[Wien] Inconsistency in kgen

[balabi]

Dear Prof. Peter Blaha,

Thank you very much for your reply. I apologize if I may have been a bit persistent, but unfortunately, the issue still persists. Your recent emails have been explaining concepts that I already understand, or at least, I believe I fully comprehend the explanations of internal coordinates and Cartesian coordinates you provided in those emails.

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.

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." 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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