[QE-users] Irreducible set of k-points

Lukas Cvitkovich lukas.cvitkovich at physik.uni-regensburg.de
Mon Feb 10 14:13:34 CET 2025


Dear QE users and developers,

I am currently trying to reproduce the construction of an irreducible 
k-point set as done by QE.
For this, I set "verbosity = high" to get the symmetry operations 
printed in the output file.
I start from a uniform k-point mesh. Then, using the same symmetry 
operations as QE, I transform every k-point and fold it back in the 
first Brillouin zone.
If the resulting k-point falls on another k-point of the uniform grid, 
it is NOT irreducible.
In this manner, as also described by Blöchl et al (Phys. Rev. B *49*, 
16223, 1994) I find the set of irreducible kpoints.

My code agrees with QE for a simple structure (fcc crystal tested and 
verified) but I have problems with a more complicated case (the 2D 
magnet FGT).
In this example, 6 symmetry operations are found (see attached QE-output 
file).
Starting from a 3x3x3 uniform grid, the irreducible set of kpoints - 
according to QE - contains 7 points. However, I find 12 irreducible 
k-points.

First, please note, that every point found by QE is also contained in my 
set. But I find additional points which (according to QE) should be 
related by some symmetry operation. By looking at the weights, I could 
figure out which kpoints should belong together.
For instance: According to QE, the kpoints [1/3, 0, 0] and [2/3, 0, 0] 
are equivalent, as well as [0, 0, 1/3] and [0, 0, 2/3] should be 
equivalent too. I recognized that all the extra points could be 
transformed into each other by translating the lattice. However, 
applying all the symmetry operations from the QE output file (these are 
exclusively rotations and not translations), I cannot transform these 
points into each other. You might try for yourself.

So the question that I would like to ask is: Are there any "hidden" 
symmetry operations which are not explicitly printed in the output file? 
Could fractional translations be the reason? Is it maybe related to 
differences between point group and space group? Any other hints to what 
I am missing?

Thank you! Your help would be highly appreciated!

Best,
Lukas
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     Program PWSCF v.7.4 starts on  7Feb2025 at 16:19:20 

     This program is part of the open-source Quantum ESPRESSO suite
     for quantum simulation of materials; please cite
         "P. Giannozzi et al., J. Phys.:Condens. Matter 21 395502 (2009);
         "P. Giannozzi et al., J. Phys.:Condens. Matter 29 465901 (2017);
         "P. Giannozzi et al., J. Chem. Phys. 152 154105 (2020);
          URL http://www.quantum-espresso.org", 
     in publications or presentations arising from this work. More details at
     http://www.quantum-espresso.org/quote

     Parallel version (MPI), running on    24 processors

     MPI processes distributed on     1 nodes
     127903 MiB available memory on the printing compute node when the environment starts
 
     Reading input from scf.in
Warning: card &CELL ignored
Warning: card     CELL_DYNAMICS  = 'BFGS' ignored
Warning: card     CELL_DOFREE    = '2DXY' ignored
Warning: card / ignored

     Current dimensions of program PWSCF are:
     Max number of different atomic species (ntypx) = 10
     Max number of k-points (npk) =  40000
     Max angular momentum in pseudopotentials (lmaxx) =  4
     file Ge.pbe-dn-rrkjus_psl.1.0.0.UPF: wavefunction(s)  3D renormalized

     IMPORTANT: XC functional enforced from input :
     Exchange-correlation= SLA+PW
                           (   1   4   0   0   0   0   0)
     Any further DFT definition will be discarded
     Please, verify this is what you really want

 
     K-points division:     npool     =       4
     R & G space division:  proc/nbgrp/npool/nimage =       6
     Subspace diagonalization in iterative solution of the eigenvalue problem:
     a serial algorithm will be used

 
     Parallelization info
     --------------------
     sticks:   dense  smooth     PW     G-vecs:    dense   smooth      PW
     Min        1123     561    152               183807    64971    9090
     Max        1124     562    153               183814    64980    9101
     Sum        6739    3367    913              1102859   389843   54559
 
     Using Slab Decomposition
 


     bravais-lattice index     =            4
     lattice parameter (alat)  =       7.4575  a.u.
     unit-cell volume          =     884.6643 (a.u.)^3
     number of atoms/cell      =            6
     number of atomic types    =            3
     number of electrons       =        94.00
     number of Kohn-Sham states=           56
     kinetic-energy cutoff     =     220.0000  Ry
     charge density cutoff     =    1760.0000  Ry
     scf convergence threshold =      1.0E-08
     mixing beta               =       0.3000
     number of iterations used =            8  plain     mixing
     Exchange-correlation= SLA+PW
                           (   1   4   0   0   0   0   0)

     celldm(1)=   7.457458  celldm(2)=   0.000000  celldm(3)=   2.463063
     celldm(4)=   0.000000  celldm(5)=   0.000000  celldm(6)=   0.000000

     crystal axes: (cart. coord. in units of alat)
               a(1) = (   1.000000   0.000000   0.000000 )  
               a(2) = (  -0.500000   0.866025   0.000000 )  
               a(3) = (   0.000000   0.000000   2.463063 )  

     reciprocal axes: (cart. coord. in units 2 pi/alat)
               b(1) = (  1.000000  0.577350  0.000000 )  
               b(2) = (  0.000000  1.154701  0.000000 )  
               b(3) = (  0.000000  0.000000  0.405999 )  


