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Why EPW code gets stuck at wannierization-step with USPPS 
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Why EPW code gets stuck at wannierization-step with USPPS
Hi everyone,
I am using QE-6.4 which supports EPW calculation with USPPs.
I am facing a problem in wannierization step in the EPW calculations with USPPs.
Basically, code is running in the background. It is stuck at the following in EPW.out file::
- Number of bands is ( 26)
- Number of total bands is ( 30)
- Number of excluded bands is ( 4)
- Number of wannier functions is ( 26)
- All guiding functions are given

Reading data about k-point neighbours

- All neighbours are found

AMN
k points = 225 in 12 pools
1 of 19 on ionode
2 of 19 on ionode
3 of 19 on ionode
4 of 19 on ionode
5 of 19 on ionode
6 of 19 on ionode
7 of 19 on ionode
8 of 19 on ionode
9 of 19 on ionode
10 of 19 on ionode
11 of 19 on ionode
12 of 19 on ionode
13 of 19 on ionode
14 of 19 on ionode
15 of 19 on ionode
16 of 19 on ionode
17 of 19 on ionode
18 of 19 on ionode
19 of 19 on ionode

AMN calculated

MMN
k points = 225 in 12 pools
1 of 19 on ionode
2 of 19 on ionode
3 of 19 on ionode
4 of 19 on ionode
5 of 19 on ionode
6 of 19 on ionode
7 of 19 on ionode
8 of 19 on ionode
9 of 19 on ionode
10 of 19 on ionode
11 of 19 on ionode
12 of 19 on ionode
13 of 19 on ionode
14 of 19 on ionode
15 of 19 on ionode
16 of 19 on ionode
17 of 19 on ionode
18 of 19 on ionode
19 of 19 on ionode
MMN calculated

Running Wannier90


However, there is no progress reflected in case.wout file.


I tried running the code in two different machines. But the results are the same. It gets stuck at wannierization step. I don't understand what is wrong with it. Please help me to resolve this issue.


Mon Sep 09, 2019 10:50 pm
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Re: Why EPW code gets stuck at wannierization-step with USP
Hi,

One thing, I forget to mention above that I am using PBE+vdW+SOC along with full relativistic USPPs. Has it been coded for non-collinear cases?


Mon Sep 09, 2019 11:20 pm
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Post Re: Why EPW code gets stuck at wannierization-step with USP
Hi,

Yes, SOC should be supported by USPP with the develop version of QE/EPW that you can download from GitLab.

Best,
Roxana

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Tue Sep 10, 2019 12:42 pm
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Re: Why EPW code gets stuck at wannierization-step with USP
Thank you for the information.


Tue Sep 10, 2019 4:08 pm
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Re: Why EPW code gets stuck at wannierization-step with USP
Dear Sir,

I have installed and tried using new develop version of QE/EPW downloaded from GitLAb. But it has poor or no link to QE. Thus, pw2wannier step is not completing and it is not moving to wannierization part in EPW calculations.

In the latest version of QE-6.4.1, they have provided a patch file which fixes the problem but due to using vdW+SOC, I have found unphysical results like the negative spread of wannier functions.

On the other hand, though, in the develop version of QE/EPW which you mentioned above, I think that a new patch file is required because pw2wannier90.f90 routine has changed now compared to QE-6.4.1/PP/src/pw2wannier90.f90 routine.
How can I get a new patch file?


Wed Sep 11, 2019 5:34 am
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Post Re: Why EPW code gets stuck at wannierization-step with USP
Dear Gautam,

Can you please clarify the following two points?

1) Does the wannierization procedure works fine using wannier90 and pw2wannier90 outside EPW? You mentioned getting unphysical wannier functions and it is not clear if this happens with the EPW code or the Wannier90 code as well.

2) What is the name of the subroutine (or which lines) in the pw2wannier90.f90 where the patch to vdW+SOC is implemented? I can take a look and see if this can be easily updated in the EPW code.

Best,
Roxana

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Wed Sep 11, 2019 5:49 pm
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Re: Why EPW code gets stuck at wannierization-step with USP
Dear Sir,

I am using QE-6.4.1 stable version downloaded from GitHub and installed it using a patch file as given on the website since without patch file it does not link to wannier90.

