Full k point set

mfechner - 2019-11-18

Dear Harry,

I think the procedure would be to take the symmetry reduced set and than apply all operations listed in the SYMCRYS.OUT. Once this is done you should end up with the full k-point set. I assume that some of the k-points may appear several times.

best regards
Michael

Harry K - 2019-11-18

Dear Michael,

Okay, so SYMCRYS.OUT is the file I want. I'm not really sure what it means to "apply" these operations. What exactly do I need to apply them to?

Regards,
Harry

mfechner - 2019-11-18

what you have to do is

lets take the example here (short paste from my current project).
This is one symmetry operation of the crystal, where the spatial translation is a shift of the lattice (T) and the spatial rotation a rotation matrix (R). In this case the former is zero and the latter is a inversion and a mirror in principle.

Crystal symmetry : 2
spatial translation :
0.000000000 0.000000000 0.000000000
spatial rotation :
0 -1 0
-1 0 0
0 0 -1

next we take a k-point of my lattice of the reduced zone as listed in KPOINTS,OUT
like K=(0.5,0.5,0.5) and apply first the rotation and then the shift as
R.K+T=K'
where K' is now a symmetry equivalent point to the k-point K. If you perform this procedure to all your K-points you will finally get the list of all points in the brillouin zone and also how they are connected to each other. In principle this procedure is equivalent to the construction of a chemical zell from wykoff postions. There you also start from a single postion and than apply all generators of a specific Space Group (see->http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-getgen) to get the full crystal lattice.

Okay last point although I was pretty sure that the matrizies you need are contained in SYMCRYS it maybe also that they are within SYMLAT. There you only have the Rotational matrizies without the shift. Maybe you try out :-) and I would start from SYMLAT as this is already a very python compatible format.

best regards
Michael

Harry K - 2019-11-18

Thanks so much for the detailed explanation Michael, I'll give this a go!

Regards,
Harry

Dear Harry,

no problem, would be nice if you report back which file worked :-).

best regards
Michael

Last, one remark a great workshop for all the ''symmetry'' stuff is the bilbao crytallographic workshops as listed -->( http://www.cryst.ehu.es/cryst/workshops_and_schools.html ). They also teach you how to use their tools in all kind of ways. If you have time/founding it is definitly worth going.

Hi All,

I'm trying to understand how to go from the symmetry reduced set of k-points to the full set over the reciprocal unit cell (RUC). For example, for a articular calculation I set a 5x5x10 k point grid and let the code fully symmetry reduce this down to 30 irreducable k points (KPOINTS.OUT output below for reference).

Given the symmetry output of elk (SYMLAT, SYMCRYS etc), how do I go about getting the full set of 5x5x10=250 k-points from these 30? For a particular k-point in the 5x5x10 array which maps the full RUC, is there a easy way to figure out which of the 30 irreducable points it is equivalent to?

I hope this is clear, and thanks in advance!

Regards,
Harry

    30 : nkpt; k-point, vkl, wkpt, nmat below
     1   0.000000000       0.000000000       0.000000000      0.4000000000E-02     341
     2  0.2000000000       0.000000000       0.000000000      0.2400000000E-01     344
     3  0.4000000000       0.000000000       0.000000000      0.2400000000E-01     336
     4  0.2000000000      0.2000000000       0.000000000      0.2400000000E-01     335
     5  0.4000000000      0.2000000000       0.000000000      0.2400000000E-01     348
     6   0.000000000       0.000000000      0.1000000000      0.8000000000E-02     335
     7  0.2000000000       0.000000000      0.1000000000      0.4800000000E-01     339
     8  0.4000000000       0.000000000      0.1000000000      0.4800000000E-01     339
     9  0.2000000000      0.2000000000      0.1000000000      0.4800000000E-01     341
    10  0.4000000000      0.2000000000      0.1000000000      0.4800000000E-01     344
    11   0.000000000       0.000000000      0.2000000000      0.8000000000E-02     340
    12  0.2000000000       0.000000000      0.2000000000      0.4800000000E-01     341
    13  0.4000000000       0.000000000      0.2000000000      0.4800000000E-01     347
    14  0.2000000000      0.2000000000      0.2000000000      0.4800000000E-01     344
    15  0.4000000000      0.2000000000      0.2000000000      0.4800000000E-01     344
    16   0.000000000       0.000000000      0.3000000000      0.8000000000E-02     352
    17  0.2000000000       0.000000000      0.3000000000      0.4800000000E-01     346
    18  0.4000000000       0.000000000      0.3000000000      0.4800000000E-01     347
    19  0.2000000000      0.2000000000      0.3000000000      0.4800000000E-01     346
    20  0.4000000000      0.2000000000      0.3000000000      0.4800000000E-01     342
    21   0.000000000       0.000000000      0.4000000000      0.8000000000E-02     352
    22  0.2000000000       0.000000000      0.4000000000      0.4800000000E-01     342
    23  0.4000000000       0.000000000      0.4000000000      0.4800000000E-01     347
    24  0.2000000000      0.2000000000      0.4000000000      0.4800000000E-01     348
    25  0.4000000000      0.2000000000      0.4000000000      0.4800000000E-01     347
    26   0.000000000       0.000000000      0.5000000000      0.4000000000E-02     352
    27  0.2000000000       0.000000000      0.5000000000      0.2400000000E-01     342
    28  0.4000000000       0.000000000      0.5000000000      0.2400000000E-01     348
    29  0.2000000000      0.2000000000      0.5000000000      0.2400000000E-01     342
    30  0.4000000000      0.2000000000      0.5000000000      0.2400000000E-01     352