[Pw_forum] phonon frequencies are different when treated as insulator(semiconductor) and metal

W. YU yuwen_66 at yahoo.com
Fri Jan 7 04:36:31 CET 2005


Dear pw users, 

I am doing phonon dispersion calculations for a simple
cubic system Cu3N. My band structure calculation has
confirmed it is a semiconductor with a gap of about
0.15ev. But as the pressure increases, this system
changes to semimental. I once posted a similar problem
in this forum and got some answers. I was told that
the results should be the same even if I treat an
insulator as a metal(with some restrictions for the
parameters when treating it as a metal), But I still
got different results when I treat it differently as
metal or as insulator(semiconductor). I have been
driven mad by this problem. So I post is here again
with some input and output results. Hope some one
could give me more explanations to clear my mind.
thanks a lot!

Note: in the input file, the lattice parameters
correspon to the equilibrium semicondutor case. I know
the k point mesh 4x4x4 maybe too small, but the
results are quite close for some frequencies and quite
different for other frequencies, why this happens?
*******************************************************
Treated as metal,input file:

#!/bin/sh

# set the needed environment variables

ESPRESSO_ROOT=$HOME/pwscf/
PSEUDO_DIR=$HOME/pwscf/pseudo/
TMP_DIR=$HOME/pwscf_workspace/tmp

# self-consistent calculation
cat > cu3n.scf.in << EOF
 &control
    calculation='scf'
    restart_mode='from_scratch',
    prefix='cu3n',
    pseudo_dir = '$PSEUDO_DIR/',
    outdir='$TMP_DIR/',
    tstress = .true. 
 /
 &system    
    ibrav = 1, celldm(1) = 7.090, nat = 4, ntyp = 2,
    ecutwfc = 75.0 ,ecutrho=450.0,
    occupations = 'smearing', degauss = 0.02 ,
    smearing = 'methfessel-paxton'
/
 &electrons
    conv_thr =  1.0d-8
    mixing_beta = 0.7
 /
ATOMIC_SPECIES
 N   14.00674   N.pz-rrkjus.UPF 
 Cu  63.54600  Cu.pz-d-rrkjus.UPF 
ATOMIC_POSITIONS
  N      0.000000000    0.000000000    0.000000000   
0  0  0 
  Cu     0.500000000    0.000000000    0.000000000   
0  0  0 
  Cu     0.000000000    0.500000000    0.000000000   
0  0  0 
  Cu     0.000000000    0.000000000    0.500000000   
0  0  0 
K_POINTS automatic
4 4 4 1 1 1
EOF
echo "  running the scf calculation...\c"
$ESPRESSO_ROOT/bin/pw.x < cu3n.scf.in > cu3n.scf.out
echo " done"

# phonons
cat > cu3n.phG.in << EOF
phonons of Cu3N at Gamma
 &inputph
  tr2_ph=1.0d-14,
  prefix='cu3n',
  amass(1)=14.00674, 
  amass(2)=63.546,
  outdir='$TMP_DIR/',
  fildyn='cu3n.dynG',
 /
0.0 0.0 0.0
EOF
echo "  running the phonon calculation at Gamma...\c"
$ESPRESSO_ROOT/bin/ph.x < cu3n.phG.in > cu3n.phG.out
echo " done"

# These are k-points of a (444) uniform grid in the
irreducible
# Brillouin Zone of the scc lattice (Gamma is treated
separately)
/bin/rm cu3n.nscf.out cu3n.ph.out

 
qpoints=" 0.25,0.00,0.00\
          0.50,0.00,0.00\
          0.25,0.25,0.00\
          0.50,0.25,0.00\
          0.50,0.50,0.00\
          0.25,0.25,0.25\
          0.50,0.25,0.25\
          0.50,0.50,0.25\
          0.50,0.50,0.50 "