Using QE-6.4.1 stable version and wannier90-3.0.0, I see the following:

1(a) If I use wannier90 as a standalone program then it works perfectly fine with USPP (PBE+SOC), with proper spread of wannier functions and I am able to obtain the electronic band structure accurately which is superimposing the electronic band structure computed using usual Quantum ESPRESSO methods.

This is screen shot of case.wout when wannier90 is used as standalone program using PBE+SOC for USPPs.
------------------------------------------------------------------------------
Cycle: 4420
WF centre and spread 1 ( -0.000004, 2.128701, 9.123921 ) 1.26767900
WF centre and spread 2 ( -0.000004, 2.128701, 9.123921 ) 1.26767902
WF centre and spread 3 ( -0.559684, 2.451758, 8.308179 ) 1.45804631
WF centre and spread 4 ( 0.559679, 2.451755, 8.308179 ) 1.45805250
WF centre and spread 5 ( -0.000001, 1.482548, 8.308081 ) 1.45816933
WF centre and spread 6 ( -0.000000, 1.482548, 8.308081 ) 1.45816931
WF centre and spread 7 ( 1.843517, 1.064358, 5.276143 ) 1.26732163
WF centre and spread 8 ( 1.843517, 1.064358, 5.276143 ) 1.26732161
WF centre and spread 9 ( 1.283677, 0.741212, 6.091920 ) 1.45855980
WF centre and spread 10 ( 2.403354, 0.741210, 6.091920 ) 1.45855386
WF centre and spread 11 ( 1.843514, 1.710693, 6.092018 ) 1.45867762
WF centre and spread 12 ( 1.843514, 1.710693, 6.092018 ) 1.45867759
WF centre and spread 13 ( 0.000000, -0.000001, 7.199974 ) 2.08932502
WF centre and spread 14 ( 0.000000, -0.000001, 7.199974 ) 2.08932493
WF centre and spread 15 ( -1.283672, 0.741210, 6.091920 ) 1.45855347
WF centre and spread 16 ( 1.283830, -0.741301, 8.308179 ) 1.45804569
WF centre and spread 17 ( 1.283677, 0.741212, 6.091920 ) 1.45855986
WF centre and spread 18 ( -1.283834, -0.741303, 8.308179 ) 1.45805190
WF centre and spread 19 ( -0.000000, 0.000010, 7.199993 ) 2.35647021
WF centre and spread 20 ( -0.000000, 0.000010, 7.199993 ) 2.35648214
WF centre and spread 21 ( 0.000000, -0.000008, 7.199993 ) 2.36252326
WF centre and spread 22 ( 0.000000, -0.000008, 7.199993 ) 2.36250186
Sum of centres and spreads ( 11.061079, 19.158352,158.400644 ) 36.18674593

4420 -0.637E-10 0.0001202077 36.1867394148 307.38 <-- CONV
O_D= 0.0198180 O_OD= 3.7432054 O_TOT= 36.1867394 <-- SPRD
Delta: O_D= 0.1283411E-11 O_OD= -0.6494183E-10 O_TOT= -0.6365042E-10 <-- DLTA
------------------------------------------------------------------------------

<<< Delta < 1.000E-10 over 3 iterations >>>
<<< Wannierisation convergence criteria satisfied >>>



1(b) However, when I am using wannier90 through EPW code, then it does not function properly for USPP (PBE+SOC). I am getting negative values for the spread of the wannier functions.

