The ABINIT Users Mailing List ( CLOSED )

["Lee Geunsik" <maxgeun@postech.ac.kr>]

Dear Abinitors,

I have one interesting problem in anaddb.
Eigenvectors are largely dependent on small deviations from zero for 
dynamical matrix elements.
The phonon mode is q=(0,0,0) of silicon with diamond structure.
Before diagonalizing dynamical matrix, I printed dynamical matrix.
Following is the relevant part in 'phfrq3.f'.

 do i2=1,3*natom
  do i1=1,i2
!   if (abs(displ(1+2*(i1-1)+2*(i2-1)*3*natom)).lt.1.0d-20) 
displ(1+2*(i1-1)+2*(i2-1)*3*natom)=0.d0
   matrx(1,ii)=displ(1+2*(i1-1)+2*(i2-1)*3*natom)
   matrx(2,ii)=displ(2+2*(i1-1)+2*(i2-1)*3*natom)
   print*,i1,i2,matrx(1,ii),matrx(2,ii)
   ii=ii+1
  enddo
 enddo
 allocate(zhpev1(2,2*3*natom-1),zhpev2(3*3*natom-2))
#if defined T3E
 call CHPEV ('V','U',3*natom,matrx,eigval,eigvec,3*natom,zhpev1,&
&    zhpev2,ier)
#else
 call ZHPEV ('V','U',3*natom,matrx,eigval,eigvec,3*natom,zhpev1,&
&    zhpev2,ier)
#endif

The martix is

 1 1 5.675772985184775E-06 0.0
 1 2 5.814862374116712E-22 0.0
 2 2 5.675772985184775E-06 0.0
 1 3 -1.567325801096383E-38 0.0
 2 3 -5.814862374116711E-22 0.0
 3 3 5.675772985184775E-06 0.0
 1 4 -5.675772985178078E-06 0.0
 2 4 -5.814862374109848E-22 0.0
 3 4 1.567325801096383E-38 0.0
 4 4 5.675772985184775E-06 0.0
 1 5 -5.814862374109848E-22 0.0
 2 5 -5.675772985178078E-06 0.0
 3 5 5.814862374109847E-22 0.0
 4 5 5.814862374116712E-22 0.0
 5 5 5.675772985184775E-06 0.0
 1 6 0.0 0.0
 2 6 5.814862374109847E-22 0.0
 3 6 -5.675772985178078E-06 0.0
 4 6 -1.567325801096383E-38 0.0
 5 6 -5.814862374116711E-22 0.0
 6 6 5.675772985184775E-06 0.0

and eigendisplacements are

  Mode number    1   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  2.62290068E-04  2.83420899E-03 -1.29023688E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  2.62290068E-04  2.83420899E-03 -1.29023688E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    2   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  1.48329843E-04  1.28196511E-03  2.84619248E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  1.48329843E-04  1.28196511E-03  2.84619248E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    3   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  3.11053855E-03 -3.00121197E-04 -2.69274801E-05
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  3.11053855E-03 -3.00121197E-04 -2.69274801E-05
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    4   Energy    3.369206E-03
   1  3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2 -3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    5   Energy    3.369206E-03
   1  0.00000000E+00  3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00 -3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    6   Energy    3.369206E-03
   1  0.00000000E+00  0.00000000E+00  3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00  0.00000000E+00 -3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00

These do not look consistent with irreps of vibrations for accoustic modes.

But if I set very small values as exact zero(commented line in `phfrq3.f`), I 
get correct eigendisplacements.
Following is the results.

Dynamical matrix:
 1 1 5.675772985184775E-06 0.0
 1 2 0.0 0.0
 2 2 5.675772985184775E-06 0.0
 1 3 0.0 0.0
 2 3 0.0 0.0
 3 3 5.675772985184775E-06 0.0
 1 4 -5.675772985178078E-06 0.0
 2 4 0.0 0.0
 3 4 0.0 0.0
 4 4 5.675772985184775E-06 0.0
 1 5 0.0 0.0
 2 5 -5.675772985178078E-06 0.0
 3 5 0.0 0.0
 4 5 0.0 0.0
 5 5 5.675772985184775E-06 0.0
 1 6 0.0 0.0
 2 6 0.0 0.0
 3 6 -5.675772985178078E-06 0.0
 4 6 0.0 0.0
 5 6 0.0 0.0
 6 6 5.675772985184775E-06 0.0

Eigendisplacements:
  Mode number    1   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  0.00000000E+00  3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00  3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    2   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    3   Energy    0.000000E+00
 Attention : low frequency mode.
   (Could be unstable or acoustic mode)
   1  0.00000000E+00  0.00000000E+00  3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00  0.00000000E+00  3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    4   Energy    3.369206E-03
   1  0.00000000E+00  3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00 -3.12509966E-03  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    5   Energy    3.369206E-03
   1  0.00000000E+00  0.00000000E+00  3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2  0.00000000E+00  0.00000000E+00 -3.12509966E-03
      0.00000000E+00  0.00000000E+00  0.00000000E+00
  Mode number    6   Energy    3.369206E-03
   1  3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00
   2 -3.12509966E-03  0.00000000E+00  0.00000000E+00
      0.00000000E+00  0.00000000E+00  0.00000000E+00

So my questions are

(i) Does this problem arise only for my computer system? For test, I attach 
necessary input files for anaddb.

(ii) Is it safe to set very small values as zero?

Thanks a lot
Geunsik.

Attachment: input.tar.gz
Description: GNU Zip compressed data