[Pw_forum] the problem about eigndisplacement of phonon?

[degironc]

let's say that
(1) \Phi U = M \omega^2 U
and
(2) M^(-1/2) \Phi M^(-1/2) V = \omega^2 V

if V is a solution of (2) U = M^(1/2) V is a solution of (1).

What is printed in matdyn is U (NORMALIZED so that <U|U> = 1).

if you want V (normalized such that <V|V> = 1) you should take U divide
by sqrt of M and
renormalize.
Units of mass are irrelevant (due to the renormalization) mass ratio
betwen different species matters.

stefano


针叶 朱 wrote:

> Dear Professor Stefano Baroni :
> Thank you give me answers. i will give you a clear question.i have
> calculate the phonon of PbTiO3 at q=0. there is the eignvector of
> atoms under every phonon.
> for example,omega( 1) = -4.221301 [THz] = -140.808368 [cm-1],
> eignvector of Pb atom is -0.092855 -0.004178 0.001020.now i want to
> calculte the eigndisplacement of Pb atom under this phonon. i have
> konw eigndisplacement |u> =M^(-1/2) | v>. |v> is eignvector. i donnot
> know how to select M mass of Pb atom. in your letter, M should be
> 207.2 amu.namely, for Pb atom, eigndisplacement |u> =207.2^(-1/2) |
> v>. is my opinion true?
> there is phonons of PbTiO3 as below:
> omega( 1) = -4.22301 [THz] = -140.808368 [cm-1]
> ( -0.092855 0.000000 -0.004178 0.000000 0.001020 0.000000 )
> ( -0.185613 0.000000 -0.008352 0.000000 0.002040 0.000000 )
> ( 0.598322 0.000000 0.026924 0.000000 -0.005371 0.000000 )
> ( 0.598322 0.000000 0.021990 0.000000 -0.006576 0.000000 )
> ( 0.488678 0.000000 0.026924 0.000000 -0.006576 0.000000 )
> omega( 2) = -4.221301 [THz] = -140.808368 [cm-1]
> ( 0.000638 0.000000 0.008439 0.000000 0.092568 0.000000 )
> ( 0.001275 0.000000 0.016869 0.000000 0.185040 0.000000 )
> ( -0.004108 0.000000 -0.054377 0.000000 -0.487170 0.000000 )
> ( -0.004108 0.000000 -0.044413 0.000000 -0.596476 0.000000 )
> ( -0.003356 0.000000 -0.054377 0.000000 -0.596476 0.000000 )
> omega( 3) = -4.221301 [THz] = -140.808368 [cm-1]
> ( -0.004254 0.000000 0.092476 0.000000 -0.008401 0.000000 )
> ( -0.008503 0.000000 0.184856 0.000000 -0.016794 0.000000 )
> ( 0.027409 0.000000 -0.595882 0.000000 0.044214 0.000000 )
> ( 0.027409 0.000000 -0.486685 0.000000 0.054134 0.000000 )
> ( 0.022386 0.000000 -0.595882 0.000000 0.054134 0.000000 )
> omega( 4) = -0.669952 [THz] = -22.347350 [cm-1]
> ( -0.041557 0.000000 -0.005329 0.000000 0.392444 0.000000 )
> ( -0.052468 0.000000 -0.006728 0.000000 0.495474 0.000000 )
> ( -0.047053 0.000000 -0.006034 0.000000 0.440840 0.000000 )
> ( -0.047053 0.000000 -0.005986 0.000000 0.444344 0.000000 )
> ( -0.046682 0.000000 -0.006034 0.000000 0.444344 0.000000 )
> omega( 5) = -0.669952 [THz] = -22.347350 [cm-1]
> ( -0.169027 0.000000 0.356408 0.000000 -0.013059 0.000000 )
> ( -0.213403 0.000000 0.449978 0.000000 -0.016488 0.000000 )
> ( -0.191381 0.000000 0.403543 0.000000 -0.014670 0.000000 )
> ( -0.191381 0.000000 0.400360 0.000000 -0.014787 0.000000 )
> ( -0.189872 0.000000 0.403543 0.000000 -0.014787 0.000000 )
> omega( 6) = -0.669952 [THz] = -22.347350 [cm-1]
> ( 0.354218 0.000000 0.169447 0.000000 0.039810 0.000000 )
> ( 0.447213 0.000000 0.213933 0.000000 0.050262 0.000000 )
> ( 0.401063 0.000000 0.191857 0.000000 0.044720 0.000000 )
