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["matthieu verstraete" <matthieu.jean.verstraete@gmail.com>]

 Analysis of degeneracies and characters (maximum tolerance=1.00E-06 a.u.)
 Symmetry characters of vibration mode #   1
       degenerate with vibration modes #   2 to    3
  3.0  1.0 -1.0  1.0  1.0  1.0  1.0  1.0

 Symmetry characters of vibration mode #   4
        degenerate with vibration mode #   5
  2.0  0.0 -2.0  0.0  0.0  0.0  0.0  0.0
 Symmetry characters of vibration mode #   6
  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0

 Symmetry characters of vibration mode #   7
        degenerate with vibration mode #   8
  2.0  0.0 -2.0  0.0  0.0  0.0  0.0  0.0
 Symmetry characters of vibration mode #   9
  1.0  1.0  1.0  1.0 -1.0 -1.0 -1.0 -1.0

 Symmetry characters of vibration mode #  10
        degenerate with vibration mode #  11
  2.0  0.0 -2.0  0.0  0.0  0.0  0.0  0.0
 Symmetry characters of vibration mode #  12
  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0

 Symmetry characters of vibration mode #  13
        degenerate with vibration mode #  14
  2.0  0.0 -2.0  0.0  0.0  0.0  0.0  0.0
 Symmetry characters of vibration mode #  15
  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0


This is the bit you are interested in. Check the character tables (in solid state books or other reference works in group theory or on the bilbao group theory server http://www.cryst.ehu.es/) for the space group of your crystal (http://www.cryst.ehu.es/cgi-bin/rep/programs/sam/point.py?sg=99). Decomposing the representations above into irreducible ones is described in all solid state text books, and I'm afraid I can't explain it here (see e.g. Harrison "Solid state theory" Dover NY (1970)). It looks like modes 6 12 & 15 are A1 mode 9 is A2 - I may be wrong. For the rest you'll have to extract them. You can probably even guess them by looking at the other irreps in the web site.

The IR modes are those which have the irreducible representations of the translations, ie the operators x, y, and z, which are normally listed alongside the character tables: A1 and E in your case.

For determining the Raman active modes, find an article in the literature which has the correspondence. The calculation is algebraically simple but a little involved and I don't have a reference. A good crystallography book should explain how to do it.


To all: Please note that this has been an exception: use this email to
learn how to analyze your data, and do not expect us to
do it for you.

Matthieu

PS: you are using an antiquated version of abinit, I would recommend you upgrade it.

On Tue, Nov 18, 2008 at 6:47 PM, Mozhgan Amini <mozhganamini@yahoo.com> wrote:

Dear Matthieu,

 

As you said, I attached my anaddb output file for tetragonal phase of PbTiO3 to this email.

I have 15 modes for PbTiO3 (12optic+3acoustic), but from those 12 optic modes I don't know how to show them with symmetry elements (which of them is A1 or E or B1..)?

and are these frequencies both Raman and IR modes?

 

thanks alot,

mozhgan

--- On Sun, 11/2/08, matthieu verstraete <matthieu.jean.verstraete@gmail.com> wrote:

From: matthieu verstraete <matthieu.jean.verstraete@gmail.com>
Subject: Re: [abinit-forum] Phonon frequencies and group theory
To: forum@abinit.org
Date: Sunday, November 2, 2008, 9:02 PM

Check the anaddb output file, for the q=0 phonons. It will give you the characters of each of the modes wrt each of the symmetry operations. Then you match those to the character tables of the irreducible representations of the group, and you can assign the A1 E B1 etc...

Matthieu

On Sat, Nov 1, 2008 at 9:58 AM, <mozhganamini@yahoo.com> wrote:

Dear all,

I have done Response Function(1-5) to compute phonon frequencies of PbTiO3 and
I got 15 frequencies.
Could anyone tell me that, is it possible to demonstrate these frequencie in
standard group theory? (gamma= 4A1+5E+B1)
if yes, how can I indicate these frequencies by symmetry elements(A1,E,B1)?

Thanks alot in advance

Best Regards,
Mozhgan Amini

--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF) 
Dpto. Fisica de Materiales, 
U. del Pais Vasco,            
Centro Joxe Mari Korta, Av. de Tolosa, 72,   Phone: +34-943018393
E-20018 Donostia-San Sebastian, Spain        Fax  : +34-943018390

Mail : matthieu.jean.verstraete@gmail.com
http://www-users.york.ac.uk/~mjv500

-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF) 
Dpto. Fisica de Materiales, 
U. del Pais Vasco,            
Centro Joxe Mari Korta, Av. de Tolosa, 72,   Phone: +34-943018393
E-20018 Donostia-San Sebastian, Spain        Fax  : +34-943018390

Mail : matthieu.jean.verstraete@gmail.com
http://www-users.york.ac.uk/~mjv500