[Pw_forum] LO-TO splitting
Fethi SOYALP
fsoyalp at yyu.edu.tr
Fri Feb 4 22:15:25 CET 2005
> You guess? The acoustic mode is 3-fold degenerate. The other three =20
> modes are split in a singlet (LO) plus a doublet (TO). Why LT and TO =20
> modes are split would require some more explanation, and I would like =20=
>
> to urge you to consult any text-book in solid-state physics to =20
> understant why. If after studying your favorite text you still do not =20=
>
> understand, please revert to us and we will give further help.
Dear Stefano,
Thank you very much for your help about LO-TO splitting in example06.
Now I calculate vibration modes for a CaF2 structure.I am confused
because there isn’t degenerate some direcion, for egzample (110). How can
I determine which modes are LO-TO and which modes are LA-TA when
degeneracy disapear. according to the output file, first two and last five
eigenvectors are below. for first three eigenvectors, because of the
small modes, I can say first three modes are acoustic, last six modes are
optic .Near the X point (last four eigenvectors) acoustic and optic
branches are crossing. I can’t determine acouistic and optic modes from
their greatnes. please gave me some comments. I have need your help.
q = 0.0250 0.0250 0.0000
**************************************************************************
omega( 1) = 0.512971 [THz] = 17.110993 [cm-1]
( -0.406694 0.025294 0.406694 -0.025294 0.000000 0.000000 )
( -0.404596 0.057287 0.404596 -0.057287 0.000000 0.000000 )
( -0.408577 -0.006711 0.408577 0.006711 0.000000 0.000000 )
omega( 2) = 0.542446 [THz] = 18.094187 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.574443 0.045210 )
( -0.002253 -0.014223 -0.002253 -0.014223 -0.570445 0.090350 )
( 0.000000 0.014401 0.000000 0.014401 -0.577556 0.000000 )
omega( 3) = 0.671957 [THz] = 22.414210 [cm-1]
( 0.031989 0.406461 0.031989 0.406461 0.000000 0.000000 )
( 0.063866 0.403232 0.063866 0.403232 -0.020143 0.003190 )
( 0.000000 0.408258 0.000000 0.408258 0.020394 0.000000 )
omega( 4) = 9.419107 [THz] = 314.189680 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.129018 0.010154 )
( -0.075525 -0.476846 -0.075525 -0.476846 0.157578 -0.024958 )
( 0.000000 0.482790 0.000000 0.482790 0.159542 0.000000 )
omega( 5) = 9.420889 [THz] = 314.249133 [cm-1]
( -0.007168 -0.091078 -0.007168 -0.091078 0.000000 0.000000 )
( 0.017643 0.111392 0.017643 0.111392 0.674393 -0.106813 )
( 0.000000 0.112780 0.000000 0.112780 -0.682799 0.000000 )
omega( 6) = 9.448169 [THz] = 315.159105 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.097607 0.490380 -0.097607 -0.490380 0.000000 0.000000 )
( -0.019693 -0.499612 0.019693 0.499612 0.000000 0.000000 )
omega( 7) = 9.751590 [THz] = 325.280207 [cm-1]
( 0.246460 0.309902 -0.246460 -0.309902 0.000000 0.000000 )
( -0.282494 -0.302995 0.282494 0.302995 0.000000 0.000000 )
( -0.231618 -0.343456 0.231618 0.343456 0.000000 0.000000 )
omega( 8) = 9.773977 [THz] = 326.026956 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.531826 -0.041856 )
( -0.025955 -0.163873 -0.025955 -0.163873 -0.543362 0.086060 )
( 0.000000 0.165916 0.000000 0.165916 -0.550135 0.000000 )
omega( 9) = 9.775480 [THz] = 326.077074 [cm-1]
( -0.029580 -0.375850 -0.029580 -0.375850 0.000000 0.000000 )
( 0.060880 0.384382 0.060880 0.384382 -0.231528 0.036670 )
( 0.000000 0.389173 0.000000 0.389173 0.234414 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
17.111000 TA (because all atoms vibrate same direction)
18.094200 LA (L because the vibrational eigenvector has non-vanishing z
