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[Takeshi NISHIMATSU <t_nissie@yahoo.co.jp>]

Dear Prof. Gonze and all,

> Please, see Philippe Ghosez's thesis, precisely on BaTiO3 :
> http://www.phythema.ulg.ac.be/Download/download.php
> You will find interesting information about the cut-off energy  
> convergence in an appendix
> of this thesis.

Thank you for your advice. I took a look in that very
nice thesis and found that Teter's pseudopotentials
were in use. But the pseudopotential for oxygen
(r_c = 1.65) was softer than 8o.phoney.mod (r_c = 1.49).

Here, I picked up three eigenvalues [eV/Angstrom^2] of
the force constant matrix at the Gamma point and listed
their ecut [Hartree] dependence. Modes are the
Gamma15 soft mode, the acoustic translational mode
(Ideally, it should be zero.) and the Gamma25 mode.

ecut Gamma15    Acoustic   Gamma25
35  -0.456122   0.195207   5.003634
40  -0.994634  -0.028809   4.869130
45  -0.400629   0.046698   4.906948
50  -0.616130   0.037663   4.925377
55  -0.638695   0.025415   4.917949
57  -0.652137   0.013472   4.910288
60  -0.644218   0.014311   4.912821
61  -0.643811   0.014193   4.912773
62  -0.642569   0.014140   4.912736
65  -0.656336   0.007038   4.910474
70  -0.685880   0.007253   4.908248
75  -0.685909   0.007671   4.909921
80  -0.648047   0.008204   4.911302


Frozen-phonon calculation with ecut=60:
a0 =   3.9388898 [Angstrom]
eigenvalues [eV/Angstrom^2] and eigenvectors of force_constant_matrix
1  -0.630966  -0.2163  -0.7518   0.2721   0.2721   0.4899
2   0.014762   0.4549   0.4690   0.4393   0.4393   0.4327
3   4.913130   0.0000   0.0000   0.7071  -0.7071   0.0000
4   9.570920   0.8536  -0.4055  -0.2310  -0.2310   0.0112
5  14.546354  -0.1327   0.2245  -0.4239  -0.4239   0.7568
(Just for reference, input files are attached to this mail.)


And, here is the ecut dependence of phonon frequency in
[cm^-1] unit (The LO-TO splittings are not included.).
I have done
pwd ; grep -A 8 '  Phonon wavevector' perovskite-Gamma.out | grep '^-'
in each directory.

