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[yukihiro_okuno@fujifilm.co.jp]

Dear ABINIT Users.

I'm now calculating the  piezoelectric coefficient , elastic constant 
of the PbTiO3,(PT) by Density functional perturbation theory, (DFPT).

I found the Born effective charge are 
calculated reasonably good vaule, but 
the piezoelectric coefficient is far from the experiments and 
other calculate values ( PRL  vol(80) p4321).

I'm informed in this mailing list that the reason is possibly due to 
the pseudopotential I used.

I used Teter's extended norm conserved pseudo potential which is downloaded 
from the ABINIT Home Page.   I also check  the TM norm conserved potentials 
which are generated fhi98PP code. I check two 
TM norm conserved pseudo potential one of which is 
made by myself, and other is downloaded from the ABINIT web site.

The value of poezoelectric tensor from the Teter's pseudo potential
whici is down loaded from the web site, 

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

 Calculation of the piezoelectric tensor

-begin at tcpu      0.037   and twall      0.117sec

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

      0.00000000      0.00000000      0.33709523
      0.00000000      0.00000000      0.33709521
      0.00000000      0.00000000     -0.73010205
      0.00000000      0.14564668      0.00000000
      0.14564654      0.00000000      0.00000000
      0.00000000      0.00000000     -0.00000002

phonon modes warning- :
accoustic 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:   -9.481483E-03    3.209976E-03   -9.481370E-03

phonon modes warning- :
unstable eigenvalue detected in force constant matrix at Gamma point
the system under calculation is physically unstabale.

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

      0.00001074      0.00001665      3.66885153
      0.00001320      0.00001685      3.66884157
      0.00002883      0.00007794     15.60848674
      0.00000405     -2.89251432      0.00001611
     -2.89249871      0.00000253      0.00001237
      0.00000000      0.00000000      0.00000095

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


The piezoelectric tensor which is calculated the pseudopotential which is 
generated by Fhi98PP code. ( In this case , the ground state 
calculation is conserved by nband = 26, or iscf = 3)

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

 Calculation of the piezoelectric tensor

-begin at tcpu      0.037   and twall      0.241sec

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

      0.00000000      0.00000000     -0.34997886
      0.00000000      0.00000000     -0.34997886
      0.00000000      0.00000000      0.82928878
      0.00000000     -0.09788078      0.00000000
     -0.09788078      0.00000000      0.00000000
      0.00000000      0.00000000      0.00000000

phonon modes warning- :
accoustic 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:    9.096939E-04   -1.034723E-03    9.098799E-04

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

      0.00001277      0.00001374     -1.79825769
      0.00001491      0.00000232     -1.79824556
      0.00001185      0.00004332     -4.39017143
      0.00000854     -3.44122842      0.00000877
     -3.44126548      0.00000690      0.00000169
      0.00000000      0.00000000      0.00000000

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

Results of these value are different each other 
and also both of results are different from the experimental values.

I had checked the pseudo-potential of PbTiO3 by checking the each element 
pseudo potential reproduce 
the lattice constants within the 1% from the experimantal values. ( Pb fcc 
for Pb pseudo potential 
and TiC for Ti pseudo potential).    

Is the responce function calculation so sensitive to the pseudo potential in 
general ? Or we must calculate more 
accurately in the step of ground state caluculation than usual 
ground state calculation?    

Sincerely, 

Yukihiro Okuno.


My input file is below, ( I take the experimental atomic coorinate from PRL 
vol(80) 4321 ).

# Crystalline AlP - rhombohedral distortion imposed
# Piezoelectroc tensor calculation

ndtset  4

#Common Data Definition of the unit cell
acell       7.3730000000       7.3730000000       7.8522450000
rprim     1.000000000000     0.000000000000     0.000000000000
          0.000000000000     1.000000000000     0.000000000000
          0.000000000000     0.000000000000     1.000000000000
ntypat    3 
znucl 82 8 22 
natom    5 
typat 1 3 2 2 2 

xcart 
    0.000000000000     0.000000000000     0.000000000000 
    3.686500000000     3.686500000000     4.224507810000 
    3.686500000000     3.686500000000     0.918712665000 
    3.686500000000     0.000000000000     4.805573940000 
    0.000000000000     3.686500000000     4.805573940000 
ecut 50
ixc 3
ngkpt 4 4 4
nband 26
nbdbuf 0
occopt 1
nstep 500
prtden 1
prtvol 10 
tolwfr 1.0d-12
diemac 12.0 

# First dataset : Self-consistent ground state run
iscf1 5
kptopt1 1

# Second dataset : Non-self-consistent run for full k point set 
# we recover full 6 6 6 k space (not kptopt1 = 1)
iscf2 -2
kptopt2 3
#use calculated results of dataset 1 
getden2 1
getwfk2 1 

## Third data set : finite-difference d/dk ground-state calculation 
berryopt3 -2
getwfk3 2
getden3 1
iscf3 -2
kptopt3 3
# idir = 1 1 1 is needed because piezoelectric tensor need all d/dk 
components 
rfdir3  1 1 1 

# Fourth dataset : electric field and strain responce 
getwfk4  2     
getddk4  3
iscf4  3     
kptopt4 3 

#
rfdir4  1 1 1    

# only generation of the first-order responce to the electric field 
# assuming that the data on derivative of ground state-wave function
# with respect to k is available on disk 
rfelfd4  3     

# run strain responce function both uniaxial and shear strain  
rfstrs4  3

# activate the calculation of the atomic dispacement 
rfphon4  1

rfatpol4 1 5

nqpt4 1
qpt4 0.0 0.0 0.0 
  

# run phonon 


# strain perturbation is only available for v4.2 or over.
# but still iscf = 2 or iscf = 3 and diemix <= 0.5 is reccomended 
diemix4  0.45

diemac4  1.0