[QE-users] Symmetries in the dynamical matrix
JAY Antoine
Antoine.JAY at isae-supaero.fr
Tue Oct 16 17:10:42 CEST 2018
Dear all,
I'am trying to understand the symmetries of the dynamical matrix given in the phonon output :
Dynamical Matrix in cartesian axes
q = ( 0.000000000 0.000000000 0.000000000 )
1 1
0.26846543 0.00000000 -0.00021832 0.00000000 -0.00074984 0.00000000
-0.00021197 0.00000000 0.26867942 0.00000000 -0.00021197 0.00000000
-0.00074984 0.00000000 -0.00021832 0.00000000 0.26846543 0.00000000
[...]
which has the form:
A B C
D E D
C B F
Here 6 values A,B,C,D,E and F have been calculated whereas the 3 other force constants have been filled due to the crystal symmetry operations.
But what I do not understand is why is this dynamical matrix not symmetric?
in the subroutine write_dyn_mat, when phi(i,j,na,nb) is written, its definition is:
1/sqrt(Mna*Mnb)*
d^2E/dxadxb d^2E/dxadyb d^2E/dxadzb
d^2E/dyadxb d^2E/dyadyb d^2E/dyadzb
d^2E/dzadxb d^2E/dzadyb d^2E/dzadzb
Due to the Schwarz theorem in the case where na=nb,
d^2E/dxadya = d^2E/dyadxa, so in addition to the crystal symmetry operations,
the algorithm should fill exactelly D=b with only one calcul.
However, it seems that two calculs have been performed in this case giving slighly different values...
Another example is given here
1 2
-0.06563923 0.00000000 -0.04490934 0.00000000 -0.04404086 0.00000000
-0.04493368 0.00000000 -0.06590828 0.00000000 -0.04493368 0.00000000
-0.04404086 0.00000000 -0.04490934 0.00000000 -0.06563923 0.00000000
[...]
2 1
-0.06528947 0.00000000 -0.04495765 0.00000000 -0.04411243 0.00000000
-0.04490286 0.00000000 -0.06585596 0.00000000 -0.04490286 0.00000000
-0.04411243 0.00000000 -0.04495765 0.00000000 -0.06528947 0.00000000
I was expecting d^2E/dx1dx2 = d^2E/dx1dx2 and so on...
but two calculs have been done and -0.06563923 .neq. -0.06528947!
What I am missing there?
System is a simple vacancy in a supercell of 215 silicon atoms (ibrav=1), QE V6.0, input given bellow
Regards,
Antoine Jay
LAAS-CNRS, Toulouse France
scf.in:
&control
calculation = 'scf'
prefix = 'Si_1V_D2d',
tstress = .true.
tprnfor = .true.
pseudo_dir = '/pseudo/',
outdir = 'tmp_Si_1V_D2d/',
etot_conv_thr=1.0d-6
forc_conv_thr=1.0d-4
nstep=1400
/
&system
ibrav = 1,
celldm(1) = 30.613571,
celldm(2) = 1 ,
celldm(3) = 1 ,
nat = 215,
ntyp = 1,
ecutwfc = 20.0,
/
&electrons
diagonalization='david'
mixing_beta = 0.7,
conv_thr = 1.0d-9,
electron_maxstep=800,
/
ATOMIC_SPECIES
Si 28.086 Si.pz-vbc.UPF
ATOMIC_POSITIONS {crystal}
Si 0.000162336 0.00014327 0.000162336
Si 0.08330307 0.084189225 0.08330307
Si 0.166992459 0.16800145 0.00058752
Si 0.250912336 0.250721016 0.084924085
Si 0.166156275 -0.000106871 0.166156275
Si 0.249895433 0.082528066 0.249895433
Si 0.00058752 0.16800145 0.166992459
Si 0.084924085 0.250721016 0.250912336
Si 0.333438217 0.001346258 -0.00050172
Si 0.417071186 0.084081282 0.083872754
Si 0.499961127 0.168420495 0.001124771
Si 0.582907731 0.251646989 0.085458254
Si 0.500336958 -0.000934751 0.16550848
Si 0.584924657 0.08068021 0.248592644
Si 0.333277507 0.16668747 0.168141141
Si 0.417190875 0.24867044 0.25351339
Si 0.001507258 0.333858164 0.001507258
Si 0.086913471 0.416162509 0.086913471
Si 0.167357425 0.499603001 0.000978135
Si 0.250615274 0.581869305 0.085464282
Si 0.173265996 0.334321177 0.173265996
Si 0.262140675 0.414034508 0.262140675
Si 0.000978135 0.499603001 0.167357425
Si 0.085464282 0.581869305 0.250615274
Si -0.00050172 0.001346258 0.333438217
Si 0.083872754 0.084081282 0.417071186
Si 0.168141141 0.16668747 0.333277507
Si 0.25351339 0.24867044 0.417190875
Si 0.16550848 -0.000934751 0.500336958
Si 0.248592644 0.08068021 0.584924657
Si 0.001124771 0.168420495 0.499961127