component; the wavevector is directed along xy, hence the mode is
transverse)
22.414200 ?A
314.189697 O (O because small atoms vibrations are bigger than small atom)
314.249115 ?O
315.159088 TO
325.280212 TO
326.027008 ?O
326.077087 ?O
q = 0.0500 0.0500 0.0000
**************************************************************************
omega( 1) = 0.622850 [THz] = 20.776190 [cm-1]
( 0.405477 -0.048461 -0.405477 0.048461 0.000000 0.000000 )
( 0.392739 -0.111248 -0.392739 0.111248 0.000000 0.000000 )
( 0.407894 0.015560 -0.407894 -0.015560 0.000000 0.000000 )
omega( 2) = 0.715136 [THz] = 23.854512 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.570236 0.090317 )
( -0.008890 -0.027362 -0.008890 -0.027362 -0.547730 0.177968 )
( 0.000000 0.028770 0.000000 0.028770 -0.575918 0.000000 )
omega( 3) = 1.066602 [THz] = 35.578241 [cm-1]
( -0.064032 -0.404285 -0.064032 -0.404285 0.000000 0.000000 )
( -0.125672 -0.386777 -0.125672 -0.386777 0.038912 -0.012643 )
( 0.000000 -0.406682 0.000000 -0.406682 -0.040915 0.000000 )
omega( 4) = 9.355051 [THz] = 312.052975 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.204219 -0.032345 )
( 0.139849 0.430410 0.139849 0.430410 -0.249827 0.081174 )
( 0.000000 -0.452560 0.000000 -0.452560 -0.262684 0.000000 )
omega( 5) = 9.362934 [THz] = 312.315930 [cm-1]
( 0.022737 0.143558 0.022737 0.143558 0.000000 0.000000 )
( -0.057382 -0.176604 -0.057382 -0.176604 -0.608907 0.197846 )
( 0.000000 -0.185692 0.000000 -0.185692 0.640243 0.000000 )
omega( 6) = 9.454900 [THz] = 315.383604 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.068326 0.495310 -0.068326 -0.495310 0.000000 0.000000 )
( 0.088078 -0.492181 -0.088078 0.492181 0.000000 0.000000 )
omega( 7) = 9.758643 [THz] = 325.515459 [cm-1]
( 0.101694 0.381763 -0.101694 -0.381763 0.000000 0.000000 )
( -0.168110 -0.379074 0.168110 0.379074 0.000000 0.000000 )
( -0.042742 -0.412469 0.042742 0.412469 0.000000 0.000000 )
omega( 8) = 9.831911 [THz] = 327.959444 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.486764 -0.077096 )
( -0.080649 -0.248212 -0.080649 -0.248212 -0.468179 0.152121 )
( 0.000000 0.260985 0.000000 0.260985 -0.492272 0.000000 )
omega( 9) = 9.837634 [THz] = 328.150317 [cm-1]
( -0.054427 -0.343638 -0.054427 -0.343638 0.000000 0.000000 )
( 0.107811 0.331810 0.107811 0.331810 -0.350098 0.113754 )
( 0.000000 0.348885 0.000000 0.348885 0.368115 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
20.776199
23.854500
35.578201
312.053009
312.315887
315.383606
325.515503
327.959412
328.150299
last five eigenvector.
q = 0.9000 0.9000 0.0000
**************************************************************************
omega( 1) = 5.112475 [THz] = 170.534951 [cm-1]
( 0.453049 -0.311934 -0.453049 0.311934 0.000000 0.000000 )
( -0.301186 0.089491 0.301186 -0.089491 0.000000 0.000000 )
( -0.191063 0.249433 0.191063 -0.249433 0.000000 0.000000 )
omega( 2) = 5.481749 [THz] = 182.852665 [cm-1]
( -0.172532 0.530999 -0.172532 0.530999 0.000000 0.000000 )
( -0.175797 0.241963 -0.175797 0.241963 0.078318 0.056902 )
( 0.000000 0.299083 0.000000 0.299083 -0.096807 0.000000 )
omega( 3) = 7.581087 [THz] = 252.879509 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.078334 0.025452 )
( 0.093007 -0.128014 0.093007 -0.128014 0.540610 0.392776 )
( 0.000000 0.158234 0.000000 0.158234 0.668231 0.000000 )
omega( 4) = 7.745696 [THz] = 258.370336 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.493523 -0.160355 )
( -0.228501 0.314505 -0.228501 0.314505 0.203237 0.147660 )
