Force constants calculation with cutoff pair-distance#
Here the detail of the command option –cutoff_pair is explained.
See also a reference paper.
What is cutff pair-distance in phono3py?#
Using --cutoff-pair option, number of supercells with
displacements to be calculated is reduced. But of course this
sacrifices the accuracy of third-order force constants (fc3).
In phono3py, to obtain supercell-fc3, \(\Phi_{\alpha\beta\gamma}(jl, j'l', j''l'')\), forces in many supercells having different pairs of displaced atoms are computed using some force-calculator such as ab-initio code. In the phono3py default behaviour, full elements of supercell-fc3 are computed. In this case, though depending on the number of atoms in the supercell and the crystal symmetry, the number of atomic-pair configuration can be huge and beyond our computational resource.
Sometimes we may expect that interaction range of fc3 among triplets
of atoms is shorter than chosen supercell size. If it is the case, we
may be allowed to omit computing some elements of supercell-fc3. This
is what achieved by --cutoff-pair option.
A supercell-fc3 element is specified by three atomic displacements. Two of three are finitely displaced (\(\Delta\mathbf{r}_1\) and \(\Delta\mathbf{r}_2\)) but one of them is included in a force given by the force calculator such as \(\mathbf{F}_3=-\frac{\partial V}{\partial\mathbf{r}_3}\). The cutoff distance \(d_\text{cut}\) is defined as the upper bound of the distance between the atoms 1 and 2. By this, the set of atomic pairs \(\{(\mathbf{r}_1,\mathbf{r}_2)| |\mathbf{r}_1 - \mathbf{r}_2| < d_\text{cut}\}\) is selected for the supercell-fc3 calculation. By this, when three distances among the three atoms of triplets are all larger than \(d_\text{cut}\), those fc3 elements can not be obtained and so they are simply set zero.
Usage#
Creating supercells with displacements#
--cutoff-pair option is employed when creating supercells with
displacements, therefore this option must be used with -d option
when running phono3py, for the Si-PBEsol example:
% phono3py --cutoff-pair=5 -d --dim="2 2 2" -c POSCAR-unitcell
...
Unit cell was read from "POSCAR-unitcell".
Displacement distance: 0.03
Number of displacements: 111
Cutoff distance for displacements: 5.0
Number of displacement supercell files created: 51
Displacement dataset was written in "phono3py_disp.yaml".
...
% ls POSCAR-0*
POSCAR-00001 POSCAR-00032 POSCAR-00043 POSCAR-00080 POSCAR-00097
POSCAR-00002 POSCAR-00033 POSCAR-00070 POSCAR-00081 POSCAR-00098
POSCAR-00003 POSCAR-00034 POSCAR-00071 POSCAR-00082 POSCAR-00099
POSCAR-00016 POSCAR-00035 POSCAR-00072 POSCAR-00083 POSCAR-00100
POSCAR-00017 POSCAR-00036 POSCAR-00073 POSCAR-00084 POSCAR-00101
POSCAR-00018 POSCAR-00037 POSCAR-00074 POSCAR-00085 POSCAR-00102
POSCAR-00019 POSCAR-00038 POSCAR-00075 POSCAR-00086 POSCAR-00103
POSCAR-00024 POSCAR-00039 POSCAR-00076 POSCAR-00087
POSCAR-00025 POSCAR-00040 POSCAR-00077 POSCAR-00088
POSCAR-00026 POSCAR-00041 POSCAR-00078 POSCAR-00089
POSCAR-00027 POSCAR-00042 POSCAR-00079 POSCAR-00096
% ls POSCAR-0*|wc -l
51
Number of displacements: 111 shows the number of supercells with
displacements when this is run without --cutoff-pair
option. Number of displacement supercell files created: 51 gives
the contracted number of supercells with displacements by
--cutoff-pair option. There number of POSCAR-0xxxx files is found 51.
