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[<annie_beya@yahoo.fr>]

Dear All,

I am trying to calculate the piezoelectric constants of GaN using the response
function theory.
When I run anaddb, I find the same  piezo coefficients e_33 and e_31 for the
clamped ion as those published by Bernardini et al. in PRB 56 R10024 (1997)
where they used the berry phase approach. 
But the  values for the relaxed ions are not realistic and I have the 
following
message "piezo9 : WARNING -
  Unstable eigenvalue detected in force constant matrix at Gamma point
  The system under calculation is physically unstable."

I have used both hgh (with ecut= 100 Ha) and pspnc pseudopotentials. and have
the same results. The values that are used for acell are the optimized values.
please find below the input file and the anaddb output file.

Thanks for your help.

Annie

Input file
ndtset 3 
jdtset 1 2 3 
# Set 1 : initial self-consistency

kptopt1   1
tolvrs1 1.0d-18
iscf1 7


#set 2 the ddk 
rfelfd2 2  # only derivative of the gs wf
rfdir2 1 1 1
nqpt2 1
qpt2 0.0 0.0 0.0 #only the gamma point
getwfk2 1
getddk2 2
kptopt2 3
iscf2 -3
tolwfr2 1.0d-20

# Set 3 : response-function strain calculation

rfphon3 1
rfatpol3 1 2 
rfelfd3 3
rfdir3 1 1 1
nqpt3 1
qpt3 0 0 0
rfstrs3  3
getwfk3 1
getddk3 2
kptopt3 3
tolvrs3 1.0d-16
iscf3 7

#common input data
paral_rf 1 # activate parallelization over perturbations
ngroup_rf 4 # number of groups for  parallelization over perturbations

   ecut   100.0
   ecutsm 0.5
   iscf   7
   npulayit 7
   diemac 12.0
   
   nline 15
iprcel 45

   ixc  1
  nband   18
  nbdbuf 0
  occopt 1

  ngkpt   4 4 10
nshiftk   1
shiftk    0.0 0.0 0.5

  nstep   100
 natom   4
 ntypat   2 
  znucl  31 7
  typat   1 1 2 2
   xred   3.3333333333E-01  6.6666666667E-01  0.0
              6.6666666667E-01  3.3333333333E-01  5.0005858110E-01
              3.3333333333E-01  6.6666666667E-01  3.7602730263E-01
              6.6666666667E-01  3.3333333333E-01  8.7602730263E-01

  acell    5.9779130104E+00  5.9779130104E+00  9.7655186937E+00


   rprim
               8.6602540378E-01  5.0000000000E-01  0.0000000000E+00
             -8.6602540378E-01  5.0000000000E-01  0.0000000000E+00
              0.0000000000E+00  0.0000000000E+00  1.0000000000E+00


#anaddb output

read the DDB information and perform some checks

-begin at tcpu      0.055  and twall      0.055 sec

 Real(R)+Recip(G) space primitive vectors, cartesian coordinates
(Bohr,Bohr^-1):
 R(1)=  5.1770245  2.9889565  0.0000000  G(1)=  0.0965806  0.1672825  
0.0000000
 R(2)= -5.1770245  2.9889565  0.0000000  G(2)= -0.0965806  0.1672825  
0.0000000
 R(3)=  0.0000000  0.0000000  9.7655187  G(3)=  0.0000000  0.0000000  
0.1024011
 Unit cell volume ucvol=  3.0222134E+02 bohr^3
 Angles (23,13,12)=  9.00000000E+01  9.00000000E+01  1.20000000E+02 degrees
 Now the whole DDB is in central memory

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

 Calculation of the internal-strain  tensor

-begin at tcpu      0.059   and twall      0.058sec

 Force-response internal strain tensor(Unit:Hartree/bohr)

