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.
best regards
------------------------------------------------------------------------
------------------ Original ------------------
From: "A Mailing list for WIEN2k users" <peter.bl...@tuwien.ac.at>;
Date: Fri, Mar 22, 2024 03:17 PM
To: "wien"<wien@zeus.theochem.tuwien.ac.at>;
Subject: Re: [Wien] Inconsistency in kgen
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.
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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
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