# [Pw_forum] Electron-phonon matrix calculation and elph.#iq.#irr.xml

Jaehong Park ignasio.ssp at gmail.com
Wed May 20 13:25:57 CEST 2015

```Dear Paolo;

Thank you very much for your answer

However, it is difficult for me to understand your answer. Can you be more
specific?

For example, singularity of acoustic phonon at gamma and  zero
coefficient...

and to make my original question more specific,

following is my output of ph.x

at Gamma point (q=0)
-----------------------------------------------------------------------------------------------

Mode symmetry, D_3h (-62m) point group:

Atomic displacements:
There are   6 irreducible representations

Representation     1      1 modes -A'_1  To be done

Representation     2      2 modes -E'  To be done

Representation     3      2 modes -E'  To be done

Representation     4      1 modes -A''2  To be done

Representation     5      1 modes -A''2  To be done

Representation     6      2 modes -E''  To be done

...
...

Diagonalizing the dynamical matrix

q = (    0.000000000   0.000000000   0.000000000 )

**************************************************************************
freq (    1) =      -0.266351 [THz] =      -8.884502 [cm-1]
freq (    2) =       0.470018 [THz] =      15.678118 [cm-1]
freq (    3) =       0.470018 [THz] =      15.678119 [cm-1]
freq (    4) =       8.700163 [THz] =     290.206203 [cm-1]
freq (    5) =       8.700164 [THz] =     290.206217 [cm-1]
freq (    6) =      11.760562 [THz] =     392.290107 [cm-1]
freq (    7) =      11.760562 [THz] =     392.290126 [cm-1]
freq (    8) =      12.300285 [THz] =     410.293340 [cm-1]
freq (    9) =      14.310518 [THz] =     477.347485 [cm-1]
**************************************************************************

Mode symmetry, D_3h (-62m) point group:

freq (  1 -  1) =         -8.9  [cm-1]   --> A''2            I
freq (  2 -  3) =         15.7  [cm-1]   --> E'              I+R
freq (  4 -  5) =        290.2  [cm-1]   --> E''             R
freq (  6 -  7) =        392.3  [cm-1]   --> E'              I+R
freq (  8 -  8) =        410.3  [cm-1]   --> A'_1            R
freq (  9 -  9) =        477.3  [cm-1]   --> A''2            I

----------------------------------------------------------------------------------------------------

At the gamma point as you can see from above, two dimensional irrep, E',
appears twice as "Representation 2" and "Representation 3".

and i get elph.1.2.xml , elph.1.3.xml for them, which may be printed in
order according to elphon.f90 code ( i am interested in extracting
electron-phonon matrix element).

but the two irrep E'  are definitely inequivalent (different freq.) and i
do not know whether the frequency of "Representation 2" is "15.7" or
"392.3".

This problem makes me hard to identify  elph.1.2.xml and elph.1.3.xml since
i cannot assign the frequency.

This problem becomes even worse when the site symmetry of q-point is reduced

q = (    0.000000000   0.128300065   0.000000000 )
-------------------------------------------------------------------------------------------

Mode symmetry, C_2v (mm2)  point group:

Atomic displacements:
There are   9 irreducible representations

Representation     1      1 modes -A_1  D_1  S_1  To be done

Representation     2      1 modes -A_1  D_1  S_1  To be done

Representation     3      1 modes -A_1  D_1  S_1  To be done

Representation     4      1 modes -A_2  D_2  S_2  To be done

Representation     5      1 modes -B_1  D_3  S_3  To be done

Representation     6      1 modes -B_1  D_3  S_3  To be done

Representation     7      1 modes -B_2  D_4  S_4  To be done

Representation     8      1 modes -B_2  D_4  S_4  To be done

Representation     9      1 modes -B_2  D_4  S_4  To be done

...
...
...

Mode symmetry, C_2v (mm2)  point group:

freq (  1 -  1) =         11.2  [cm-1]   --> B_2  D_4  S_4
freq (  2 -  2) =         56.2  [cm-1]   --> B_1  D_3  S_3
freq (  3 -  3) =         90.1  [cm-1]   --> A_1  D_1  S_1
freq (  4 -  4) =        292.5  [cm-1]   --> A_2  D_2  S_2
freq (  5 -  5) =        300.9  [cm-1]   --> B_2  D_4  S_4
freq (  6 -  6) =        385.3  [cm-1]   --> A_1  D_1  S_1
freq (  7 -  7) =        390.9  [cm-1]   --> B_1  D_3  S_3
freq (  8 -  8) =        414.1  [cm-1]   --> A_1  D_1  S_1
freq (  9 -  9) =        466.7  [cm-1]   --> B_2  D_4  S_4

--------------------------------------------------------------------------------------------

As you can see, irrep A_1 appears triply.

How can i resolve this problem ?

(I found similar thread in pw_forum

http://qe-forge.org/pipermail/pw_forum/2009-March/086475.html

but i couldn't find solution.)

Thank you in advance.

Best regards

Jaehong Park
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