for qpoint in $qpoints ; do

# non self-consistent calculation 
qx=`echo $qpoint | cut -d, -f1`
qy=`echo $qpoint | cut -d, -f2`
qz=`echo $qpoint | cut -d, -f3`
cat > cu3n.nscf.in << EOF
 &control
    calculation='phonon'
    restart_mode='from_scratch',
    prefix='cu3n',
    pseudo_dir = '$PSEUDO_DIR/',
    outdir='$TMP_DIR/'
 /
 &system    
    ibrav = 1, celldm(1) = 7.090, nat = 4, ntyp = 2,
    ecutwfc = 75.0 ,ecutrho=450.0,
    occupations = 'smearing', degauss = 0.02 ,
    smearing = 'methfessel-paxton'
/
 &electrons
    conv_thr = 1.0d-8 ,
 /
 &phonon
    xqq(1) = $qx, xqq(2) = $qy, xqq(3) = $qz
 /
ATOMIC_SPECIES
 N   14.00674   N.pz-rrkjus.UPF 
 Cu  63.54600  Cu.pz-d-rrkjus.UPF 
ATOMIC_POSITIONS
    N      0.000000000    0.000000000    0.000000000  
 0  0  0 
   Cu      0.500000000    0.000000000    0.000000000  
 0  0  0 
   Cu      0.000000000    0.500000000    0.000000000  
 0  0  0 
   Cu      0.000000000    0.000000000    0.500000000  
 0  0  0 
K_POINTS  automatic
4 4 4 1 1 1
EOF

echo "  running the nscf calculation at
q=$qpoint...\c"
$ESPRESSO_ROOT/bin/pw.x < cu3n.nscf.in >>
cu3n.nscf.out
echo " done"

# phonon calculation
cat > cu3n.ph.in << EOF
phonons of Cu3N at $qpoint
 &inputph
  tr2_ph=1.0d-14,
  prefix='cu3n',
  amass(1)=14.00674, 
  amass(2)=63.546,
  outdir='$TMP_DIR/',
  fildyn='dyn.$qpoint'
 /
$qpoint
EOF
echo "  running the phonon calculation at
q=$qpoint...\c"
$ESPRESSO_ROOT/bin/ph.x < cu3n.ph.in >> cu3n.ph.out
echo " done"

done

cat > q2r.in <<EOF
 &input
   nr1=4,nr2=4, nr3=4, zasr=.true., fild='cu3n444.fc'
 /
10
cu3n.dynG
dyn.0.25,0.00,0.00
dyn.0.50,0.00,0.00
dyn.0.25,0.25,0.00
dyn.0.50,0.25,0.00
dyn.0.50,0.50,0.00
dyn.0.25,0.25,0.25
dyn.0.50,0.25,0.25
dyn.0.50,0.50,0.25
dyn.0.50,0.50,0.50
EOF

echo "  transforming C(q) => C(R)...\c"
$ESPRESSO_ROOT/bin/q2r.x < q2r.in > q2r.out
echo " done"

cat > matdyn.in <<EOF
 &input
    asr=.true.,  amass(1)=14.00674, amass(2)=63.546, 
    flfrc='cu3n444.fc', flfrq='cu3n.freq'
 /
 31
  0.00 0.00 0.00  0.0
  0.05 0.00 0.00  0.0
  0.10 0.00 0.00  0.0
  0.15 0.00 0.00  0.0
  0.20 0.00 0.00  0.0  
  0.25 0.00 0.00  0.0
  0.30 0.00 0.00  0.0
  0.35 0.00 0.00  0.0  
  0.40 0.00 0.00  0.0
  0.45 0.00 0.00  0.0  
  0.50 0.00 0.00  0.0  
  0.50 0.05 0.00  0.0
  0.50 0.10 0.00  0.0
  0.50 0.15 0.00  0.0
  0.50 0.20 0.00  0.0
  0.50 0.25 0.00  0.0
  0.50 0.30 0.00  0.0
  0.50 0.35 0.00  0.0
  0.50 0.40 0.00  0.0
  0.50 0.45 0.00  0.0
  0.50 0.50 0.00  0.0
  0.50 0.50 0.05  0.0
  0.50 0.50 0.10  0.0
  0.50 0.50 0.15  0.0
  0.50 0.50 0.20  0.0
  0.50 0.50 0.25  0.0
  0.50 0.50 0.30  0.0
  0.50 0.50 0.35  0.0
  0.50 0.50 0.40  0.0 
  0.50 0.50 0.45  0.0
  0.50 0.50 0.50  0.0
EOF

