# [Pw_forum] phonon eigenvectors

Stefano Baroni baroni at sissa.it
Thu Aug 31 10:05:04 CEST 2006

```Eric: do not be satisfied by meaningful answer to your meaningful and
legitimate questions. You have to *understand* them (i.e. do not stop
thinking and striving to understand, until answers given by others
you are sure that you can answer all of them).

Coming now to your present doubt. You have to understand here that
what is arbitrary here is the overall _phase_ of the eigenvectors.
This obviously implies (in some sense) that the imaginary part is
arbitrary, but *NOT* that it can (always) be neglected, as this
specic case  shows. What has to be nonzero is NOT the real part of
the eigenvector, but its modulus.

Is it clearer now? Could you answer similar questions by yourself in
the future?

Signed: Stefano B.

On Aug 31, 2006, at 6:07 AM, Eric Abel wrote:

> Hello PWSCF users,
>
> I have a question which is sort of a follow-up to a similar
> the imaginary part of the phonon eigenvectors, which at the time,
> Stefano had informed me are more or less arbitrary.   At the time
> that made sense.  But now I am trying to make sense of the
> following eigenvectors:
>
> q =       0.0000      0.0563      0.0000
> **********************************************************************
> ****
>     omega( 1) =      -0.308036 [THz] =     -10.275037 [cm-1]
> (  0.000000   0.000000     0.000000  -0.142674    -0.338669
> 0.000000   )
> (  0.000000   0.000000     0.031918  -0.201463    -0.388896
> -0.061613   )
> (  0.000000   0.000000     0.019612  -0.123787    -0.367551
> -0.058231   )
> (  0.000000   0.000000     0.000000  -0.226888    -0.354765
> 0.000000   )
> (  0.000000   0.000000     0.036445  -0.230039    -0.328252
> -0.052005   )
> (  0.000000   0.000000     0.000000  -0.096682    -0.403396
> 0.000000   )
>     omega( 2) =       0.617574 [THz] =      20.600196 [cm-1]
> ( -0.403925  -0.012145     0.000000   0.000000     0.000000
> 0.000000   )
> ( -0.397050  -0.075201     0.000000   0.000000     0.000000
> 0.000000   )
> ( -0.397199  -0.075229     0.000000   0.000000     0.000000
> 0.000000   )
> ( -0.404073  -0.012149     0.000000   0.000000     0.000000
> 0.000000   )
> ( -0.408949  -0.077455     0.000000   0.000000     0.000000
> 0.000000   )
> ( -0.416112  -0.012511     0.000000   0.000000     0.000000
> 0.000000   )
>     omega( 3) =       0.788199 [THz] =      26.291668 [cm-1]
> (  0.000000   0.000000     0.000000   0.389819    -0.233273
> 0.000000   )
> (  0.000000   0.000000    -0.055122   0.347926    -0.110454
> -0.017499   )
> (  0.000000   0.000000    -0.061881   0.390589    -0.148121
> -0.023467   )
> (  0.000000   0.000000     0.000000   0.342277    -0.187111
> 0.000000   )
> (  0.000000   0.000000    -0.050913   0.321357    -0.249835
> -0.039581   )
> (  0.000000   0.000000     0.000000   0.384275    -0.092029
> 0.000000   )
>
> These are the first 3 (accoustic) modes of the spectrum.  If the
> imaginary part doesn't matter, then it would appear that the
> accoustic displacement along the b-direction is practically zero.
> However, the imaginary part is the same magnitude as the
> displacements in the other orthogonal directions.  Is there any
> physical meaning to this, or is it just an artifact of the
> calculation?
>
> Eric,
> Ph.D. Student, M.I.T.
>
>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

Please, if possible, don't  send me MS Word or PowerPoint attachments
Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html

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