( 0.000000 -0.388749 0.000000 -0.388749 0.251214 0.000000 )
omega( 5) = 7.974611 [THz] = 266.006149 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( -0.360316 -0.346659 0.360316 0.346659 0.000000 0.000000 )
( 0.495263 0.068665 -0.495263 -0.068665 0.000000 0.000000 )
omega( 6) = 8.411441 [THz] = 280.577334 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.576853 -0.187431 )
( 0.229436 -0.315791 0.229436 -0.315791 -0.086098 -0.062554 )
( 0.000000 0.390339 0.000000 0.390339 -0.106424 0.000000 )
omega( 7) = 10.869387 [THz] = 362.566124 [cm-1]
( -0.022070 0.067924 -0.022070 0.067924 0.000000 0.000000 )
( 0.140863 -0.193881 0.140863 -0.193881 0.498735 0.362352 )
( 0.000000 -0.239650 0.000000 -0.239650 -0.616470 0.000000 )
omega( 8) = 11.043721 [THz] = 368.381318 [cm-1]
( 0.123427 -0.222049 -0.123427 0.222049 0.000000 0.000000 )
( 0.341637 -0.317828 -0.341637 0.317828 0.000000 0.000000 )
( 0.089575 -0.457937 -0.089575 0.457937 0.000000 0.000000 )
omega( 9) = 11.085726 [THz] = 369.782482 [cm-1]
( -0.071758 0.220847 -0.071758 0.220847 0.000000 0.000000 )
( 0.232682 -0.320260 0.232682 -0.320260 -0.294668 -0.214089 )
( 0.000000 -0.395863 0.000000 -0.395863 0.364229 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
170.535004
182.852707
252.879501
258.370300
266.006104
280.577301
362.566101
368.381287
369.782501
q = 0.9250 0.9250 0.0000
**************************************************************************
omega( 1) = 5.167330 [THz] = 172.364732 [cm-1]
( 0.442339 -0.329097 -0.442339 0.329097 0.000000 0.000000 )
( -0.287867 0.123077 0.287867 -0.123077 0.000000 0.000000 )
( -0.200616 0.240351 0.200616 -0.240351 0.000000 0.000000 )
omega( 2) = 5.378558 [THz] = 179.410579 [cm-1]
( -0.129809 0.540692 -0.129809 0.540692 0.000000 0.000000 )
( -0.138284 0.271397 -0.138284 0.271397 0.064520 0.032874 )
( 0.000000 0.304596 0.000000 0.304596 -0.072412 0.000000 )
omega( 3) = 7.584358 [THz] = 252.988617 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.042364 -0.010171 )
( -0.054594 0.107147 -0.054594 0.107147 -0.610927 -0.311283 )
( 0.000000 -0.120254 0.000000 -0.120254 -0.685660 0.000000 )
omega( 4) = 7.808341 [THz] = 260.459944 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.440308 -0.105709 )
( -0.193961 0.380669 -0.193961 0.380669 0.160424 0.081740 )
( 0.000000 -0.427235 0.000000 -0.427235 0.180048 0.000000 )
omega( 5) = 7.946584 [THz] = 265.071270 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( -0.405802 0.292104 0.405802 -0.292104 0.000000 0.000000 )
( 0.228960 -0.444497 -0.228960 0.444497 0.000000 0.000000 )
omega( 6) = 8.319704 [THz] = 277.517305 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.662283 0.159000 )
( -0.164136 0.322134 -0.164136 0.322134 0.072537 0.036959 )
( 0.000000 -0.361540 0.000000 -0.361540 0.081410 0.000000 )
omega( 7) = 10.871653 [THz] = 362.641727 [cm-1]
( -0.013202 0.054992 -0.013202 0.054992 0.000000 0.000000 )
( 0.084463 -0.165768 0.084463 -0.165768 0.582623 0.296861 )
( 0.000000 -0.186045 0.000000 -0.186045 -0.653893 0.000000 )
omega( 8) = 11.050990 [THz] = 368.623808 [cm-1]
( 0.097862 -0.233025 -0.097862 0.233025 0.000000 0.000000 )
( 0.276325 -0.376438 -0.276325 0.376438 0.000000 0.000000 )
( 0.075308 -0.460858 -0.075308 0.460858 0.000000 0.000000 )
omega( 9) = 11.075187 [THz] = 369.430936 [cm-1]
( -0.055930 0.232966 -0.055930 0.232966 0.000000 0.000000 )
( 0.192932 -0.378651 0.192932 -0.378651 -0.254209 -0.129526 )
( 0.000000 -0.424970 0.000000 -0.424970 0.285306 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
