[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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