Si 0.085458254 0.251646989 0.582907731
Si 0.333739196 0.333959699 0.000861911
Si 0.41676146 0.41675827 0.085292632
Si 0.499782156 0.49955788 0.000861393
Si 0.582608779 0.582796164 0.08492405
Si 0.498891265 0.334010796 0.1706163
Si 0.571385857 0.419481169 0.262134574
Si 0.334633728 0.499504498 0.170620451
Si 0.416333375 0.584843238 0.253519495
Si 0.000861911 0.333959699 0.333739196
Si 0.085292632 0.41675827 0.41676146
Si 0.170620451 0.499504498 0.334633728
Si 0.253519495 0.584843238 0.416333375
Si 0.1706163 0.334010796 0.498891265
Si 0.262134574 0.419481169 0.571385857
Si 0.000861393 0.49955788 0.499782156
Si 0.08492405 0.582796164 0.582608779
Si 0.333252803 -0.000634212 0.333252803
Si 0.416757556 0.082106584 0.416757556
Si 0.501660471 0.162612654 0.331855779
Si 0.579997453 0.248677535 0.416324449
Si 0.500263622 -0.000631436 0.500263622
Si 0.583620108 0.082532896 0.583620108
Si 0.331855779 0.162612654 0.501660471
Si 0.416324449 0.248677535 0.579997453
Si 0.353262454 0.332627539 0.353262454
Si 0.48026794 0.50088329 0.353261474
Si 0.580006233 0.584849814 0.417191231
Si 0.480248976 0.332642526 0.480248976
Si 0.57137893 0.414042102 0.57137893
Si 0.353261474 0.50088329 0.48026794
Si 0.417191231 0.584849814 0.580006233
Si 0.666669731 0.000706126 -0.000324041
Si 0.750211648 0.083796546 0.083305974
Si 0.833567118 0.167199862 -0.000050503
Si 0.91655396 0.25086993 0.083680781
Si 0.833842252 0.000705685 0.166847757
Si 0.916324599 0.085133815 0.250271264
Si 0.666672794 0.166950385 0.166844061
Si 0.748059434 0.251645742 0.25061009
Si -0.000046498 0.666319325 -0.000046498
Si 0.083310474 0.749720003 0.083310474
Si 0.166849408 0.832812125 -0.000320241
Si 0.249894392 0.917536984 0.082138295
Si 0.166849157 0.666565814 0.166849157
Si 0.248598161 0.752834182 0.248598161
Si -0.000320241 0.832812125 0.166849408
Si 0.082138295 0.917536984 0.249894392
Si -0.000324041 0.000706126 0.666669731
Si 0.083305974 0.083796546 0.750211648
Si 0.166844061 0.166950385 0.666672794
Si 0.25061009 0.251645742 0.748059434
Si 0.166847757 0.000705685 0.833842252
Si 0.250271264 0.085133815 0.916324599
Si -0.000050503 0.167199862 0.833567118
Si 0.083680781 0.25086993 0.91655396
Si 0.666164587 0.333916048 0.000974095
Si 0.746609413 0.417355424 0.086910427
Si 0.832014611 0.49966197 0.001506917
Si 0.916968097 0.582647815 0.083683525
Si 0.832544541 0.333914793 0.167354433
Si 0.916760745 0.416758396 0.25046003
Si 0.660258462 0.499196553 0.173262847
Si 0.748597694 0.582797353 0.2509117
Si 0.668009708 -0.000933789 0.333180451
Si 0.749641931 0.084085043 0.41644676
Si 0.832393129 0.168419579 0.33355623
Si 0.91675807 0.251006558 0.416759205
Si 0.834019246 0.001350301 0.500079104
Si 0.91719377 0.085135734 0.583246733
Si 0.665371779 0.166694627 0.500237846
Si 0.748591761 0.250725201 0.582604154
Si 0.333559034 0.66509661 0.001128602
Si 0.416449984 0.749435486 0.083874863
Si 0.50008047 0.832171776 -0.000502798
Si 0.583626239 0.915979758 0.082135755
Si 0.500243592 0.666827982 0.168143444
Si 0.583625099 0.750989296 0.249896054
Si 0.333183009 0.834450054 0.165510985
Si 0.416760069 0.916758439 0.249516138
Si 0.001128602 0.66509661 0.333559034
Si 0.083874863 0.749435486 0.416449984
Si 0.165510985 0.834450054 0.333183009
Si 0.249516138 0.916758439 0.416760069
Si 0.168143444 0.666827982 0.500243592
Si 0.249896054 0.750989296 0.583625099
Si -0.000502798 0.832171776 0.50008047
Si 0.082135755 0.915979758 0.583626239
Si 0.000974095 0.333916048 0.666164587
Si 0.086910427 0.417355424 0.746609413
Si 0.173262847 0.499196553 0.660258462
Si 0.2509117 0.582797353 0.748597694
Si 0.167354433 0.333914793 0.832544541
Si 0.25046003 0.416758396 0.916760745
Si 0.001506917 0.49966197 0.832014611
Si 0.083683525 0.582647815 0.916968097
