0.000
L= 3 0.03920 0.039 0.000 0.000 0.000 0.000
L= 4 0.01850 0.018 0.000 0.000 0.000 0.000
L= 5 0.00424 0.004 0.000 0.000 0.000 0.000
L= 6 0.00570 0.006 0.000 0.000 0.000 0.000
BAND# 16 E= 0.48531 WEIGHT=-0.0000944
L= 0 0.15397 0.154 0.000 0.000 0.000 0.000
L= 1 1.50655 1.506 0.001 0.000 0.000 0.000
L= 2 32.88219 32.522 0.361 0.000 0.000 0.000
D-EG: 11.80890 11.682 0.127 0.000 0.000 0.000
D-T2G: 21.07329 20.839 0.234 0.000 0.000 0.000
L= 3 0.03870 0.039 0.000 0.000 0.000 0.000
L= 4 0.02843 0.028 0.000 0.000 0.000 0.000
L= 5 0.00513 0.005 0.000 0.000 0.000 0.000
L= 6 0.01108 0.011 0.000 0.000 0.000 0.000
help32dn:
BAND# 15 E= 0.48531 WEIGHT=-0.0005082
L= 0 0.15397 0.154 0.000 0.000 0.000 0.000
L= 1 1.50655 1.506 0.001 0.000 0.000 0.000
L= 2 32.88219 32.522 0.361 0.000 0.000 0.000
D-EG: 11.80890 11.682 0.127 0.000 0.000 0.000
D-T2G: 21.07329 20.839 0.234 0.000 0.000 0.000
L= 3 0.03870 0.039 0.000 0.000 0.000 0.000
L= 4 0.02843 0.028 0.000 0.000 0.000 0.000
L= 5 0.00513 0.005 0.000 0.000 0.000 0.000
L= 6 0.01108 0.011 0.000 0.000 0.000 0.000
BAND# 16 E= 0.48531 WEIGHT=-0.0000944
L= 0 0.51413 0.514 0.000 0.000 0.000 0.000
L= 1 1.32898 1.328 0.001 0.000 0.000 0.000
L= 2 60.21496 59.562 0.653 0.000 0.000 0.000
D-EG: 39.43032 39.008 0.423 0.000 0.000 0.000
D-T2G: 20.78465 20.554 0.231 0.000 0.000 0.000
L= 3 0.03920 0.039 0.000 0.000 0.000 0.000
L= 4 0.01850 0.018 0.000 0.000 0.000 0.000
L= 5 0.00424 0.004 0.000 0.000 0.000 0.000
L= 6 0.00570 0.006 0.000 0.000 0.000 0.000
I've NOT seen any problem with an even k-mesh, most likely because this
"sticking together" of bands appears only at the BZ boundary.
(I don't know if this is a general rule or happened only for this
particular symmetry just by accident)
So in summary: use an "even" k-mesh, or use a different FERMI method
(TEMP), which should not show this either.
PS: I don't quite understand why WIEN97 does not show this problem.
Eventually you did NOT use identical k-meshes (120 k can be 2 different
meshes!!)
> Dear Prof. Blaha,
>
> I am using the Wien2k-code for Myron Evans (who bought it).
> Perhaps there might be an error in the calculations, which I would
> like to describe to you very short:
> I set up a case of two Nickel atoms not in bcc-structure, but in
> simple cubic structure with basis, i.e. one atom at (0,0,0) and one
> at (0.5,0.5,0.5), which should be equivalent.
> But the self consistent calculations, even well converged, show
> different charge partitions of the two atoms. Perhaps I understood
> something wrong?! On the other hand, the same calculations carried
> out with Wien97-code show more or less the same charges
> for the two atoms in the cell, which I would expect. I have put the
> regarding files (*.inst, *.struct, *.scf) as attachment to this mail.
>
> Wien2k:
> :CUP001: SPIN-UP CHARGE IN SPHERE 1 = 13.7938142
> :CUP002: SPIN-UP CHARGE IN SPHERE ! 2 = 13.8059628
> :CDN001: SPIN-DN CHARGE IN SPHERE 1 = 13.2381990
> :CDN002: SPIN-DN CHARGE IN SPHERE 2 = 13.2249933
> :CTO001: TOTAL CHARGE IN SPHERE 1 = 27.0320132
> :CTO002: TOTAL CHARGE IN SPHERE 2 = 27.0309561
>
> Wien97:
> :CUP01: SPIN-UP CHARGE IN SPHERE 1 = 13.7982366
> :CUP02: SPIN-UP CHARGE IN SPHERE 2 = 13.7979511
> :CDN01: SPIN-DN CHARGE IN SPHERE 1 = 13.2383573
> :CDN02: SPIN-DN CHARGE IN SPHERE 2 = 13.2383438
> :CTO01: TOTAL CHARGE IN SPHERE 1 = 27.0365939
> :CTO02: TOTAL CHARGE IN SPHERE 2 = 27.0362949
>
>
> A last short question: if I compare the DOS of the bcc-calculation
> with the sc+basis calculation (now both with Wien97), which
> should be more or less equal again, there are some differences,
> which a not disappear with more planewaves or a higher grade
> of convergence. Do you have an idea of the origin of this differences?
> (please see scni.ps in the at! tachment)
>
> Thank you very much and best regards,
> Jost Koller
>
>
>
>
>
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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