this is a screen shot of case.wout file when using wannier90 through EPW code using PBE+SOC for USPPs.
------------------------------------------------------------------------------
Cycle: 1900
WF centre and spread 1 ( -0.018064, 0.015564, 7.215867 ) -3.59493083
WF centre and spread 2 ( -0.012818, 0.010867, 7.214204 ) -3.69301099
WF centre and spread 3 ( -0.346671, 0.231294, 7.128486 ) -19.36065631
WF centre and spread 4 ( 0.855645, -0.459047, 7.748742 ) -25.71614284
WF centre and spread 5 ( -0.316112, 0.653469, 7.060301 ) -23.46206674
WF centre and spread 6 ( 0.232388, -1.121790, 6.545472 ) -29.56140242
WF centre and spread 7 ( -0.098692, 0.317067, 7.297382 ) -8.43031009
WF centre and spread 8 ( -0.005728, -0.004691, 7.219264 ) -6.88013196
WF centre and spread 9 ( -0.298676, 0.232059, 7.001261 ) -9.98295138
WF centre and spread 10 ( 0.077482, 0.048029, 7.191064 ) -5.85536684
WF centre and spread 11 ( 0.050472, 2.155304, 8.857608 ) -19.25430293
WF centre and spread 12 ( 0.046595, 2.146807, 8.839971 ) -18.51962533
WF centre and spread 13 ( 0.018529, 2.303748, 8.267695 ) -6.28610637
WF centre and spread 14 ( 0.152053, 2.293421, 8.269241 ) -6.09383937
WF centre and spread 15 ( -0.044362, 2.192186, 8.286461 ) -5.43347022
WF centre and spread 16 ( -0.063543, 1.964205, 8.387294 ) -7.07388678
WF centre and spread 17 ( 1.803844, 1.079801, 5.622937 ) -17.79182924
WF centre and spread 18 ( 1.805724, 1.065768, 5.603740 ) -18.28185838
WF centre and spread 19 ( 1.628611, 0.819957, 6.176104 ) -7.78723402
WF centre and spread 20 ( 1.773585, 0.840445, 6.141179 ) -7.61481942
WF centre and spread 21 ( 1.833917, 1.366712, 6.063676 ) -8.74961753
WF centre and spread 22 ( 1.903480, 0.970270, 6.230122 ) -7.70461853
Sum of centres and spreads ( 10.977657, 19.121447,158.368069 ) -267.12817851

1900 -0.141E-01 2.6165271888 -267.1281842669 269.17 <-- CONV
O_D= 1.8370546 O_OD= 65.0916882 O_TOT= -267.1281843 <-- SPRD
Delta: O_D= -0.1567362E-02 O_OD= -0.1249986E-01 O_TOT= -0.1406722E-01 <-- DLTA
------------------------------------------------------------------------------

done



2) I am not able to use QE developer version (referred by you GitLab) because it has poor or no link to wannier90. I don't have a proper patch file that will link it to wannier90. The patch which
I generated links the wannier90 to EPW but it also gives the negative spread of wannier functions.

I guess some modification is needed in the subroutine named as "compute_amn_with_scdm_spinor" present at line number 3618 in pw2wannier90.f90 file.


Fri Sep 13, 2019 11:59 am
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Post Re: Why EPW code gets stuck at wannierization-step with USP
Hi,

I don't know what patch you are talking about. The wannier90 code should be automatically installed when you compile EPW. Have you tried using clone?

===========================
git clone https://gitlab.com/QEF/q-e.git

git clone git@gitlab.com:QEF/q-e.git (if https doesn't work)

cd q-e
git checkout develop
./configure
make epw
==========================

The "compute_amn_with_scdm_spinor" subroutine from PP/src/pw2wannier90.f90 that you mention is an alternative method for generating localised Wannier
functions without an initial guess for the Wannier projections. The subroutine doesn't have any special patch to deal with vdW interaction. This algorithm is indeed not implemented in EPW pw2wan90epw.f90 subroutine at this point.

However, the "compute_amn_para" subroutine in EPW/src/pw2wan90epw.f90 is the same as the "compute_amn" subroutine in PP/src/pw2wannier90.f90 and should work with USPP and SOC (this algorithm requires an initial guess for the Wannier projections).