     PseudoPot. # 1 for Fe read from file:
     ./pseudo/Fe.pbe-spn-rrkjus_psl.1.0.0.UPF
     MD5 check sum: 6cf5361654b607d62a57a685381c2429
     Pseudo is Ultrasoft + core correction, Zval = 16.0
     Generated using 'atomic' code by A. Dal Corso  v.7.2
     Using radial grid of 1191 points,  6 beta functions with: 
                l(1) =   0
                l(2) =   0
                l(3) =   1
                l(4) =   1
                l(5) =   2
                l(6) =   2
     Q(r) pseudized with 0 coefficients 


     PseudoPot. # 2 for Te read from file:
     ./pseudo/Te.pbe-dn-rrkjus_psl.1.0.0.UPF
     MD5 check sum: 42a6077563f7af19359f270fc7f1c196
     Pseudo is Ultrasoft + core correction, Zval = 16.0
     Generated using 'atomic' code by A. Dal Corso  v.7.2
     Using radial grid of 1245 points,  6 beta functions with: 
                l(1) =   0
                l(2) =   0
                l(3) =   1
                l(4) =   1
                l(5) =   2
                l(6) =   2
     Q(r) pseudized with 0 coefficients 


     PseudoPot. # 3 for Ge read from file:
     ./pseudo/Ge.pbe-dn-rrkjus_psl.1.0.0.UPF
     MD5 check sum: d6e2113101a05d0e4e89ac29a13a60ec
     Pseudo is Ultrasoft + core correction, Zval = 14.0
     Generated using 'atomic' code by A. Dal Corso  v.7.2
     Using radial grid of 1207 points,  6 beta functions with: 
                l(1) =   0
                l(2) =   0
                l(3) =   1
                l(4) =   1
                l(5) =   2
                l(6) =   2
     Q(r) pseudized with 0 coefficients 


     atomic species   valence    mass     pseudopotential
     Fe               16.00    55.84500     Fe( 1.00)
     Te               16.00   127.60000     Te( 1.00)
     Ge               14.00    72.64000     Ge( 1.00)

     Starting magnetic structure 
     atomic species   magnetization
     Fe              0.300
     Te              0.000
     Ge              0.000

      6 Sym. Ops. (no inversion) found


                                    s                        frac. trans.

      isym =  1     identity                                     

 cryst.   s( 1) = (     1          0          0      )
                  (     0          1          0      )
                  (     0          0          1      )

 cart.    s( 1) = (  1.0000000  0.0000000  0.0000000 )
                  (  0.0000000  1.0000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


      isym =  2     120 deg rotation - cryst. axis [0,0,1]       

 cryst.   s( 2) = (     0          1          0      )
                  (    -1         -1          0      )
                  (     0          0          1      )

 cart.    s( 2) = ( -0.5000000 -0.8660254  0.0000000 )
                  (  0.8660254 -0.5000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


      isym =  3     120 deg rotation - cryst. axis [0,0,-1]      

 cryst.   s( 3) = (    -1         -1          0      )
                  (     1          0          0      )
                  (     0          0          1      )

 cart.    s( 3) = ( -0.5000000  0.8660254  0.0000000 )
                  ( -0.8660254 -0.5000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


      isym =  4     inv. 180 deg rotation - cart. axis [1,0,0]   

 cryst.   s( 4) = (    -1          0          0      )
                  (     1          1          0      )
                  (     0          0          1      )

 cart.    s( 4) = ( -1.0000000  0.0000000  0.0000000 )
                  (  0.0000000  1.0000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


      isym =  5     inv. 180 deg rotation - cryst. axis [0,1,0]  

 cryst.   s( 5) = (     1          1          0      )
                  (     0         -1          0      )
                  (     0          0          1      )

 cart.    s( 5) = (  0.5000000  0.8660254  0.0000000 )
                  (  0.8660254 -0.5000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


      isym =  6     inv. 180 deg rotation - cryst. axis [1,1,0]  

 cryst.   s( 6) = (     0         -1          0      )
                  (    -1          0          0      )
                  (     0          0          1      )

 cart.    s( 6) = (  0.5000000 -0.8660254  0.0000000 )
                  ( -0.8660254 -0.5000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )


     point group C_3v (3m)  
     there are  3 classes
     the character table:

       E     2C3   3s_v 
A_1    1.00  1.00  1.00
A_2    1.00  1.00 -1.00
E      2.00 -1.00  0.00

     the symmetry operations in each class and the name of the first element:

     E        1
          identity                                               
     2C3      2    3
          120 deg rotation - cryst. axis [0,0,1]                 
     3s_v     4    5    6
          inv. 180 deg rotation - cart. axis [1,0,0]             