At this step, a special phono3py_disp.yaml is created. This
contains information on this contraction and used in the other
calculation step, therefore this file must be kept carefully.
Supercell files#
POSCAR-xxxxx (in the other calculator interface, the prefix of the
filename is different) are not generated if distance between a pair of
atoms to be displaced is larger than the specified cutoff pair
distance. The indexing number (xxxxx) corresponds to that of the
case without setting this option, i.e., the same POSCAR-xxxxx
files are created for the same configurations of pairs of
displacements but POSCAR-xxxxx files not being included are not
generated. The reason of this indexing is that it can be useful when
changing the cutoff-pair-distance.
Special phono3py_disp.yaml#
Using --cutoff-pair option together with -d option, a special
phono3py_disp.yaml is created. This contains information on distances
between displaced atomic-pairs and whether those pairs are to be
computed or not. This special phono3py_disp.yaml is necessary to create
fc3, therefore be careful not to overwrite it by running the option
-d without --cutoff-pair or with different --cutoff-pair
with different value.
Making FORCES_FC3#
To create FORCES_FC3, only output files of the supercells created
using --cutoff-pair option are passed to phono3py as the
arguments. The special phono3py_disp.yaml file is necessary to be
located at current directory.
An example is shown below for the Si example. Here, it is supposed
that forces are calculated using VASP in disp-xxxxx
directories. After running force calculations, there should be the
output file containing forces in each directory (for VASP
vasprun.xml).
% phono3py --cf3 disp-{00001,00002,00003,00016,00017,00018,00019,00024,00025,00026,00027,00032,00033,00034,00035,00036,00037,00038,00039,00040,00041,00042,00043,00070,00071,00072,00073,00074,00075,00076,00077,00078,00079,00080,00081,00082,00083,00084,00085,00086,00087,00088,00089,00096,00097,00098,00099,00100,00101,00102,00103}/vasprun.xml
...
Displacement dataset is read from phono3py_disp.yaml.
counter (file index): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
FORCES_FC3 has been created.
Using –cf3-file option may be recommended when the number of force files is large.
% for i in `ls POSCAR-0*|sed s/POSCAR-//`;do echo disp-$i/vasprun.xml;done > file_list.dat
% phono3py --cf3-file file_list.dat
Using a python script, phono3py_disp.yaml is easily parsed. So
it is also easy to create the file list by a python
script:
#!/usr/bin/env python
from phono3py.interface.phono3py_yaml import Phono3pyYaml
p3yaml = Phono3pyYaml()
p3yaml.read("phono3py_disp.yaml")
dds = p3yaml.dataset
file_name_tmpl = "disp-%05d/vasprun.xml"
count = 1
for d1 in dds['first_atoms']:
print(file_name_tmpl % count)
count += 1
for d1 in dds['first_atoms']:
for d2 in d1['second_atoms']:
if d2['included']:
print(file_name_tmpl % count)
count += 1
Running phonon-phonon interaction calculation#
To create fc3, --cutoff-pair option is not necessary but the
special phono3py_disp.yaml is required.
% phono3py
...
----------------------------- General settings -----------------------------
Run mode: None
HDF5 data compression filter: gzip
Crystal structure was read from "phono3py_disp.yaml".
Supercell (dim): [2 2 2]
Primitive matrix:
[0. 0.5 0.5]
[0.5 0. 0.5]
[0.5 0.5 0. ]
Spacegroup: Fd-3m (227)
Use -v option to watch primitive cell, unit cell, and supercell structures.
----------------------------- Force constants ------------------------------
Imposing translational and index exchange symmetry to fc2: False
Imposing translational and index exchange symmetry to fc3: False
Imposing symmetry of index exchange to fc3 in reciprocal space: False
Displacement dataset for fc3 was read from "phono3py_disp.yaml".
Sets of supercell forces were read from "FORCES_FC3".
Computing fc3[ 1, x, x ] using numpy.linalg.pinv with a displacement:
[ 0.0300 0.0000 0.0000]
Expanding fc3.