Best,
Roxana

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Fri Sep 13, 2019 1:21 pm
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Joined: Mon Oct 22, 2018 10:31 am
Posts: 18
University: IISER-Pune
Post Re: Why EPW code gets stuck at wannierization-step with USP
Dear Sir,

As of now, I have not used vdW interaction. But I expect results to be consistent for PBE+SOC interactions. I am providing the projections manually. Following is the input I am using for EPW/bin/epw.x:

-------------------------------------------------
num_bands = 23
num_wann = 22
exclude_bands = 1-7,31-35 !!! 23 bands and 22 wannier functions
dis_win_max = 25.0d0
dis_froz_max = 15.00
dis_froz_min = -10.0d0
dis_win_min = -30.0d0
spinors = T
dis_num_iter = 100000

dis_mix_ratio = 0.5d0
guiding_centres=T
!!!wannier_plot = true
num_iter = 10000
num_print_cycles = 10
conv_window = 3
conv_tol=1e-10,
trial_step=1.0,

Begin Atoms_Frac
S 0.333333000 0.666667000 0.720635519
Zr 0.000000000 0.000000000 0.600000000
S 0.666667000 0.333333000 0.479364482
End Atoms_Frac

Begin Projections
S: p
Zr:d
End Projections

bands_num_points = 100

begin kpoint_path
M 0.50000 0.00000 0.00000 G 0.00000 0.00000 0.00000
G 0.00000 0.00000 0.00000 K 0.3333333333 0.3333333333 0.00000
K 0.3333333333 0.3333333333 0.00000 M 0.50000 0.00000 0.00000
end kpoint_path

!restart = plot
!bands_plot = true
!bands_plot_format=xmgr
Begin Unit_Cell_Cart
bohr
6.967471048 0.000000000 0.000000000
-3.483735524 6.034006928 0.000000000
0.000000000 0.000000000 22.676711863
End Unit_Cell_Cart