   Cartesian axes

     site n.     atom                  positions (alat units)
         1        Fe     tau(   1) = (   0.0000000   0.0000000   1.1161382  )
         2        Fe     tau(   2) = (   0.0000000   0.0000000   1.7301133  )
         3        Fe     tau(   3) = (   0.0000000   0.5773503   1.4231258  )
         4        Te     tau(   4) = (   0.0000000   0.5773503   0.7839756  )
         5        Te     tau(   5) = (   0.0000000   0.5773503   2.0622759  )
         6        Ge     tau(   6) = (   0.5000000   0.2886752   1.4231258  )

   Crystallographic axes

     site n.     atom                  positions (cryst. coord.)
         1        Fe     tau(   1) = (  0.0000000  0.0000000  0.4531506  )
         2        Fe     tau(   2) = (  0.0000000  0.0000000  0.7024236  )
         3        Fe     tau(   3) = (  0.3333334  0.6666667  0.5777871  )
         4        Te     tau(   4) = (  0.3333334  0.6666667  0.3182930  )
         5        Te     tau(   5) = (  0.3333334  0.6666667  0.8372812  )
         6        Ge     tau(   6) = (  0.6666667  0.3333334  0.5777871  )

     number of k points=     7  Marzari-Vanderbilt smearing, width (Ry)=  0.0200
                       cart. coord. in units 2pi/alat
        k(    1) = (   0.0000000   0.0000000   0.0000000), wk =   0.0370370
        k(    2) = (   0.0000000   0.0000000   0.1353329), wk =   0.0740741
        k(    3) = (   0.0000000   0.3849002   0.0000000), wk =   0.2222222
        k(    4) = (   0.0000000   0.3849002   0.1353329), wk =   0.2222222
        k(    5) = (   0.3333333   0.5773503   0.0000000), wk =   0.0740741
        k(    6) = (   0.3333333   0.5773503   0.1353329), wk =   0.1481481
        k(    7) = (   0.0000000  -0.3849002   0.1353329), wk =   0.2222222

                       cryst. coord.
        k(    1) = (   0.0000000   0.0000000   0.0000000), wk =   0.0370370
        k(    2) = (   0.0000000   0.0000000   0.3333333), wk =   0.0740741
        k(    3) = (   0.0000000   0.3333333   0.0000000), wk =   0.2222222
        k(    4) = (   0.0000000   0.3333333   0.3333333), wk =   0.2222222
        k(    5) = (   0.3333333   0.3333333   0.0000000), wk =   0.0740741
        k(    6) = (   0.3333333   0.3333333   0.3333333), wk =   0.1481481
        k(    7) = (   0.0000000  -0.3333333   0.3333333), wk =   0.2222222

     Dense  grid:  1102859 G-vectors     FFT dimensions: ( 100, 100, 250)

     Smooth grid:   389843 G-vectors     FFT dimensions: (  72,  72, 180)

     Dynamical RAM for                 wfc:       6.94 MB

     Dynamical RAM for     wfc (w. buffer):      34.71 MB

     Dynamical RAM for           str. fact:       8.41 MB

     Dynamical RAM for           local pot:       0.00 MB

     Dynamical RAM for          nlocal pot:      13.39 MB

     Dynamical RAM for                qrad:      10.09 MB

     Dynamical RAM for          rho,v,vnew:      36.05 MB

     Dynamical RAM for               rhoin:      12.02 MB

     Dynamical RAM for            rho*nmix:      89.75 MB

     Dynamical RAM for           G-vectors:      11.01 MB

     Dynamical RAM for          h,s,v(r/c):       0.57 MB

     Dynamical RAM for          <psi|beta>:       0.09 MB

     Dynamical RAM for                 psi:      13.88 MB

     Dynamical RAM for                hpsi:      13.88 MB

     Dynamical RAM for                spsi:      13.88 MB

     Dynamical RAM for      wfcinit/wfcrot:      13.96 MB

     Dynamical RAM for           addusdens:     137.43 MB

     Estimated static dynamical RAM per process >     156.13 MB

     Estimated max dynamical RAM per process >     383.31 MB

     Estimated total dynamical RAM >       7.41 GB
     Generating pointlists ...
     new r_m :   0.2382 (alat units)  1.7760 (a.u.) for type    1
     new r_m :   0.2636 (alat units)  1.9662 (a.u.) for type    2
     new r_m :   0.2382 (alat units)  1.7760 (a.u.) for type    3

     Initial potential from superposition of free atoms

     starting charge      93.9975, renormalised to      94.0000
     Starting wfcs are   57 randomized atomic wfcs

     total cpu time spent up to now is        6.2 secs

     Self-consistent Calculation

     iteration #  1     ecut=   220.00 Ry     beta= 0.30
     Davidson diagonalization with overlap

---- Real-time Memory Report at c_bands before calling an iterative solver
           271 MiB given to the printing process from OS
             0 MiB allocation reported by mallinfo(arena+hblkhd)
        123867 MiB available memory on the node where the printing process lives
------------------



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