[Wien] Inconsistency in kgen

[Peter Blaha]

> However, when I look at the klist file with my understanding, I still 
> find myself confused. You mentioned that "this vector points 'outside' 
> the conventional 'cube,'" and I fully understand this statement. I 
> understand that Cartesian coordinates may extend beyond the 0..1 range. 
> However, what I am referring to are internal coordinates. In my 
> understanding, the point "64 6 6 6 4 1.0" lies outside the 0..1 range of 
> internal coordinates, which means it is outside the reciprocal unit 
> cell. Therefore, in my understanding, this point needs to be mapped into 
> the reciprocal unit cell.

The klist file gives the k-point in cartesian fractional coordinates in 
the reciprocal lattice, not in internal coordinates .

> 
> However, after it is mapped into the reciprocal unit cell, I believe it 
> is equivalent to the point "22 2 2 2 4 1.0."

No !  In cartesian coordinates the BZ does NOT go from 0 to 1 !!!

As I wrote before, the transformation is done via multiplication of the 
vector with one of the bravais matrices listed in outputkgen.


  Yet, for an FBZ klist, I
> believe there shouldn't be two equivalent k points, and indeed, in 
> output1, the eigenvalues of these two points are different.
> 
> So, I have been requesting if you could provide the internal coordinates 
> for these two points, as well as the transformation formula. I believe 
> only by doing so can my confusion be resolved.
> 
> Thank you again for your assistance.
> 
> Best regards
> 
> 
> ------------------ Original ------------------
> From: "A Mailing list for WIEN2k users" <peter.blaha at tuwien.ac.at>;
> Date: Fri, Mar 22, 2024 04:36 PM
> To: "wien"<wien at zeus.theochem.tuwien.ac.at>;
> Subject: Re: [Wien] Inconsistency in kgen
> 
> In outputkgen the direct and reciprocal bravais matrices are printed.
> They can be used to multiply the corresponding vectors (coordinates) and
> transfer them.
> For instance for B (body-centered) lattices the Bravaismatrix is:
> (-1 1 1
>    1 -1 1
>    1 1 -1 )   times the lattice constants a,b,c.
> 
> So the first primitive lattice vector (0,0,1) looks in kartesian
> coordinates as (-1,1,1) (always times a,b,c). Thus you can immediately
> "see", that this vector points "outside" the conventional "cube".
> 
> In essence, this is the reason why some coordinates in carthesian
> coordinates are outside the "cube" (outside (0 ... 1))
> 
> I guess, this is enough "geometry" and introduction ....
> 
> Am 22.03.2024 um 09:14 schrieb balabi via Wien:
>  > Dear Prof. Peter Blaha,
>  >
>  > I hope this message finds you well.
>  >
>  > I wanted to express my gratitude for your prompt reply. I truly
>  > appreciate the time and effort you have taken to assist me with my query.
>  >
>  > However, I apologize for any misunderstanding. While I do have a grasp
>  > of the concepts surrounding internal and Cartesian coordinates as
>  > mentioned in your previous email, the mention of the "common
>  > denominator" is new to me.
>  >
>  > Would it be possible for you to provide me with the formula for
>  > transitioning from casename.klist to the internal coordinates within the
>  > first reciprocal unit cell, as I had mentioned in my previous
>  > correspondence? This information would greatly aid in clarifying my
>  > understanding, particularly in relation to the following k points:
>  > 22     2      2     2    4   1.0
>  > and
>  > 64     6      6     6    4   1.0
>  > Knowing their corresponding internal coordinates would be immensely
>  > helpful in resolving any confusion I may have.
>  >
>  > Once again, I sincerely appreciate your assistance with this matter.
>  >
>  > Thank you very much for your time and consideration.
>  >
> 
> 
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-- 
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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
WWW:   http://www.imc.tuwien.ac.at
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