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