[Pw_forum] phonon dynamical matrix and eigenvectors

Bo Qiu 200210qb at gmail.com
Tue Apr 17 00:01:33 CEST 2012


Dear Developers and Users,

I'm new to Quantum Espresso and I want to compute phonon dynamical 
matrix and eigenvectors for silicon. I can use the eigenvectors to 
construct normal mode amplitudes based on independent molecular dynamics 
simulated atomic velocities.

q^dot (k,\nu) =sum v_\alpha^{b,l}(t)e_\alpha^{b,*}(k,\nu)exp(-ik r_0^l)
here v is the alpha (=x,y,z) component of atomic velocity, e is the 
alpha-th portion of the eigenvector of dynamical matrix D(k) and branch \nu

I tried to compare the dynamical matrix and eigenvectors for silicon at 
q=(-0.333333000  -0.333333000  -0.666667000) from both Quantum Espresso 
and GULP (a lattice dynamics code based on classical interatomic 
potentials, chosen to be SW silicon). However, I found the dynamical 
matrices do not agree. The eigenvectors are also completely different.
As a result, if I use the eigenvector e*(k,\nu) from GULP to construct 
q^dot, its Fourier transform shows single peak at the corresponding 
phonon mode frequency, which is expected for single mode (k,\nu). 
However, if I use the eigenvector e'*(k,\nu) from QE, the FT shows 
multiple peaks, with peak positions corresponding to frequencies of 
multiple branches (\nu, \nu', \nu'', etc), which is incorrect.

I first thought maybe there is some discrepancy in the definition of 
coordinate systems so e'*(k,\nu) from QE may be linear combinations of 
e*(k,\nu) from GULP. However I made sure the primitive cell vectors for 
both computation is
cubic
       0.000000000    0.500000000    0.500000000
       0.500000000    0.000000000    0.500000000
       0.500000000    0.500000000    0.000000000
and the internal coordinates for both are:
     1    1      0.0000000      0.0000000      0.0000000
     2    1      0.2500000      0.2500000      0.2500000

I suppose when the dynamical matrices are defined under the same 
coordinate systems and they should be very similar (despite inaccuracy 
of classical SW potential), so should the corresponding eigenvectors. I 
don't quite understand what went wrong or if there is some hidden 
transformation to the dynamical matrix/ eigenvectors in QE. Could you 
please help me with that? Sorry for the lengthy email!

===========================
QE:
dynamical matrix:
     1    1
   0.26584460  0.00000000    0.01095706  0.00000000    0.01178255  
0.00797619
   0.01095706  0.00000000    0.26584460  0.00000000    0.01178255  
0.00797619
   0.01178255 -0.00797619    0.01178255 -0.00797619    0.29527850  
0.00000000
     1    2
   0.10051503 -0.05636929   -0.11838412 -0.03489786   -0.07026611  
0.03761305
  -0.11838412 -0.03489786    0.10051503 -0.05636929   -0.07026611  
0.03761305
  -0.07026611  0.03761305   -0.07026611  0.03761305    0.11544724 
-0.05301088
     2    1
   0.10051503  0.05636929   -0.11838412  0.03489786   -0.07026611 
-0.03761305
  -0.11838412  0.03489786    0.10051503  0.05636929   -0.07026611 
-0.03761305
  -0.07026611 -0.03761305   -0.07026611 -0.03761305    0.11544724  
0.05301088
     2    2
   0.26584460  0.00000000    0.01095706  0.00000000    0.01178255 
-0.00797619
   0.01095706  0.00000000    0.26584460  0.00000000    0.01178255 
-0.00797619
   0.01178255  0.00797619    0.01178255  0.00797619    0.29527850  
0.00000000

GULP:
dynamical matrix:
   Real Dynamical matrix :