> ( 0.401063 0.000000 0.190344 0.000000 0.045075 0.000000 )
> ( 0.397900 0.000000 0.191857 0.000000 0.045075 0.000000 )
> omega( 7) = 3.378427 [THz] = 112.692954 [cm-1]
> ( -0.224846 0.000000 -0.197313 0.000000 -0.001099 0.000000 )
> ( 0.706263 0.000000 0.619778 0.000000 0.003451 0.000000 )
> ( 0.075451 0.000000 0.066211 0.000000 0.000316 0.000000 )
> ( 0.075451 0.000000 0.056787 0.000000 0.000369 0.000000 )
> ( 0.064711 0.000000 0.066211 0.000000 0.000369 0.000000 )
> omega( 8) = 3.378427 [THz] = 112.692954 [cm-1]
> ( -0.197127 0.000000 0.224701 0.000000 -0.011833 0.000000 )
> ( 0.619195 0.000000 -0.705805 0.000000 0.037169 0.000000 )
> ( 0.066149 0.000000 -0.075402 0.000000 0.003406 0.000000 )
> ( 0.066149 0.000000 -0.064669 0.000000 0.003971 0.000000 )
> ( 0.056734 0.000000 -0.075402 0.000000 0.003971 0.000000 )
> omega( 9) = 3.378427 [THz] = 112.692954 [cm-1]
> ( -0.008630 0.000000 0.008170 0.000000 0.298912 0.000000 )
> ( 0.027108 0.000000 -0.025663 0.000000 -0.938909 0.000000 )
> ( 0.002896 0.000000 -0.002742 0.000000 -0.086028 0.000000 )
> ( 0.002896 0.000000 -0.002351 0.000000 -0.100304 0.000000 )
> ( 0.002484 0.000000 -0.002742 0.000000 -0.100304 0.000000 )
> omega(10) = 6.809520 [THz] = 227.142638 [cm-1]
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( -0.706639 0.000000 -0.025709 0.000000 0.000000 0.000000 )
> ( 0.706639 0.000000 0.000000 0.000000 0.000444 0.000000 )
> ( 0.000000 0.000000 0.025709 0.000000 -0.000444 0.000000 )
> omega(11) = 6.809520 [THz] = 227.142638 [cm-1]
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( -0.000153 0.000000 -0.008007 0.000000 0.000000 0.000000 )
> ( 0.000153 0.000000 0.000000 0.000000 -0.707061 0.000000 )
> ( 0.000000 0.000000 0.008007 0.000000 0.707061 0.000000 )
> omega(12) = 6.809520 [THz] = 227.142638 [cm-1]
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 )
> ( -0.025712 0.000000 0.706594 0.000000 0.000000 0.000000 )
> ( 0.025712 0.000000 0.000000 0.000000 -0.007996 0.000000 )
> ( 0.000000 0.000000 -0.706594 0.000000 0.007996 0.000000 )
> omega(13) = 15.128567 [THz] = 504.638023 [cm-1]
> ( 0.007689 0.000000 -0.000587 0.000000 0.000000 0.000000 )
> ( 0.010929 0.000000 -0.000834 0.000000 0.000000 0.000000 )
> ( 0.362132 0.000000 -0.027649 0.000000 0.000000 0.000000 )
> ( 0.362132 0.000000 0.065311 0.000000 0.000000 0.000000 )
> ( -0.855422 0.000000 -0.027649 0.000000 0.000000 0.000000 )
> omega(14) = 15.128567 [THz] = 504.638023 [cm-1]
> ( 0.000587 0.000000 0.007689 0.000000 0.000000 0.000000 )
> ( 0.000834 0.000000 0.010929 0.000000 0.000000 0.000000 )
> ( 0.027649 0.000000 0.362132 0.000000 0.000000 0.000000 )
> ( 0.027649 0.000000 -0.855422 0.000000 0.000000 0.000000 )
> ( -0.065311 0.000000 0.362132 0.000000 0.000000 0.000000 )
> omega(15) = 15.128567 [THz] = 504.638023 [cm-1]
> ( 0.000000 0.000000 0.000000 0.000000 0.007711 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.010961 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 -0.857912 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.363186 0.000000 )
> ( 0.000000 0.000000 0.000000 0.000000 0.363186 0.000000 )
> Regards
> zhuzhenye
>
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