[Pw_forum] about born effective charge tensors

[sun jason]

Dear all,

I calculated the born effective charges of some crystals, I find in high 
symmetric systems, such as zincblende or wurtzite, the effective charge 
tensors are symmetric, but in the hexagonal crystal, the effective charge 
tensors of some atoms are not symmetric, the non-digonal components of the 
tensors are nonzero, 

as follow, atom13 and atom14 are symmetric but the others are not, does it 
bring by numerical errors ? 

the structure are fully relaxed. does it mean that the optimization is not 
accurate enough ?

I'm not sure about whether the born effective charge tensor should be 
symmetric in crystals. Does it dependent on the structural symmetry of 
crystal itself ?


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

          Effective charges E-U in cartesian axis 
 
           atom     1
          (        2.74126        0.04349        0.00000 )
          (       -0.01156        2.12774        0.00000 )
          (        0.00000        0.00000        2.00705 )
           atom     2
          (        2.74535        0.04826        0.00000 )
          (       -0.00889        2.12477        0.00000 )
          (        0.00000        0.00000        2.00768 )
           atom     3
          (        2.29495       -0.24612        0.00000 )
          (       -0.30117        2.57405        0.00000 )
          (        0.00000        0.00000        2.00705 )
           atom     4
          (        2.29697       -0.24998        0.00000 )
          (       -0.30714        2.57316        0.00000 )
          (        0.00000        0.00000        2.00768 )
           atom     5
          (        2.26729        0.28520        0.00000 )
          (        0.23015        2.60171        0.00000 )
          (        0.00000        0.00000        2.00705 )
           atom     6
          (        2.26287        0.28745        0.00000 )
          (        0.23030        2.60725        0.00000 )
          (        0.00000        0.00000        2.00768 )
           atom     7
          (       -1.89044       -0.46772        0.00000 )
          (       -0.58373       -1.49548        0.00000 )
          (        0.00000        0.00000       -1.65545 )
           atom     8
          (       -1.88988       -0.46559        0.00000 )
          (       -0.57784       -1.49690        0.00000 )
          (        0.00000        0.00000       -1.65530 )
           atom     9
          (       -2.04951        0.49189        0.00000 )
          (        0.37588       -1.33642        0.00000 )
          (        0.00000        0.00000       -1.65545 )
           atom    10
          (       -2.04696        0.48715        0.00000 )
          (        0.37490       -1.33982        0.00000 )
          (        0.00000        0.00000       -1.65530 )
           atom    11
          (       -1.13893        0.14984        0.00000 )
          (        0.03383       -2.24699        0.00000 )
          (        0.00000        0.00000       -1.65545 )
           atom    12
          (       -1.14332        0.14681        0.00000 )
          (        0.03457       -2.24346        0.00000 )
          (        0.00000        0.00000       -1.65530 )
           atom    13
          (       -2.21608       -0.24947        0.00000 )
          (        0.24947       -2.21608        0.00000 )
          (        0.00000        0.00000       -1.05841 )
           atom    14
          (       -2.21688       -0.25857        0.00000 )
          (        0.25857       -2.21688        0.00000 )
          (        0.00000        0.00000       -1.06086 )
------------------------------------------------------------------------------



Thank you very much!


Best regards,

Jian SUN