Si 0.333180451 -0.000933789 0.668009708
Si 0.41644676 0.084085043 0.749641931
Si 0.500237846 0.166694627 0.665371779
Si 0.582604154 0.250725201 0.748591761
Si 0.500079104 0.001350301 0.834019246
Si 0.583246733 0.085135734 0.91719377
Si 0.33355623 0.168419579 0.832393129
Si 0.416759205 0.251006558 0.91675807
Si 0.66290372 0.334011565 0.334627374
Si 0.748225544 0.416761348 0.416758187
Si 0.832659302 0.499558247 0.333738078
Si 0.916760139 0.582512335 0.416760604
Si 0.832656476 0.333962688 0.499779238
Si 0.916758081 0.416760103 0.583059854
Si 0.662903816 0.499510524 0.498889939
Si 0.748059644 0.581874995 0.582908128
Si 0.331862275 0.670901493 0.331862275
Si 0.41676139 0.751413603 0.41676139
Si 0.500266765 0.834151423 0.333253539
Si 0.584002636 0.916760833 0.416758952
Si 0.501662794 0.670907012 0.501662794
Si 0.584925566 0.752840906 0.584925566
Si 0.333253539 0.834151423 0.500266765
Si 0.416758952 0.916760833 0.584002636
Si 0.334627374 0.334011565 0.66290372
Si 0.416758187 0.416761348 0.748225544
Si 0.498889939 0.499510524 0.662903816
Si 0.582908128 0.581874995 0.748059644
Si 0.499779238 0.333962688 0.832656476
Si 0.583059854 0.416760103 0.916758081
Si 0.333738078 0.499558247 0.832659302
Si 0.416760604 0.582512335 0.916760139
Si 0.666526427 0.66551749 0.000586888
Si 0.750217128 0.749327852 0.083303101
Si 0.833356432 0.833375286 0.000162424
Si 0.916760578 0.916758078 0.083567138
Si 0.832934733 0.665517797 0.166993386
Si 0.917198881 0.748383414 0.250273119
Si 0.667363941 0.833624266 0.166155641
Si 0.751383807 0.915979925 0.249892713
Si 0.667360273 -0.000101737 0.667360273
Si 0.750213428 0.084193206 0.750213428
Si 0.832928801 0.168004203 0.666523002
Si 0.916963111 0.250870651 0.749835955
Si 0.833354131 0.000146272 0.833354131
Si 0.916758642 0.083504699 0.916758642
Si 0.666523002 0.168004203 0.832928801
Si 0.749835955 0.250870651 0.916963111
Si 0.000586888 0.66551749 0.666526427
Si 0.083303101 0.749327852 0.750217128
Si 0.166155641 0.833624266 0.667363941
Si 0.249892713 0.915979925 0.751383807
Si 0.166993386 0.665517797 0.832934733
Si 0.250273119 0.748383414 0.917198881
Si 0.000162424 0.833375286 0.833356432
Si 0.083567138 0.916758078 0.916760578
Si 0.665380336 0.666831005 0.333277607
Si 0.749646639 0.749439394 0.417071213
Si 0.834023558 0.832171881 0.333437911
Si 0.91675889 0.916760845 0.416759799
Si 0.832393772 0.665100367 0.49996154
Si 0.916323235 0.748385702 0.583248032
Si 0.668009949 0.834455299 0.500337021
Si 0.751381555 0.917542097 0.583625291
Si 0.660252589 0.334326299 0.660252589
Si 0.746606463 0.416165083 0.746606463
Si 0.832543349 0.499605526 0.66616452
Si 0.916554188 0.582648947 0.749838499
Si 0.832011417 0.333858507 0.832011417
Si 0.916759573 0.416758985 0.916759573
Si 0.66616452 0.499605526 0.832543349
Si 0.749838499 0.582648947 0.916554188
Si 0.333277607 0.666831005 0.665380336
Si 0.417071213 0.749439394 0.749646639
Si 0.500337021 0.834455299 0.668009949
Si 0.583625291 0.917542097 0.751381555
Si 0.49996154 0.665100367 0.832393772
Si 0.583248032 0.748385702 0.916323235
Si 0.333437911 0.832171881 0.834023558
Si 0.416759799 0.916760845 0.91675889
Si 0.666673889 0.666571113 0.666673889
Si 0.750212344 0.749724309 0.750212344
Si 0.833840442 0.832815634 0.666669721
Si 0.916758455 0.91676045 0.749952566
Si 0.833568833 0.666321048 0.833568833
Si 0.916761377 0.750013726 0.916761377
Si 0.666669721 0.832815634 0.833840442
Si 0.749952566 0.91676045 0.916758455
K_POINTS {automatic}
1 1 1 0 0 0
ph.in:
phonon of Si_1V_D2d
&inputph
tr2_ph=1.0d-14,
prefix='Si_1V_D2d',
amass(1)=28.0855,
outdir='tmp_Si_1V_D2d/'
fildyn='Si_1V_D2d.dyn1',
fildrho='Si_1V_D2d.drho',
/
0.0 0.0 0.0
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