echo "  recalculating omega(q) from C(R)...\c"
$ESPRESSO_ROOT/bin/matdyn.x < matdyn.in > matdyn.out
echo " done"

cat > phdos.in <<EOF
 &input
    asr=.true.,  dos=.true. amass(1)=14.00674,
amass(2)=63.546, 
    flfrc='cu3n444.fc', fldos='cu3n.phdos',
nk1=6,nk2=6,nk3=6
 /
EOF

echo "  calculating phonon DOS ...\c"
$ESPRESSO_ROOT/bin/matdyn.x < phdos.in > phdos.out
echo " done"

echo
echo "ALL: done"
*****************************************************
*****************************************************
Treated as insolator(semiconductor),input file:

#!/bin/sh

# set the needed environment variables

ESPRESSO_ROOT=$HOME/pwscf/
PSEUDO_DIR=$HOME/pwscf/pseudo/
TMP_DIR=$HOME/pwscf_workspace/tmp1

# self-consistent calculation
cat > cu3n.scf.in << EOF
 &control
    calculation='scf'
    restart_mode='from_scratch',
    prefix='cu3n',
    pseudo_dir = '$PSEUDO_DIR/',
    outdir='$TMP_DIR/',
    tstress = .true. 
 /
 &system    
    ibrav = 1, celldm(1) = 7.090, nat = 4, ntyp = 2,
    ecutwfc = 75.0 ,ecutrho=450.0,
/
 &electrons
    conv_thr =  1.0d-8
    mixing_beta = 0.7
 /
ATOMIC_SPECIES
 N   14.00674   N.pz-rrkjus.UPF 
 Cu  63.54600  Cu.pz-d-rrkjus.UPF 
ATOMIC_POSITIONS
  N      0.000000000    0.000000000    0.000000000   
0  0  0 
  Cu     0.500000000    0.000000000    0.000000000   
0  0  0 
  Cu     0.000000000    0.500000000    0.000000000   
0  0  0 
  Cu     0.000000000    0.000000000    0.500000000   
0  0  0 
K_POINTS automatic
4 4 4 1 1 1
EOF
echo "  running the scf calculation...\c"
$ESPRESSO_ROOT/bin/pw.x < cu3n.scf.in > cu3n.scf.out
echo " done"

# phonons
cat > cu3n.phG.in << EOF
phonons of Cu3N at Gamma
 &inputph
  tr2_ph=1.0d-14,
  prefix='cu3n',
  epsil=.true.,
  amass(1)=14.00674, 
  amass(2)=63.546,
  outdir='$TMP_DIR/',
  fildyn='cu3n.dynG',
 /
0.0 0.0 0.0
EOF
echo "  running the phonon calculation at Gamma...\c"
$ESPRESSO_ROOT/bin/ph.x < cu3n.phG.in > cu3n.phG.out
echo " done"

# These are k-points of a (444) uniform grid in the
irreducible
# Brillouin Zone of the scc lattice (Gamma is treated
separately)
/bin/rm cu3n.nscf.out cu3n.ph.out

 
qpoints=" 0.25,0.00,0.00\
          0.50,0.00,0.00\
          0.25,0.25,0.00\
          0.50,0.25,0.00\
          0.50,0.50,0.00\
          0.25,0.25,0.25\
          0.50,0.25,0.25\
          0.50,0.50,0.25\
          0.50,0.50,0.50 "