    0.612757   0.007542   0.000000  -0.162617   0.306835   0.000000
    0.007542   0.612757   0.000000   0.306835  -0.162617   0.000000
    0.000000   0.000000   0.650468   0.000000   0.000000  -0.162617
   -0.162617   0.306835   0.000000   0.612757   0.007542   0.000000
    0.306835  -0.162617   0.000000   0.007542   0.612757   0.000000
    0.000000   0.000000  -0.162617   0.000000   0.000000   0.650468

   Imaginary Dynamical matrix :

    0.000000   0.000000  -0.026128   0.000001   0.000000   0.177151
    0.000000   0.000000  -0.026128   0.000000   0.000001   0.177151
    0.026128   0.026128   0.000000   0.177151   0.177151   0.000001
   -0.000001   0.000000  -0.177151   0.000000   0.000000   0.026128
    0.000000  -0.000001  -0.177151   0.000000   0.000000   0.026128
   -0.177151  -0.177151  -0.000001  -0.026128  -0.026128   0.000000

====================================

The corresponding eigenvectors:
QE:
      omega( 1) =       3.843790 [THz] =     128.215027 [cm-1]
  ( -0.466622  0.179622  0.466622 -0.179622  0.000000  0.000000 )
  (  0.481928 -0.133213 -0.481928  0.133213  0.000000  0.000000 )
      omega( 2) =       5.191233 [THz] =     173.160893 [cm-1]
  (  0.240380 -0.225674  0.240380 -0.225674 -0.500138  0.180108 )
  ( -0.302624 -0.130882 -0.302624 -0.130882  0.531580  0.000000 )
      omega( 3) =       9.773114 [THz] =     325.995997 [cm-1]
  ( -0.301588 -0.275885 -0.301588 -0.275885 -0.088915 -0.397439 )
  ( -0.335073 -0.234081 -0.335073 -0.234081 -0.407264  0.000000 )
      omega( 4) =      12.316327 [THz] =     410.828451 [cm-1]
  ( -0.266508 -0.236976 -0.266508 -0.236976 -0.152029 -0.471719 )
  (  0.307303  0.180967  0.307303  0.180967  0.495612  0.000000 )
      omega( 5) =      14.170455 [THz] =     472.675510 [cm-1]
  ( -0.445864  0.226286  0.445864 -0.226286  0.000000  0.000000 )
  ( -0.465825  0.181680  0.465825 -0.181680  0.000000  0.000000 )
      omega( 6) =      14.480825 [THz] =     483.028344 [cm-1]
  (  0.214285 -0.226094  0.214285 -0.226094 -0.551429  0.043056 )
  (  0.231234  0.208727  0.231234  0.208727 -0.553107  0.000000 )


GULP:
  Frequency     192.1405                 270.1120                    
368.8443
                 Real    Imaginary           Real    Imaginary          
Real    Imaginary

      1 x      -0.473100 -0.161793  0.000000  0.358390  0.000002  0.368133
      1 y       0.473100  0.161793  0.000000  0.358390  0.000002  0.368133
      1 z       0.000000  0.000000  0.493066  0.000003 -0.478494 -0.000001
      2 x      -0.473100 -0.161792  0.000002 -0.358390 -0.000002  0.368133
      2 y       0.473100  0.161792  0.000002 -0.358390 -0.000002  0.368133
      2 z       0.000000  0.000000  0.493066  0.000000  0.478494  0.000000
  Frequency     434.9274                     540.5867                    
541.2499
                Real    Imaginary               Real    Imaginary        
Real    Imaginary

      1 x      -0.000002 -0.348650 -0.018584 -0.499655  0.000000  0.338346
      1 y      -0.000002 -0.348650  0.018584  0.499655  0.000000  0.338346
      1 z       0.506840  0.000000  0.000000  0.000000  0.520618  0.000001
      2 x      -0.000001  0.348650  0.018585  0.499654 -0.000001  0.338346
      2 y      -0.000001  0.348650 -0.018585 -0.499654 -0.000001  0.338346
      2 z       0.506840  0.000000  0.000000  0.000000 -0.520618  0.000000



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