Re: [Wien] Inconsistency in kgen

balabi via Wien Thu, 21 Mar 2024 22:38:12 -0700

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:


&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0 -7.0&nbsp; 1.5&nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp;0 k, div: (&nbsp; 4&nbsp; 4&nbsp; 4)
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;9&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 10&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 11&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 12&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 13&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 14&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 15&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 16&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 17&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 18&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 19&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 20&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 21&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 22&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
...
...
&nbsp; &nbsp; &nbsp; &nbsp; 62&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 63&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
&nbsp; &nbsp; &nbsp; &nbsp; 64&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp;4&nbsp; 1.0
END





In the output from kgen, there's a block labeled "internal and cartesian 
k-vectors" which states:


&nbsp; internal and cartesian k-vectors:
&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; 
&nbsp;0.00000
&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.25000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.22411&nbsp; &nbsp;0.22411&nbsp; 
&nbsp;0.00000
&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.50000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.44822&nbsp; &nbsp;0.44822&nbsp; 
&nbsp;0.00000
&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.00000&nbsp; &nbsp;0.75000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.67233&nbsp; &nbsp;0.67233&nbsp; 
&nbsp;0.00000
...
...
&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.00000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.67233&nbsp; &nbsp;0.67233&nbsp; 
&nbsp;0.18668
&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.25000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.89644&nbsp; &nbsp;0.89644&nbsp; 
&nbsp;0.18668
&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.50000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1.12055&nbsp; &nbsp;1.12055&nbsp; 
&nbsp;0.18668
&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.75000&nbsp; &nbsp;0.75000&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1.34465&nbsp; &nbsp;1.34465&nbsp; 
&nbsp;0.18668
&nbsp; NO. OF INEQUIVALENT K-POINTS&nbsp; &nbsp; 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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;0&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; 1.0
I think this corresponds to internal coordinate
0.25000&nbsp; &nbsp;0.25000&nbsp; &nbsp;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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;6&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; 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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;64&nbsp; &nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4&nbsp; &nbsp; 
&nbsp; &nbsp; &nbsp; &nbsp;4
&nbsp; 0.500000000000000&nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp;0.00000&nbsp; &nbsp; &nbsp;0.00000&nbsp; &nbsp; 
&nbsp;0.00000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
0.00000&nbsp; &nbsp; &nbsp; 0.00000&nbsp; &nbsp; &nbsp; 0.00000
&nbsp; &nbsp; &nbsp;0.25000&nbsp; &nbsp; &nbsp;0.25000&nbsp; &nbsp; 
&nbsp;0.00000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
2.00000&nbsp; &nbsp; &nbsp; 2.00000&nbsp; &nbsp; &nbsp; 0.00000
&nbsp; &nbsp; &nbsp;0.50000&nbsp; &nbsp; &nbsp;0.50000&nbsp; &nbsp; 
&nbsp;0.00000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
4.00000&nbsp; &nbsp; &nbsp; 4.00000&nbsp; &nbsp; &nbsp; 0.00000
&nbsp; &nbsp; &nbsp;0.75000&nbsp; &nbsp; &nbsp;0.75000&nbsp; &nbsp; 
&nbsp;0.00000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
6.00000&nbsp; &nbsp; &nbsp; 6.00000&nbsp; &nbsp; &nbsp; 0.00000
...
...
&nbsp; &nbsp; &nbsp;0.75000&nbsp; &nbsp; &nbsp;0.75000&nbsp; &nbsp; 
&nbsp;1.50000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
6.00000&nbsp; &nbsp; &nbsp; 6.00000&nbsp; &nbsp; &nbsp;12.00000
&nbsp; &nbsp; &nbsp;1.00000&nbsp; &nbsp; &nbsp;1.00000&nbsp; &nbsp; 
&nbsp;1.50000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
8.00000&nbsp; &nbsp; &nbsp; 8.00000&nbsp; &nbsp; &nbsp;12.00000
&nbsp; &nbsp; &nbsp;1.25000&nbsp; &nbsp; &nbsp;1.25000&nbsp; &nbsp; 
&nbsp;1.50000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp;10.00000&nbsp; &nbsp; &nbsp;10.00000&nbsp; &nbsp; &nbsp;12.00000
&nbsp; &nbsp; &nbsp;1.50000&nbsp; &nbsp; &nbsp;1.50000&nbsp; &nbsp; 
&nbsp;1.50000&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 
&nbsp;12.00000&nbsp; &nbsp; &nbsp;12.00000&nbsp; &nbsp; &nbsp;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





------------------&nbsp;Original&nbsp;------------------
From:                                                                           
                                             "A Mailing list for WIEN2k users"  
                                                                                
  <peter.bl...@tuwien.ac.at&gt;;
Date:&nbsp;Thu, Mar 21, 2024 03:48 PM
To:&nbsp;"wien"<wien@zeus.theochem.tuwien.ac.at&gt;;

Subject:&nbsp;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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Re: [Wien] Inconsistency in kgen

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