 Atom dir   strainxx    strainyy    strainzz    strainyz    strainxz   
strainxy
  1  x     0.1629756  -0.1629756   0.0000000   0.0000000  -0.1119998  
0.0000000
  1  y     0.0000000   0.0000000   0.0000000  -0.1119998   0.0000000 
-0.1629756
  1  z    -0.1078308  -0.1078308   0.1989130   0.0000000   0.0000000  
0.0000000
  2  x    -0.1629756   0.1629757   0.0000000   0.0000000  -0.1119998  
0.0000000
  2  y     0.0000000   0.0000000   0.0000000  -0.1119998   0.0000000  
0.1629756
  2  z    -0.1078308  -0.1078308   0.1989130   0.0000000   0.0000000  
0.0000000
  3  x     0.1876248  -0.1876249   0.0000000   0.0000000   0.1119998  
0.0000000
  3  y     0.0000000   0.0000000   0.0000000   0.1119998   0.0000000 
-0.1876248
  3  z     0.1078308   0.1078308  -0.1989130   0.0000000   0.0000000  
0.0000000
  4  x    -0.1876248   0.1876248   0.0000000   0.0000000   0.1119998  
0.0000000
  4  y     0.0000000   0.0000000   0.0000000   0.1119998   0.0000000  
0.1876248
  4  z     0.1078308   0.1078308  -0.1989130   0.0000000   0.0000000  
0.0000000

 instr9 : WARNING -
  Acoustic sum rule violation met : the eigenvalues of accoustic mode
  are too large at Gamma point.
  Increase cutoff energy or k-points sampling.
  The three eigenvalues are:   -6.937594E-02    4.140198E-03   -6.937595E-02

 instr9 : WARNING -
  Unstable eigenvalue detected in force constant matrix at Gamma point
 The system under calculation is physically unstable.

 Displacement-response internal strain tensor (Unit:Bohr)

 Atom dir   strainxx    strainyy    strainzz    strainyz    strainxz   
strainxy
  1  x     1.6258106  -1.6258105   0.0000000   0.0000000  -0.5457645  
0.0000000
  1  y     0.0000000   0.0000000   0.0000000  -0.5457645   0.0000000 
-1.6258106
  1  z    -0.5722507  -0.5722507   1.0556173   0.0000000  -0.0000001  
0.0000000
  2  x    -1.6258106   1.6258106   0.0000000   0.0000000  -0.5457645  
0.0000000
  2  y     0.0000000   0.0000000   0.0000000  -0.5457645   0.0000000  
1.6258106
  2  z    -0.5722507  -0.5722507   1.0556173   0.0000000  -0.0000001  
0.0000000
  3  x    -0.6229205   0.6229205   0.0000000   0.0000000   0.5457645  
0.0000000
  3  y     0.0000000   0.0000000   0.0000000   0.5457645   0.0000000  
0.6229203
  3  z     0.5722507   0.5722506  -1.0556173   0.0000000   0.0000001 
-0.0000001
  4  x     0.6229205  -0.6229206   0.0000000   0.0000000   0.5457645  
0.0000000
  4  y     0.0000000   0.0000000   0.0000000   0.5457645   0.0000000 
-0.6229202
  4  z     0.5722507   0.5722508  -1.0556174   0.0000000   0.0000001  
0.0000001

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

 Calculation of the elastic and compliances tensor (Voigt notation)

-begin at tcpu      0.061   and twall      0.061sec

 elast9 : WARNING - :
  Acoustic sum rule violation met : the eigenvalues of accoustic mode
  are too large at Gamma point
  increase cutoff energy or k-points sampling.
  The three eigenvalues are:   -6.937594E-02    4.140198E-03   -6.937595E-02

 elast9 : WARNING - :
  Unstable eigenvalue detected in force constant matrix at Gamma point.
  The system under calculation is physically unstable.