Cutting-off fc3 (cut-off distance: 5.000000)
Building atom mapping table...
Creating contracted fc3...
Writing fc3 to "fc3.hdf5".
Max drift of fc3: 0.047748 (yxz) 0.047748 (xyz) 0.047748 (xzy)
Displacement dataset for fc2 was read from "phono3py_disp.yaml".
Sets of supercell forces were read from "FORCES_FC3".
Writing fc2 to "fc2.hdf5".
Max drift of fc2: -0.000001 (zz) -0.000001 (zz)
----------- None of ph-ph interaction calculation was performed. -----------
Summary of calculation was written in "phono3py.yaml".
...
Once fc3.hdf5 and fc2.hdf5 are created, --cutoff-pair
option and the special phono3py_disp.yaml are not needed anymore.
% phono3py --mesh="11 11 11" --fc3 --fc2 --br
...
300.0 108.051 108.051 108.051 0.000 0.000 -0.000
...
A script extract supercell IDs from phono3py_disp.yaml#
The following script is an example to collect supercell IDs
with the cutoff-pair distance, for which included: true is used
to hook them. duplicates in phono3py_disp.yaml gives the pairs of
exactly same supercells having different IDs. Therefore one of each
pair is necessary to calculate. As a ratio, the number is not many,
but if we want to save very much the computational demand, it is good
to consider.
#!/usr/bin/env python
from phono3py.interface.phono3py_yaml import Phono3pyYaml
p3yaml = Phono3pyYaml()
p3yaml.read("phono3py_disp.yaml")
data = p3yaml.dataset
disp_ids = []
for data1 in data['first_atoms']:
disp_ids.append(data1['id'])
for data1 in data['first_atoms']:
for data2 in data1['second_atoms']:
if data2['included']:
disp_ids.append(data2['id'])
# To remove duplicates
# duplicates = dict(data['duplicates'])
# disp_ids_nodup = [i for i in disp_ids if i not in duplicates]
print(" ".join(["%05d" % i for i in disp_ids]))
Even for the case that phono3py_disp.yaml was created without
--cutoff-pair option, if we replace the line in the above script:
if data2['included']:
by
if data2['distance'] < 5.0: # 5.0 is cutoff-pair distance
we can find the supercell IDs almost equivalent to those obtained
above for --cutoff-pair="5.0".
Tests#
Si-PBE#
For testing, thermal conductivities with respect to --cutoff-pair
values are calculated as follows. Note that if FORCES_FC3 for full
fc3 elements exists, the same FORCES_FC3 file can be used for
generating contracted fc3 for each special phono3py_disp.yaml.
% egrep '^\s+pair_distance' phono3py_disp.yaml|awk '{print $2}'|sort|uniq
0.000000
2.366961
3.865232
4.532386
5.466263
5.956722
6.694777
7.100884
7.730463
9.467845
% cp phono3py_disp.yaml phono3py_disp.orig.yaml
% for i in {2..10};do d=`grep pair_distance phono3py_disp.orig.yaml|awk '{print $2}'|sort|uniq|sed "${i}q;d"`; d=$((d+0.1)); phono3py --cutoff-pair=$d -o $i -d --pa="F" --dim="2 2 2" -c POSCAR-unitcell; mv phono3py_disp.yaml phono3py_disp.$i.yaml; done
