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.bl...@tuwien.ac.at>;
*Date:* Thu, Mar 21, 2024 03:48 PM
*To:* "wien"<wien@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).
_______________________________________________
Wien mailing list
Wien@zeus.theochem.tuwien.ac.at
http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
SEARCH the MAILING-LIST at:
http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
--
--------------------------------------------------------------------------
Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300
Email: peter.bl...@tuwien.ac.at WIEN2k: http://www.wien2k.at
WWW: http://www.imc.tuwien.ac.at
-------------------------------------------------------------------------
_______________________________________________
Wien mailing list
Wien@zeus.theochem.tuwien.ac.at
http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
SEARCH the MAILING-LIST at:
http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