 Elastic Tensor (clamped ion) (unit:10^2GP):

  14.2922293   4.4214181   2.5061853   0.0000019   0.0000070   0.0002773
   4.4214181  14.2942788   2.5061602   0.0000123  -0.0000035   0.0003425
   2.5061962   2.5061520  -0.4018496   0.0000163  -0.0000352   0.0000236
  -0.0000009  -0.0000128  -0.0000309   2.9685846  -0.0000020   0.0000000
   0.0000000   0.0000000   0.0000000  -0.0000020   2.9685883  -0.0000009
  -0.0001797  -0.0002196  -0.0000020   0.0000000  -0.0000009   4.9359920

 Elastic Tensor (relaxed ion) (unit:10^2GP):
  (at fixed electric field boundary condition)

  13.7636139   4.4694689   2.9494283   0.0000019   0.0000070   0.0002773
   4.4694689  13.7656634   2.9494032   0.0000123  -0.0000035   0.0003425
   2.9494393   2.9493950  -1.2194895   0.0000163  -0.0000352   0.0000236
  -0.0000009  -0.0000128  -0.0000310   2.7305637  -0.0000020   0.0000000
   0.0000000   0.0000000   0.0000001  -0.0000020   2.7305675  -0.0000009
  -0.0001797  -0.0002196  -0.0000020   0.0000000  -0.0000009   4.6476588

 Compliance Tensor (clamped ion) (unit: 10^-2GP^-1):

   0.0606559  -0.0406439   0.1248093  -0.0000006   0.0000013  -0.0000012
  -0.0406442   0.0606526   0.1247810  -0.0000009   0.0000016  -0.0000025
   0.1248103   0.1247802  -0.9318991   0.0000045  -0.0000112  -0.0000112
   0.0000011   0.0000015  -0.0000091   0.3368609   0.0000002   0.0000000
   0.0000000   0.0000000   0.0000000   0.0000002   0.3368605   0.0000001
   0.0000005   0.0000013   0.0000097   0.0000000   0.0000001   0.2025935

 Compliance Tensor (relaxed ion)  (unit: 10^-2GP^-1):
  (at fixed electric field boundary condition)

   0.0691787  -0.0384071   0.0744243  -0.0000003   0.0000007  -0.0000017
  -0.0384072   0.0691725   0.0744067  -0.0000007   0.0000011  -0.0000032
   0.0744249   0.0744063  -0.4600574   0.0000024  -0.0000060  -0.0000076
   0.0000007   0.0000012  -0.0000048   0.3662247   0.0000003   0.0000000
   0.0000000   0.0000000   0.0000000   0.0000003   0.3662242   0.0000001
   0.0000009   0.0000018   0.0000062   0.0000000   0.0000001   0.2151621

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

 Calculation of the tensor related to piezoelectric effetc
  (Elastic indices in Voigt notation)

-begin at tcpu      0.062   and twall      0.062sec

 Proper piezoelectric constants (clamped ion) (unit:c/m^2)

      0.00000000      0.00000000      0.43993237
      0.00000000      0.00000000      0.43993237
      0.00000000      0.00000000     -0.89593477
      0.00000000      0.51206135      0.00000000
      0.51206135      0.00000000      0.00000000
      0.00000000      0.00000000      0.00000000

 piezo9 : WARNING -
  Acoustic sum rule violation met : the eigenvalues of accoustic mode
  are too large at Gamma point
  Increase cutoff energy or k-points sampling.
  The three eigenvalues are:   -6.937594E-02    4.140198E-03   -6.937595E-02

 piezo9 : WARNING -
  Unstable eigenvalue detected in force constant matrix at Gamma point
  The system under calculation is physically unstable.

 Proper piezoelectric constants (relaxed ion) (unit:c/m^2)

      0.00000000     -0.00000004     -0.74382882
      0.00000010     -0.00000002     -0.74382882
      0.00000008     -0.00000004      1.28772153
      0.00000000     -0.63730757      0.00000006
     -0.63730751      0.00000000     -0.00000016
      0.00000001     -0.00000003      0.00000000

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