% ls phono3py_disp.*.yaml
% ls phono3py_disp.*.yaml
phono3py_disp.10.yaml phono3py_disp.5.yaml phono3py_disp.9.yaml
phono3py_disp.2.yaml phono3py_disp.6.yaml phono3py_disp.orig.yaml
phono3py_disp.3.yaml phono3py_disp.7.yaml
phono3py_disp.4.yaml phono3py_disp.8.yaml
% for i in {2..10};do grep number_of_pairs_in_cutoff phono3py_disp.$i.yaml;done
number_of_pairs_in_cutoff: 10
number_of_pairs_in_cutoff: 30
number_of_pairs_in_cutoff: 50
number_of_pairs_in_cutoff: 55
number_of_pairs_in_cutoff: 75
number_of_pairs_in_cutoff: 95
number_of_pairs_in_cutoff: 103
number_of_pairs_in_cutoff: 108
number_of_pairs_in_cutoff: 110
% for i in {2..10};do cp phono3py_disp.$i.yaml phono3py_disp.yaml; phono3py --mesh="11 11 11" --br|tee std.$i.out;done
% for i in {2..10};do egrep '^\s+300' std.$i.out;done
300.0 123.606 123.606 123.606 -0.000 -0.000 0.000
300.0 118.617 118.617 118.617 -0.000 -0.000 0.000
300.0 118.818 118.818 118.818 -0.000 -0.000 0.000
300.0 118.879 118.879 118.879 -0.000 -0.000 0.000
300.0 119.468 119.468 119.468 -0.000 -0.000 0.000
300.0 119.489 119.489 119.489 -0.000 -0.000 0.000
300.0 119.501 119.501 119.501 -0.000 -0.000 0.000
300.0 119.483 119.483 119.483 -0.000 -0.000 0.000
300.0 119.481 119.481 119.481 -0.000 -0.000 0.000
% for i in {2..10};do cp phono3py_disp.$i.yaml phono3py_disp.yaml; phono3py --sym-fc --mesh="11 11 11" --br|tee std.sym-$i.out;done
% for i in {2..10};do egrep '^\s+300' std.sym-$i.out;done
300.0 124.650 124.650 124.650 -0.000 -0.000 0.000
300.0 119.765 119.765 119.765 -0.000 -0.000 0.000
300.0 118.847 118.847 118.847 -0.000 -0.000 0.000
300.0 118.782 118.782 118.782 -0.000 -0.000 0.000
300.0 119.471 119.471 119.471 -0.000 -0.000 0.000
300.0 119.366 119.366 119.366 -0.000 -0.000 0.000
300.0 119.350 119.350 119.350 -0.000 -0.000 0.000
300.0 119.339 119.339 119.339 -0.000 -0.000 0.000
300.0 119.337 119.337 119.337 -0.000 -0.000 0.000
AlN-LDA#
% egrep '^\s+pair_distance' phono3py_disp.yaml|awk '{print $2}'|sort|uniq
0.000000
1.889907
1.901086
3.069402
3.076914
3.111000
3.640065
3.645881
4.370303
4.375582
4.743307
4.743308
4.788360
4.978000
5.364501
5.388410
5.672503
5.713938
5.870162
6.205027
6.469591
7.335901
% cp phono3py_disp.yaml phono3py_disp.orig.yaml
% for i in {2..21};do d=`grep pair_distance phono3py_disp.orig.yaml|awk '{print $2}'|sort|uniq|sed "${i}q;d"`; d=$((d+0.0001)); phono3py --cutoff-pair=$d -o $i -d --dim="3 3 2" -c POSCAR-unitcell; mv phono3py_disp.yaml phono3py_disp.$i.yaml; done
% for i in {2..21};do grep number_of_pairs_in_cutoff phono3py_disp.$i.yaml;done
number_of_pairs_in_cutoff: 72
number_of_pairs_in_cutoff: 92
number_of_pairs_in_cutoff: 196
number_of_pairs_in_cutoff: 216
number_of_pairs_in_cutoff: 312
number_of_pairs_in_cutoff: 364
number_of_pairs_in_cutoff: 460
number_of_pairs_in_cutoff: 564