mp_grid = 15 15 1

begin kpoints
0.00000000 0.00000000 0.00000000 4.444444e-03
0.00000000 0.06666667 0.00000000 4.444444e-03
0.00000000 0.13333333 0.00000000 4.444444e-03
0.00000000 0.20000000 0.00000000 4.444444e-03
0.00000000 0.26666667 0.00000000 4.444444e-03
0.00000000 0.33333333 0.00000000 4.444444e-03
0.00000000 0.40000000 0.00000000 4.444444e-03
0.00000000 0.46666667 0.00000000 4.444444e-03
0.00000000 0.53333333 0.00000000 4.444444e-03
0.00000000 0.60000000 0.00000000 4.444444e-03
0.00000000 0.66666667 0.00000000 4.444444e-03
0.00000000 0.73333333 0.00000000 4.444444e-03
0.00000000 0.80000000 0.00000000 4.444444e-03
0.00000000 0.86666667 0.00000000 4.444444e-03
0.00000000 0.93333333 0.00000000 4.444444e-03
0.06666667 0.00000000 0.00000000 4.444444e-03
0.06666667 0.06666667 0.00000000 4.444444e-03
0.06666667 0.13333333 0.00000000 4.444444e-03
0.06666667 0.20000000 0.00000000 4.444444e-03
0.06666667 0.26666667 0.00000000 4.444444e-03
0.06666667 0.33333333 0.00000000 4.444444e-03
0.06666667 0.40000000 0.00000000 4.444444e-03
0.06666667 0.46666667 0.00000000 4.444444e-03
0.06666667 0.53333333 0.00000000 4.444444e-03
0.06666667 0.60000000 0.00000000 4.444444e-03
0.06666667 0.66666667 0.00000000 4.444444e-03
0.06666667 0.73333333 0.00000000 4.444444e-03
0.06666667 0.80000000 0.00000000 4.444444e-03
0.06666667 0.86666667 0.00000000 4.444444e-03
0.06666667 0.93333333 0.00000000 4.444444e-03
0.13333333 0.00000000 0.00000000 4.444444e-03
0.13333333 0.06666667 0.00000000 4.444444e-03
0.13333333 0.13333333 0.00000000 4.444444e-03
0.13333333 0.20000000 0.00000000 4.444444e-03
0.13333333 0.26666667 0.00000000 4.444444e-03
0.13333333 0.33333333 0.00000000 4.444444e-03
0.13333333 0.40000000 0.00000000 4.444444e-03
0.13333333 0.46666667 0.00000000 4.444444e-03
0.13333333 0.53333333 0.00000000 4.444444e-03
0.13333333 0.60000000 0.00000000 4.444444e-03
0.13333333 0.66666667 0.00000000 4.444444e-03
0.13333333 0.73333333 0.00000000 4.444444e-03
0.13333333 0.80000000 0.00000000 4.444444e-03
0.13333333 0.86666667 0.00000000 4.444444e-03
0.13333333 0.93333333 0.00000000 4.444444e-03
0.20000000 0.00000000 0.00000000 4.444444e-03
0.20000000 0.06666667 0.00000000 4.444444e-03
0.20000000 0.13333333 0.00000000 4.444444e-03
0.20000000 0.20000000 0.00000000 4.444444e-03
0.20000000 0.26666667 0.00000000 4.444444e-03
0.20000000 0.33333333 0.00000000 4.444444e-03
0.20000000 0.40000000 0.00000000 4.444444e-03
0.20000000 0.46666667 0.00000000 4.444444e-03
0.20000000 0.53333333 0.00000000 4.444444e-03
0.20000000 0.60000000 0.00000000 4.444444e-03
0.20000000 0.66666667 0.00000000 4.444444e-03
0.20000000 0.73333333 0.00000000 4.444444e-03
0.20000000 0.80000000 0.00000000 4.444444e-03
0.20000000 0.86666667 0.00000000 4.444444e-03
0.20000000 0.93333333 0.00000000 4.444444e-03
0.26666667 0.00000000 0.00000000 4.444444e-03
0.26666667 0.06666667 0.00000000 4.444444e-03
0.26666667 0.13333333 0.00000000 4.444444e-03
0.26666667 0.20000000 0.00000000 4.444444e-03
0.26666667 0.26666667 0.00000000 4.444444e-03
0.26666667 0.33333333 0.00000000 4.444444e-03
0.26666667 0.40000000 0.00000000 4.444444e-03
0.26666667 0.46666667 0.00000000 4.444444e-03
0.26666667 0.53333333 0.00000000 4.444444e-03
0.26666667 0.60000000 0.00000000 4.444444e-03
0.26666667 0.66666667 0.00000000 4.444444e-03
0.26666667 0.73333333 0.00000000 4.444444e-03
0.26666667 0.80000000 0.00000000 4.444444e-03
0.26666667 0.86666667 0.00000000 4.444444e-03
0.26666667 0.93333333 0.00000000 4.444444e-03
0.33333333 0.00000000 0.00000000 4.444444e-03
0.33333333 0.06666667 0.00000000 4.444444e-03
0.33333333 0.13333333 0.00000000 4.444444e-03
0.33333333 0.20000000 0.00000000 4.444444e-03
0.33333333 0.26666667 0.00000000 4.444444e-03
0.33333333 0.33333333 0.00000000 4.444444e-03
0.33333333 0.40000000 0.00000000 4.444444e-03
0.33333333 0.46666667 0.00000000 4.444444e-03
0.33333333 0.53333333 0.00000000 4.444444e-03
0.33333333 0.60000000 0.00000000 4.444444e-03