/BaTiO3-phonon-24-a0-3.940-8x8x8-ecut35-5.6.4
- -7.058621E+01 -7.058621E+01 -7.058388E+01  3.066612E+01  3.066721E+01
-  3.066721E+01  1.905540E+02  1.905544E+02  1.905544E+02  2.916225E+02
-  2.916225E+02  2.916225E+02  4.911043E+02  4.911045E+02  4.911045E+02
/BaTiO3-phonon-17-abinitio-a0-8x8x8-ecut40-5.6.4/force-constant-matrix
- -9.439416E+01 -9.439416E+01 -9.439344E+01 -1.322782E+01 -1.322782E+01
- -1.322750E+01  1.854138E+02  1.854140E+02  1.854140E+02  2.876762E+02
-  2.876762E+02  2.876762E+02  4.889197E+02  4.889198E+02  4.889198E+02
/BaTiO3-phonon-22-a0-3.940-8x8x8-ecut45-5.6.4
- -6.368055E+01 -6.367916E+01 -6.367916E+01  1.575238E+01  1.575238E+01
-  1.575554E+01  1.873933E+02  1.873933E+02  1.873935E+02  2.887912E+02
-  2.887912E+02  2.887912E+02  4.907777E+02  4.907777E+02  4.907777E+02
/BaTiO3-phonon-23-a0-3.940-8x8x8-ecut50-5.6.4
- -7.754560E+01 -7.754560E+01 -7.754443E+01  1.441634E+01  1.441634E+01
-  1.441651E+01  1.871320E+02  1.871322E+02  1.871322E+02  2.893330E+02
-  2.893330E+02  2.893330E+02  4.904599E+02  4.904600E+02  4.904600E+02
/BaTiO3-phonon-26-a0-3.940-8x8x8-ecut55-5.6.4
- -7.839328E+01 -7.839328E+01 -7.838663E+01  1.193403E+01  1.193621E+01
-  1.193621E+01  1.869438E+02  1.869441E+02  1.869441E+02  2.891148E+02
-  2.891148E+02  2.891148E+02  4.900809E+02  4.900818E+02  4.900818E+02
/BaTiO3-phonon-26-a0-3.940-8x8x8-ecut55-5.6.4
- -7.839328E+01 -7.839328E+01 -7.838663E+01  1.193403E+01  1.193621E+01
-  1.193621E+01  1.869438E+02  1.869441E+02  1.869441E+02  2.891148E+02
-  2.891148E+02  2.891148E+02  4.900809E+02  4.900818E+02  4.900818E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut57
- -7.873250E+01 -7.873250E+01 -7.873052E+01  8.751815E+00  8.759139E+00
-  8.759139E+00  1.866568E+02  1.866574E+02  1.866574E+02  2.888895E+02
-  2.888895E+02  2.888895E+02  4.900179E+02  4.900179E+02  4.900179E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut60
- -7.824132E+01 -7.824132E+01 -7.823997E+01  9.019223E+00  9.021527E+00
-  9.021527E+00  1.866891E+02  1.866893E+02  1.866893E+02  2.889640E+02
-  2.889640E+02  2.889640E+02  4.900738E+02  4.900739E+02  4.900739E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut61
- -7.821165E+01 -7.821165E+01 -7.820821E+01  8.985857E+00  8.986975E+00
-  8.986975E+00  1.866876E+02  1.866880E+02  1.866880E+02  2.889626E+02
-  2.889626E+02  2.889626E+02  4.900728E+02  4.900732E+02  4.900732E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut62
- -7.813268E+01 -7.813268E+01 -7.813056E+01  8.964342E+00  8.966948E+00
-  8.966948E+00  1.866836E+02  1.866838E+02  1.866838E+02  2.889615E+02
-  2.889615E+02  2.889615E+02  4.900803E+02  4.900805E+02  4.900805E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut65
- -7.858113E+01 -7.858037E+01 -7.858037E+01  6.359724E+00  6.359724E+00
-  6.362257E+00  1.865175E+02  1.865175E+02  1.865175E+02  2.888950E+02
-  2.888950E+02  2.888950E+02  4.900551E+02  4.900551E+02  4.900551E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut70
- -8.031784E+01 -8.031746E+01 -8.031746E+01  6.454205E+00  6.454205E+00
-  6.456866E+00  1.865108E+02  1.865108E+02  1.865110E+02  2.888295E+02
-  2.888295E+02  2.888295E+02  4.898023E+02  4.898024E+02  4.898024E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut75
- -8.035355E+01 -8.035317E+01 -8.035317E+01  6.635282E+00  6.635282E+00
-  6.637831E+00  1.864521E+02  1.864521E+02  1.864522E+02  2.888787E+02
-  2.888787E+02  2.888787E+02  4.899633E+02  4.899633E+02  4.899633E+02
/BaTiO3-phonon-27-a0-3.940-8x8x8-Gamma-ecut-dep-5.6.4/ecut80
- -7.816902E+01 -7.816902E+01 -7.816585E+01  6.855128E+00  6.855128E+00
-  6.858712E+00  1.865275E+02  1.865275E+02  1.865275E+02  2.889193E+02
-  2.889193E+02  2.889193E+02  4.901485E+02  4.901490E+02  4.901490E+02


I conclude that I can safely use ecut=60, maybe...


Thank you again,
-- Takeshi Nishimatsu

Attachment: perovskite-frozen-phonon-Gamma.files
Description: 3506925743-perovskite-frozen-phonon-Gamma.files

Attachment: perovskite-frozen-phonon-Gamma.in
Description: 2083894646-perovskite-frozen-phonon-Gamma.in

Attachment: perovskite-frozen-phonon-Gamma.nqs
Description: 804162021-perovskite-frozen-phonon-Gamma.nqs

Attachment: frozen_phonon_Gamma.F
Description: 2273680177-frozen_phonon_Gamma.F