172.364700
179.410599
252.988602
260.459900
265.071289
277.517303
362.641693
368.623810
369.430908
q = 0.9500 0.9500 0.0000
**************************************************************************
omega( 1) = 5.207227 [THz] = 173.695562 [cm-1]
( 0.393952 -0.387044 -0.393952 0.387044 0.000000 0.000000 )
( -0.254228 0.181294 0.254228 -0.181294 0.000000 0.000000 )
( -0.185762 0.250982 0.185762 -0.250982 0.000000 0.000000 )
omega( 2) = 5.302235 [THz] = 176.864690 [cm-1]
( 0.086726 -0.547564 0.086726 -0.547564 0.000000 0.000000 )
( 0.095328 -0.293390 0.095328 -0.293390 -0.045832 -0.014892 )
( 0.000000 -0.308488 0.000000 -0.308488 0.048190 0.000000 )
omega( 3) = 7.587883 [THz] = 253.106224 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.019256 -0.003050 )
( -0.025701 0.079099 -0.025701 0.079099 -0.663000 -0.215422 )
( 0.000000 -0.083170 0.000000 -0.083170 -0.697119 0.000000 )
omega( 4) = 7.859171 [THz] = 262.155459 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.345835 -0.054775 )
( -0.142325 0.438032 -0.142325 0.438032 0.114290 0.037135 )
( 0.000000 -0.460575 0.000000 -0.460575 0.120172 0.000000 )
omega( 5) = 7.926161 [THz] = 264.390041 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.264399 -0.424374 -0.264399 0.424374 0.000000 0.000000 )
( -0.120319 0.485307 0.120319 -0.485307 0.000000 0.000000 )
omega( 6) = 8.244308 [THz] = 275.002344 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.776467 0.122980 )
( -0.094861 0.291952 -0.094861 0.291952 0.047725 0.015507 )
( 0.000000 -0.306977 0.000000 -0.306977 0.050181 0.000000 )
omega( 7) = 10.872635 [THz] = 362.674492 [cm-1]
( -0.006135 0.038735 -0.006135 0.038735 0.000000 0.000000 )
( 0.039328 -0.121039 0.039328 -0.121039 0.649278 0.210963 )
( 0.000000 -0.127268 0.000000 -0.127268 -0.682692 0.000000 )
omega( 8) = 11.055931 [THz] = 368.788605 [cm-1]
( 0.067935 -0.242448 -0.067935 0.242448 0.000000 0.000000 )
( 0.194892 -0.424640 -0.194892 0.424640 0.000000 0.000000 )
( 0.054132 -0.464082 -0.054132 0.464082 0.000000 0.000000 )
omega( 9) = 11.066863 [THz] = 369.153260 [cm-1]
( -0.038426 0.242610 -0.038426 0.242610 0.000000 0.000000 )
( 0.138374 -0.425871 0.138374 -0.425871 -0.186942 -0.060741 )
( 0.000000 -0.447787 0.000000 -0.447787 0.196562 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
173.695602
176.864700
253.106201
262.155487
264.390015
275.002289
362.674500
368.788605
369.153290
q = 0.9750 0.9750 0.0000
**************************************************************************
omega( 1) = 5.231455 [THz] = 174.503706 [cm-1]
( 0.243465 -0.496342 -0.243465 0.496342 0.000000 0.000000 )
( -0.158826 0.268252 0.158826 -0.268252 0.000000 0.000000 )
( -0.114907 0.289795 0.114907 -0.289795 0.000000 0.000000 )
omega( 2) = 5.255377 [THz] = 175.301680 [cm-1]
( 0.043417 -0.551666 0.043417 -0.551666 0.000000 0.000000 )
( 0.048621 -0.306979 0.048621 -0.306979 -0.023775 -0.003766 )
( 0.000000 -0.310806 0.000000 -0.310806 0.024071 0.000000 )
omega( 3) = 7.590739 [THz] = 253.201497 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.004963 0.000391 )
( 0.006713 -0.042387 0.006713 -0.042387 0.695815 0.110206 )
( 0.000000 0.042915 0.000000 0.042915 0.704489 0.000000 )
omega( 4) = 7.895472 [THz] = 263.366337 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.198742 -0.015641 )
( -0.076350 0.482056 -0.076350 0.482056 0.060190 0.009533 )
( 0.000000 -0.488065 0.000000 -0.488065 0.060941 0.000000 )
omega( 5) = 7.913739 [THz] = 263.975668 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.131005 -0.482533 -0.131005 0.482533 0.000000 0.000000 )
