[QE-users] Symmetries in the dynamical matrix
Paolo Giannozzi
p.giannozzi at gmail.com
Thu Oct 18 10:25:54 CEST 2018
Not sure about this specific case, but only some of the symmetries of the
dynamical matrix are enforced in the calculation (in particular: symmetries
wrt operations of the small group of q). Other symmetries are not enforced
and should "emerge naturally" from the calculation. If I remember
correctly, the symmetry of dynamical matrix with respect to exchange of
indices belongs to the second category. Another famous example is the
acoustic sum rule. In the subsequent processing by auxiliary codes (dynmat,
q2r, matdyn) that symmetry is explicitly imposed. Incomplete scf
convergence, for instance, may lead to a small loss of symmetry.
On Tue, Oct 16, 2018 at 5:11 PM JAY Antoine <Antoine.JAY at isae-supaero.fr>
wrote:
> 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 _______________________________________________
> users mailing list
> users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
--
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20181018/802a84fe/attachment.html>
More information about the users
mailing list