[Wien] Inconsistency in kgen
Peter Blaha
peter.blaha at tuwien.ac.at
Fri Mar 22 08:17:52 CET 2024
Come on !
You can specify coordinates in absolute units, or in fractions of the
(reciprocal) lattice vectors.
E.g. an atom position can be given as (3.123,2.332,1.966) in units of
Ang; or as (0.5,0.5,0.5) in units of a,b, and c.
This is exactly what is done in outputkgen.
0.00000 0.00000 0.25000 0.22411 0.22411 0.00000
fractions of primitive rec.lattice carthes. coord (bohr^-1)
0.25000 0.25000 0.00000 2.00000 2.00000 0.00000
fractional carth. coord same as left, but multiplied by 8 to
find a common denominator.
Am 22.03.2024 um 06:21 schrieb balabi via Wien:
> Dear Prof. Peter Blaha,
>
> Thank you so much for your reply. But I think you might have
> misunderstood me. I understand the difference between internal and
> cartesian coordinates.
>
> Let me take for example, Let us generate 4x4x4 mesh by 'x kgen -fbz' for
> CaFe2As2 I4/mmm structure. The klist is as below:
>
> 1 0 0 0 4 1.0 -7.0 1.5
> 0 k, div: ( 4 4 4)
> 2 1 1 0 4 1.0
> 3 2 2 0 4 1.0
> 4 3 3 0 4 1.0
> 5 1 0 1 4 1.0
> 6 2 1 1 4 1.0
> 7 3 2 1 4 1.0
> 8 4 3 1 4 1.0
> 9 2 0 2 4 1.0
> 10 3 1 2 4 1.0
> 11 4 2 2 4 1.0
> 12 5 3 2 4 1.0
> 13 3 0 3 4 1.0
> 14 4 1 3 4 1.0
> 15 5 2 3 4 1.0
> 16 6 3 3 4 1.0
> 17 0 1 1 4 1.0
> 18 1 2 1 4 1.0
> 19 2 3 1 4 1.0
> 20 3 4 1 4 1.0
> 21 1 1 2 4 1.0
> 22 2 2 2 4 1.0
> ...
> ...
> 62 4 4 6 4 1.0
> 63 5 5 6 4 1.0
> 64 6 6 6 4 1.0
> END
>
> In the output from kgen, there's a block labeled "internal and cartesian
> k-vectors" which states:
>
> internal and cartesian k-vectors:
> 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
> 0.00000 0.00000 0.25000 0.22411 0.22411 0.00000
> 0.00000 0.00000 0.50000 0.44822 0.44822 0.00000
> 0.00000 0.00000 0.75000 0.67233 0.67233 0.00000
> ...
> ...
> 0.75000 0.75000 0.00000 0.67233 0.67233 0.18668
> 0.75000 0.75000 0.25000 0.89644 0.89644 0.18668
> 0.75000 0.75000 0.50000 1.12055 1.12055 0.18668
> 0.75000 0.75000 0.75000 1.34465 1.34465 0.18668
> NO. OF INEQUIVALENT K-POINTS 64
>
> I clearly understand this "internal and cartesian k-vectors" block. The
> left three columns represent coordinates relative to reciprocal vectors,
> and the right three columns are coordinates in Cartesian, i.e.,
> {x,y,z}.reciprocalVectorMatrix. All coordinates are unique and appear
> very reasonable.
>
> However, my confusion arises with the k-list. It seems that the order of
> this block is not the same as that in the k-list file. For example, the
> second line in the k-list is:
> 2 1 1 0 4 1.0
> I think this corresponds to internal coordinate
> 0.25000 0.25000 0.00000
> right? But this is not the 2nd line in "internal and cartesian
> k-vectors" block. Why is that?
> Also, what is the relation between "internal and cartesian k-vectors"
> block and klist? Why are they in different order?
>
> Moreover, regarding the last line in the k-list:
> 64 6 6 6 4 1.0
> What internal coordinate does it correspond to? Given that {6,6,6} is
> outside the 4x4x4 range, should we not modulo it by 4 to get {2,2,2},
> which corresponds to 0.50000 0.50000 0.50000? If this is correct, then
> this 64th point is a duplication of the 22nd point in the k-list. Why,
> then, are the eigenvalues on the 22nd and 64th k points different? If
> WIEN2k is using the correct k point, it suggests my understanding is
> incorrect. Could you please provide me with a formula to convert x, y, z
> in the klist to the correct internal coordinates for this particular
> case? This would help me understand where my error lies.
>
> Finally, in the last part of outputkgen, there is a block says
> NKP,NDIV,afact 64 4 4 4
> 0.500000000000000
> 0.00000 0.00000 0.00000 0.00000
> 0.00000 0.00000
> 0.25000 0.25000 0.00000 2.00000
> 2.00000 0.00000
> 0.50000 0.50000 0.00000 4.00000
> 4.00000 0.00000
> 0.75000 0.75000 0.00000 6.00000
> 6.00000 0.00000
> ...
> ...
> 0.75000 0.75000 1.50000 6.00000
> 6.00000 12.00000
> 1.00000 1.00000 1.50000 8.00000
> 8.00000 12.00000
> 1.25000 1.25000 1.50000 10.00000
> 10.00000 12.00000
> 1.50000 1.50000 1.50000 12.00000
> 12.00000 12.00000
>
> The left three columns is just 2nd,3rd,4th column of klist divided by 4,
> but what is the meaning of the right 3 columns?
>
> best regards
>
>
> ------------------ Original ------------------
> *From:* "A Mailing list for WIEN2k users" <peter.blaha at tuwien.ac.at>;
> *Date:* Thu, Mar 21, 2024 03:48 PM
> *To:* "wien"<wien at zeus.theochem.tuwien.ac.at>;
> *Subject:* Re: [Wien] Inconsistency in kgen
>
> Hi,
> No, you should not modify the kmesh.
> The k-vectors are generated in the primitive (non-orthogonal) basis, but
> transformed afterwards to carthesian coordinates.
> By this operation, some of the k-points may obtain values larger than one.
> Note, that in carthesian coordinates, the BZ does not go from 0-1 in
> kx,ky,kz.
> You also noted that (0,0,0) yields different eigenvalues than (1,1,1).
>
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300
Email: peter.blaha at tuwien.ac.at WIEN2k: http://www.wien2k.at
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