# [Pw_forum] phonon eigenvectors

Eric Abel etabel at hotmail.com
Thu Aug 31 15:22:21 CEST 2006

```>From: Stefano Baroni <baroni at sissa.it>
>To: pw_forum at pwscf.org
>Subject: Re: [Pw_forum] phonon eigenvectors
>Date: Thu, 31 Aug 2006 10:05:04 +0200
>
>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   sound
>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.

Stefano, I apologize if it sounded as though I was trying to trivialize your
(previous) answer.  I read most of the postings to this users forum, and
understand there are a great many who prefer to simply ask questions rather
than seek out the answers themselves.  As for me, I am too proud to ask for
help, so when I do, it's because I feel I have no where else to turn.  That
said, I probably didn't ask the question in the proper way.  My bad.  My gut
instinct was that the modulus, rather than the real part, was the important
value...I just wanted confirmation.   The questions which I asked myself
before posting to the forum were the following:

Question: What is the meaning of an eigenvector?
Answer:  An eigenvector tells how the atoms are displaced in the vibration.

Question: What is the imaginary part?
Answer: The imaginary part is a phase factor.  If one atom has a significant
imaginary part with respect to the rest, then then it's displacement in the
vibration will be phase shifted with respect to the others.  In the case of
a completely imaginary eigenvector, the displacement will be completely out
of phase.

Question:  If the imaginary part is a phase factor, then what does it mean
if all of the components are imaginary?
Answer:  First answer: nothing.  If all of the atoms are "out of phase",
then they are "in phase" with respect to eachother, therefore, having a
completely imaginary or completely real eigenvector should be equivalent.

Question:  Great.  If this is the case, then why does this eigenvector come
up imaginary when all of the other vectors come up real?
Answer:  Hmmm.  That's a good one.  There must be some reason that the code
chooses an imaginary eigenvector for this mode...time to get help on this
one.  We are fresh out of answers.

And with this I come first to the pwscf discussion archive.  I didn't find
any discussion of imaginary eigenvectors with real eigenvalues.  I looked to
the literature, with the same result.  There comes a time when one asks
himself questions to which he doesn't have the answers, then it comes time
to discuss with his peers.  With that I come to you with my question:

Why did the code "choose" to make this displacement imaginary.  Is this
simply an artifact of the matrix diagonalization, or is there some physical
implications to this?

Thank you for your time and patience.

Eric
>
>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  question
>>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.
>>
>>
>>_______________________________________________
>>Pw_forum mailing list
>>Pw_forum at pwscf.org
>>http://www.democritos.it/mailman/listinfo/pw_forum
>
>---
>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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