0.33333333 0.66666667 0.00000000 4.444444e-03
0.33333333 0.73333333 0.00000000 4.444444e-03
0.33333333 0.80000000 0.00000000 4.444444e-03
0.33333333 0.86666667 0.00000000 4.444444e-03
0.33333333 0.93333333 0.00000000 4.444444e-03
0.40000000 0.00000000 0.00000000 4.444444e-03
0.40000000 0.06666667 0.00000000 4.444444e-03
0.40000000 0.13333333 0.00000000 4.444444e-03
0.40000000 0.20000000 0.00000000 4.444444e-03
0.40000000 0.26666667 0.00000000 4.444444e-03
0.40000000 0.33333333 0.00000000 4.444444e-03
0.40000000 0.40000000 0.00000000 4.444444e-03
0.40000000 0.46666667 0.00000000 4.444444e-03
0.40000000 0.53333333 0.00000000 4.444444e-03
0.40000000 0.60000000 0.00000000 4.444444e-03
0.40000000 0.66666667 0.00000000 4.444444e-03
0.40000000 0.73333333 0.00000000 4.444444e-03
0.40000000 0.80000000 0.00000000 4.444444e-03
0.40000000 0.86666667 0.00000000 4.444444e-03
0.40000000 0.93333333 0.00000000 4.444444e-03
0.46666667 0.00000000 0.00000000 4.444444e-03
0.46666667 0.06666667 0.00000000 4.444444e-03
0.46666667 0.13333333 0.00000000 4.444444e-03
0.46666667 0.20000000 0.00000000 4.444444e-03
0.46666667 0.26666667 0.00000000 4.444444e-03
0.46666667 0.33333333 0.00000000 4.444444e-03
0.46666667 0.40000000 0.00000000 4.444444e-03
0.46666667 0.46666667 0.00000000 4.444444e-03
0.46666667 0.53333333 0.00000000 4.444444e-03
0.46666667 0.60000000 0.00000000 4.444444e-03
0.46666667 0.66666667 0.00000000 4.444444e-03
0.46666667 0.73333333 0.00000000 4.444444e-03
0.46666667 0.80000000 0.00000000 4.444444e-03
0.46666667 0.86666667 0.00000000 4.444444e-03
0.46666667 0.93333333 0.00000000 4.444444e-03
0.53333333 0.00000000 0.00000000 4.444444e-03
0.53333333 0.06666667 0.00000000 4.444444e-03
0.53333333 0.13333333 0.00000000 4.444444e-03
0.53333333 0.20000000 0.00000000 4.444444e-03
0.53333333 0.26666667 0.00000000 4.444444e-03
0.53333333 0.33333333 0.00000000 4.444444e-03
0.53333333 0.40000000 0.00000000 4.444444e-03
0.53333333 0.46666667 0.00000000 4.444444e-03
0.53333333 0.53333333 0.00000000 4.444444e-03
0.53333333 0.60000000 0.00000000 4.444444e-03
0.53333333 0.66666667 0.00000000 4.444444e-03
0.53333333 0.73333333 0.00000000 4.444444e-03
0.53333333 0.80000000 0.00000000 4.444444e-03
0.53333333 0.86666667 0.00000000 4.444444e-03
0.53333333 0.93333333 0.00000000 4.444444e-03
0.60000000 0.00000000 0.00000000 4.444444e-03
0.60000000 0.06666667 0.00000000 4.444444e-03
0.60000000 0.13333333 0.00000000 4.444444e-03
0.60000000 0.20000000 0.00000000 4.444444e-03
0.60000000 0.26666667 0.00000000 4.444444e-03
0.60000000 0.33333333 0.00000000 4.444444e-03
0.60000000 0.40000000 0.00000000 4.444444e-03
0.60000000 0.46666667 0.00000000 4.444444e-03
0.60000000 0.53333333 0.00000000 4.444444e-03
0.60000000 0.60000000 0.00000000 4.444444e-03
0.60000000 0.66666667 0.00000000 4.444444e-03
0.60000000 0.73333333 0.00000000 4.444444e-03
0.60000000 0.80000000 0.00000000 4.444444e-03
0.60000000 0.86666667 0.00000000 4.444444e-03
0.60000000 0.93333333 0.00000000 4.444444e-03
0.66666667 0.00000000 0.00000000 4.444444e-03
0.66666667 0.06666667 0.00000000 4.444444e-03
0.66666667 0.13333333 0.00000000 4.444444e-03
0.66666667 0.20000000 0.00000000 4.444444e-03
0.66666667 0.26666667 0.00000000 4.444444e-03
0.66666667 0.33333333 0.00000000 4.444444e-03
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0.93333333 0.93333333 0.00000000 4.444444e-03
end kpoints


Fri Sep 13, 2019 5:17 pm
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Joined: Fri Jan 22, 2016 6:48 pm
Posts: 144
University: SUNY-Binghamton
Post Re: Why EPW code gets stuck at wannierization-step with USP
Can you provide the exact input you are using with EPW?

_________________
Roxana Margine
Associate Professor
Department of Physics, Applied Physics and Astronomy
Binghamton University, State University of New York
PO Box 6000
Binghamton, NY 13902-6000


Fri Sep 13, 2019 6:39 pm
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