[Pw_forum] orthogonality of phonon eigenvectors?

[Sonu Kumar]

Dear all QE users,

I am not getting the orthogonality of  phonon eigenvectors
obtained in xx.dyn  file. However normalization condition is satisfied.

For example:
1. for four atom unit cell, eigen vectors are:

    omega( 1) =      -0.330081 [THz] =     -11.010398 [cm-1]
 ( -0.000126  0.000000 -0.494472  0.000000  0.000000  0.000000 )
 ( -0.000128  0.000000 -0.501752  0.000000  0.000000  0.000000 )
 ( -0.000128  0.000000 -0.501868  0.000000  0.000000  0.000000 )
 ( -0.000128  0.000000 -0.501868  0.000000  0.000000  0.000000 )
    omega( 2) =      -0.330081 [THz] =     -11.010398 [cm-1]
 (  0.494472  0.000000 -0.000126  0.000000  0.000000  0.000000 )
 (  0.501752  0.000000 -0.000128  0.000000  0.000000  0.000000 )
 (  0.501868  0.000000 -0.000128  0.000000  0.000000  0.000000 )
 (  0.501868  0.000000 -0.000128  0.000000  0.000000  0.000000 )
    omega( 3) =      -0.293090 [THz] =      -9.776500 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000  0.499253  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.500310  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.500218  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.500218  0.000000 )
    omega( 4) =       2.476743 [THz] =      82.615796 [cm-1]
 ( -0.506652  0.000000 -0.000002  0.000000  0.000000  0.000000 )
 (  0.559568  0.000000  0.000002  0.000000  0.000000  0.000000 )
 (  0.463782  0.000000  0.000002  0.000000  0.000000  0.000000 )
 (  0.463782  0.000000  0.000002  0.000000  0.000000  0.000000 )
    omega( 5) =       2.476743 [THz] =      82.615796 [cm-1]
 ( -0.000002  0.000000  0.506652  0.000000  0.000000  0.000000 )
 (  0.000002  0.000000 -0.559568  0.000000  0.000000  0.000000 )
 (  0.000002  0.000000 -0.463782  0.000000  0.000000  0.000000 )
 (  0.000002  0.000000 -0.463782  0.000000  0.000000  0.000000 )
    omega( 6) =       9.011016 [THz] =     300.577143 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000 -0.562468  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.797241  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.154980  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.154980  0.000000 )
    omega( 7) =      10.988751 [THz] =     366.547723 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.707107  0.000000  0.000001  0.000000  0.000000  0.000000 )
 ( -0.707107  0.000000 -0.000001  0.000000  0.000000  0.000000 )
    omega( 8) =      10.988751 [THz] =     366.547724 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 ( -0.000001  0.000000  0.707107  0.000000  0.000000  0.000000 )
 (  0.000001  0.000000 -0.707107  0.000000  0.000000  0.000000 )
    omega( 9) =      11.334621 [THz] =     378.084770 [cm-1]
 (  0.018232  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.283432  0.000000  0.000000  0.000000  0.000000  0.000000 )
 ( -0.677987  0.000000 -0.000001  0.000000  0.000000  0.000000 )
 ( -0.677987  0.000000 -0.000001  0.000000  0.000000  0.000000 )
    omega(10) =      11.334621 [THz] =     378.084771 [cm-1]
 (  0.000000  0.000000 -0.018232  0.000000  0.000000  0.000000 )
 (  0.000000  0.000000 -0.283432  0.000000  0.000000  0.000000 )
 ( -0.000001  0.000000  0.677987  0.000000  0.000000  0.000000 )
 ( -0.000001  0.000000  0.677987  0.000000  0.000000  0.000000 )
    omega(11) =      17.157192 [THz] =     572.306135 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000 -0.097293  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000 -0.168080  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.693644  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.693644  0.000000 )
    omega(12) =      20.428646 [THz] =     681.430811 [cm-1]
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000 -0.707107  0.000000 )
 (  0.000000  0.000000  0.000000  0.000000  0.707107  0.000000 )

My Output:

    mode# mode# sum of prod of modes
      4   6      0.00000
      5   7      0.00000
      6   8      0.00000
      7   9      0.00000
      8  10      0.00000
      9  11      0.00000
     10  12      0.00000
     12   5      0.00000
      1   3      0.00000
      2   4      0.49575 <-----why not zero.

Similarly :
    mode# mode# sum of prod of modes
      1   4     -0.00013
      2   5      0.00013
      3   6      0.27310 <---
      4   7      0.00000
      5   8      0.00000
      6   9      0.00000
      7  10      0.00000
      8  11      0.00000
      9  12      0.00000
     10   1     -0.52929<--
     11   2      0.00000
     12   3      0.00000

However all modes follow the  normalization conditon:
     mode# sum of sqr of modes
      1      1.00000
      2      1.00000
      3      1.00000
      4      1.00000
      5      1.00000
      6      1.00000
      7      1.00000
      8      1.00000
      9      1.00000
     10      1.00000
     11      1.00000
     12      1.00000

Thank you !!

regards,
==========================================
Sonu Kumar
Phd Student,Physics Department
Indian Institute of Technology ,Delhi-110016, India
web:-http://www.iitd.ac.in/
==========================================