number_of_pairs_in_cutoff: 660
number_of_pairs_in_cutoff: 712
number_of_pairs_in_cutoff: 764
number_of_pairs_in_cutoff: 784
number_of_pairs_in_cutoff: 888
number_of_pairs_in_cutoff: 928
number_of_pairs_in_cutoff: 980
number_of_pairs_in_cutoff: 1020
number_of_pairs_in_cutoff: 1116
number_of_pairs_in_cutoff: 1156
number_of_pairs_in_cutoff: 1208
number_of_pairs_in_cutoff: 1248
% for i in {2..21};do cp phono3py_disp.$i.yaml phono3py_disp.yaml; phono3py --mesh="13 13 9" --br --nac --io $i|tee std.$i.out; done
% for i in {2..21};do egrep '^\s+300\.0' std.$i.out;done
300.0 205.550 205.550 193.665 -0.000 -0.000 -0.000
300.0 218.963 218.963 204.942 -0.000 -0.000 -0.000
300.0 213.624 213.624 193.863 -0.000 -0.000 -0.000
300.0 219.932 219.932 199.819 -0.000 -0.000 -0.000
300.0 235.516 235.516 218.843 -0.000 -0.000 -0.000
300.0 234.750 234.750 217.384 -0.000 -0.000 -0.000
300.0 234.355 234.355 218.030 -0.000 -0.000 -0.000
300.0 235.381 235.381 218.609 -0.000 -0.000 -0.000
300.0 235.996 235.996 219.785 -0.000 -0.000 -0.000
300.0 236.220 236.220 219.867 -0.000 -0.000 -0.000
300.0 236.161 236.161 219.298 -0.000 -0.000 -0.000
300.0 236.096 236.096 219.313 -0.000 -0.000 -0.000
300.0 234.602 234.602 217.064 -0.000 -0.000 -0.000
300.0 235.914 235.914 218.689 -0.000 -0.000 -0.000
300.0 235.049 235.049 217.935 -0.000 -0.000 -0.000
300.0 235.877 235.877 219.065 -0.000 -0.000 -0.000
300.0 236.133 236.133 219.364 -0.000 -0.000 -0.000
300.0 236.207 236.207 219.595 -0.000 -0.000 -0.000
300.0 236.035 236.035 219.463 -0.000 -0.000 -0.000
300.0 236.104 236.104 219.348 -0.000 -0.000 -0.000
% for i in {2..21};do cp phono3py_disp.$i.yaml phono3py_disp.yaml; phono3py --mesh="13 13 9" --br --nac --io $i|tee std.$i.out; done|tee std.sym-$i.out; done
% for i in {2..21};do egrep '^\s+300\.0' std.sym-$i.out;done
300.0 232.964 232.964 216.333 0.000 -0.000 -0.000
300.0 235.442 235.442 219.602 0.000 -0.000 -0.000
300.0 235.521 235.521 217.767 0.000 -0.000 -0.000
300.0 235.581 235.581 217.687 0.000 -0.000 -0.000
300.0 236.837 236.837 219.933 0.000 -0.000 -0.000
300.0 236.020 236.020 219.324 0.000 -0.000 -0.000
300.0 235.482 235.482 218.633 0.000 -0.000 -0.000
300.0 236.313 236.313 219.677 0.000 -0.000 -0.000
300.0 236.308 236.308 219.955 0.000 -0.000 -0.000
300.0 236.074 236.074 219.882 0.000 -0.000 -0.000
300.0 235.520 235.520 219.450 0.000 -0.000 -0.000
300.0 235.769 235.769 219.562 0.000 -0.000 -0.000
300.0 235.441 235.441 219.168 0.000 -0.000 -0.000
300.0 235.892 235.892 219.590 0.000 -0.000 -0.000
300.0 235.509 235.509 219.167 0.000 -0.000 -0.000
300.0 235.646 235.646 219.521 0.000 -0.000 -0.000
300.0 235.783 235.783 219.311 0.000 -0.000 -0.000
300.0 235.887 235.887 219.301 0.000 -0.000 -0.000
300.0 235.642 235.642 219.348 0.000 -0.000 -0.000
300.0 235.728 235.728 219.102 0.000 -0.000 -0.000