( -0.053908 0.497085 0.053908 -0.497085 0.000000 0.000000 )
omega( 6) = 8.191441 [THz] = 273.238867 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 -0.916819 -0.072155 )
( 0.030660 -0.193581 0.030660 -0.193581 -0.016851 -0.002669 )
( 0.000000 0.195994 0.000000 0.195994 -0.017061 0.000000 )
omega( 7) = 10.872943 [THz] = 362.684763 [cm-1]
( -0.001575 0.020019 -0.001575 0.020019 0.000000 0.000000 )
( 0.010114 -0.063855 0.010114 -0.063855 0.692254 0.109642 )
( 0.000000 -0.064651 0.000000 -0.064651 -0.700883 0.000000 )
omega( 8) = 11.058790 [THz] = 368.883976 [cm-1]
( -0.036765 0.248500 0.036765 -0.248500 0.000000 0.000000 )
( -0.104468 0.455560 0.104468 -0.455560 0.000000 0.000000 )
( -0.031917 0.466293 0.031917 -0.466293 0.000000 0.000000 )
omega( 9) = 11.061549 [THz] = 368.976011 [cm-1]
( -0.019585 0.248848 -0.019585 0.248848 0.000000 0.000000 )
( 0.072335 -0.456708 0.072335 -0.456708 -0.099078 -0.015692 )
( 0.000000 -0.462400 0.000000 -0.462400 0.100313 0.000000 )
**************************************************************************
diagonalizing the dynamical matrix ...
174.503693
175.301697
253.201508
263.366302
263.975708
273.238892
362.684814
368.884003
368.976013
q = 1.0000 1.0000 0.0000
**************************************************************************
omega( 1) = 5.239579 [THz] = 174.774706 [cm-1]
( 0.104210 -0.002667 -0.774879 0.019464 0.000000 0.000000 )
( -0.436565 0.010966 0.058711 -0.001502 0.000000 0.000000 )
( -0.436565 0.010966 0.058711 -0.001502 0.000000 0.000000 )
omega( 2) = 5.239579 [THz] = 174.774706 [cm-1]
( -0.774540 -0.030066 -0.104163 -0.004093 0.000000 0.000000 )
( -0.058685 -0.002306 -0.436374 -0.016939 0.000000 0.000000 )
( -0.058685 -0.002306 -0.436374 -0.016939 0.000000 0.000000 )
omega( 3) = 7.591846 [THz] = 253.238404 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.000000 0.000000 0.000000 0.000000 -0.707107 0.000000 )
( 0.000000 0.000000 0.000000 0.000000 -0.707107 0.000000 )
omega( 4) = 7.909569 [THz] = 263.836578 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( -0.340127 -0.006494 0.619793 0.011327 0.000000 0.000000 )
( 0.340127 0.006494 -0.619793 -0.011327 0.000000 0.000000 )
omega( 5) = 7.909569 [THz] = 263.836578 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.616368 -0.066041 0.338223 -0.036518 0.000000 0.000000 )
( -0.616368 0.066041 -0.338223 0.036518 0.000000 0.000000 )
omega( 6) = 8.171481 [THz] = 272.573075 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 1.000000 0.000296 )
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
omega( 7) = 10.872996 [THz] = 362.686515 [cm-1]
( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
( 0.000000 0.000000 0.000000 0.000000 -0.707107 0.000000 )
( 0.000000 0.000000 0.000000 0.000000 0.707107 0.000000 )
omega( 8) = 11.059725 [THz] = 368.915167 [cm-1]
( -0.150757 -0.065210 0.289515 0.123338 0.000000 0.000000 )
( -0.539143 -0.229683 0.280745 0.121436 0.000000 0.000000 )
( -0.539143 -0.229683 0.280745 0.121436 0.000000 0.000000 )
omega( 9) = 11.059725 [THz] = 368.915167 [cm-1]
( 0.306189 -0.072661 0.159606 -0.038807 0.000000 0.000000 )
( -0.297223 0.072268 -0.570194 0.135311 0.000000 0.000000 )
( -0.297223 0.072268 -0.570194 0.135311 0.000000 0.000000 )
**************************************************************************
174.774704
174.774704
253.238403
263.836609
263.836609
272.573090
362.686493
368.915192
368.915192
Best Regarts
Fethi Soyalp
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