for qpoint in $qpoints ; do

# non self-consistent calculation 
qx=`echo $qpoint | cut -d, -f1`
qy=`echo $qpoint | cut -d, -f2`
qz=`echo $qpoint | cut -d, -f3`
cat > cu3n.nscf.in << EOF
 &control
    calculation='phonon'
    restart_mode='from_scratch',
    prefix='cu3n',
    pseudo_dir = '$PSEUDO_DIR/',
    outdir='$TMP_DIR/'
 /
 &system    
    ibrav = 1, celldm(1) = 7.090, nat = 4, ntyp = 2,
    ecutwfc = 75.0 ,ecutrho=450.0
/
 &electrons
    conv_thr = 1.0d-8 ,
 /
 &phonon
    xqq(1) = $qx, xqq(2) = $qy, xqq(3) = $qz
 /
ATOMIC_SPECIES
 N   14.00674   N.pz-rrkjus.UPF 
 Cu  63.54600  Cu.pz-d-rrkjus.UPF 
ATOMIC_POSITIONS
    N      0.000000000    0.000000000    0.000000000  
 0  0  0 
   Cu      0.500000000    0.000000000    0.000000000  
 0  0  0 
   Cu      0.000000000    0.500000000    0.000000000  
 0  0  0 
   Cu      0.000000000    0.000000000    0.500000000  
 0  0  0 
K_POINTS  automatic
4 4 4 1 1 1
EOF

echo "  running the nscf calculation at
q=$qpoint...\c"
$ESPRESSO_ROOT/bin/pw.x < cu3n.nscf.in >>
cu3n.nscf.out
echo " done"

# phonon calculation
cat > cu3n.ph.in << EOF
phonons of Cu3N at $qpoint
 &inputph
  tr2_ph=1.0d-14,
  prefix='cu3n',
  amass(1)=14.00674, 
  amass(2)=63.546,
  outdir='$TMP_DIR/',
  fildyn='dyn.$qpoint'
 /
$qpoint
EOF
echo "  running the phonon calculation at
q=$qpoint...\c"
$ESPRESSO_ROOT/bin/ph.x < cu3n.ph.in >> cu3n.ph.out
echo " done"

done

cat > q2r.in <<EOF
 &input
   nr1=4,nr2=4, nr3=4, zasr=.true., fild='cu3n444.fc'
 /
10
cu3n.dynG
dyn.0.25,0.00,0.00
dyn.0.50,0.00,0.00
dyn.0.25,0.25,0.00
dyn.0.50,0.25,0.00
dyn.0.50,0.50,0.00
dyn.0.25,0.25,0.25
dyn.0.50,0.25,0.25
dyn.0.50,0.50,0.25
dyn.0.50,0.50,0.50
EOF

echo "  transforming C(q) => C(R)...\c"
$ESPRESSO_ROOT/bin/q2r.x < q2r.in > q2r.out
echo " done"

cat > matdyn.in <<EOF
 &input
    asr=.true.,  amass(1)=14.00674, amass(2)=63.546, 
    flfrc='cu3n444.fc', flfrq='cu3n.freq'
 /
  31
  0.00 0.00 0.00  0.0
  0.05 0.00 0.00  0.0
  0.10 0.00 0.00  0.0
  0.15 0.00 0.00  0.0
  0.20 0.00 0.00  0.0  
  0.25 0.00 0.00  0.0
  0.30 0.00 0.00  0.0
  0.35 0.00 0.00  0.0  
  0.40 0.00 0.00  0.0
  0.45 0.00 0.00  0.0  
  0.50 0.00 0.00  0.0  
  0.50 0.05 0.00  0.0
  0.50 0.10 0.00  0.0
  0.50 0.15 0.00  0.0
  0.50 0.20 0.00  0.0
  0.50 0.25 0.00  0.0
  0.50 0.30 0.00  0.0
  0.50 0.35 0.00  0.0
  0.50 0.40 0.00  0.0
  0.50 0.45 0.00  0.0
  0.50 0.50 0.00  0.0
  0.50 0.50 0.05  0.0
  0.50 0.50 0.10  0.0
  0.50 0.50 0.15  0.0
  0.50 0.50 0.20  0.0
  0.50 0.50 0.25  0.0
  0.50 0.50 0.30  0.0
  0.50 0.50 0.35  0.0
  0.50 0.50 0.40  0.0 
  0.50 0.50 0.45  0.0
  0.50 0.50 0.50  0.0
EOF

echo "  recalculating omega(q) from C(R)...\c"
$ESPRESSO_ROOT/bin/matdyn.x < matdyn.in > matdyn.out
echo " done"

cat > phdos.in <<EOF
 &input
    asr=.true.,  dos=.true. amass(1)=14.00674,
amass(2)=63.546, 
    flfrc='cu3n444.fc', fldos='cu3n.phdos',
nk1=6,nk2=6,nk3=6
 /
EOF

echo "  calculating phonon DOS ...\c"
$ESPRESSO_ROOT/bin/matdyn.x < phdos.in > phdos.out
echo " done"

echo
echo "ALL: done"
*****************************************************
*****************************************************
Some of the output results:

treated as metal:

Convergence has been achieved 
 
     Number of q in the star =    1
     List of q in the star:
          1   0.000000000   0.000000000   0.000000000

     Diagonalizing the dynamical matrix

     q = (    0.000000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       0.315780 [THz] =      10.533350
[cm-1]
     omega( 2) =       0.315780 [THz] =      10.533350
[cm-1]
     omega( 3) =       0.315780 [THz] =      10.533350
[cm-1]
     omega( 4) =       3.021986 [THz] =     100.803264
[cm-1]
     omega( 5) =       3.021986 [THz] =     100.803264
[cm-1]
     omega( 6) =       3.021986 [THz] =     100.803264
[cm-1]
     omega( 7) =       4.790291 [THz] =     159.787978
[cm-1]
     omega( 8) =       4.790291 [THz] =     159.787978
[cm-1]
     omega( 9) =       4.790291 [THz] =     159.787978
[cm-1]
     omega(10) =      21.171985 [THz] =     706.226098
[cm-1]
     omega(11) =      21.171985 [THz] =     706.226098
[cm-1]
     omega(12) =      21.171985 [THz] =     706.226098
[cm-1]

**************************************************************************
 
 Convergence has been achieved 
 
     Number of q in the star =    6
     List of q in the star:
          1   0.250000000   0.000000000   0.000000000
          2  -0.250000000   0.000000000   0.000000000
          3   0.000000000   0.250000000   0.000000000
          4   0.000000000  -0.250000000   0.000000000
          5   0.000000000   0.000000000   0.250000000
          6   0.000000000   0.000000000  -0.250000000

     Diagonalizing the dynamical matrix

     q = (    0.250000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.240214 [THz] =      41.369364
[cm-1]
     omega( 2) =       1.240214 [THz] =      41.369364
[cm-1]
     omega( 3) =       2.645508 [THz] =      88.245250
[cm-1]
     omega( 4) =       2.749801 [THz] =      91.724096
[cm-1]
     omega( 5) =       3.113789 [THz] =     103.865496
[cm-1]
     omega( 6) =       3.113789 [THz] =     103.865496
[cm-1]
     omega( 7) =       4.680720 [THz] =     156.133064
[cm-1]
     omega( 8) =       4.680720 [THz] =     156.133064
[cm-1]
     omega( 9) =       7.203053 [THz] =     240.269590
[cm-1]
     omega(10) =      20.475396 [THz] =     682.990228
[cm-1]
     omega(11) =      21.089697 [THz] =     703.481243
[cm-1]
     omega(12) =      21.089697 [THz] =     703.481243
[cm-1]

**************************************************************************

   Convergence has been achieved 
 
     Number of q in the star =    3
     List of q in the star:
          1   0.500000000   0.000000000   0.000000000
          2   0.000000000   0.500000000   0.000000000
          3   0.000000000   0.000000000   0.500000000

     Diagonalizing the dynamical matrix

     q = (    0.500000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.703361 [THz] =      56.818378
[cm-1]
     omega( 2) =       1.703361 [THz] =      56.818378
[cm-1]
     omega( 3) =       2.507925 [THz] =      83.655931
[cm-1]
     omega( 4) =       3.041099 [THz] =     101.440808
[cm-1]
     omega( 5) =       3.435647 [THz] =     114.601604
[cm-1]
     omega( 6) =       3.435647 [THz] =     114.601604
[cm-1]
     omega( 7) =       4.434737 [THz] =     147.927879
[cm-1]
     omega( 8) =       4.434737 [THz] =     147.927879
[cm-1]
     omega( 9) =       9.718677 [THz] =     324.182323
[cm-1]
     omega(10) =      19.972559 [THz] =     666.217279
[cm-1]
     omega(11) =      20.924142 [THz] =     697.958878
[cm-1]
     omega(12) =      20.924142 [THz] =     697.958878
[cm-1]

**************************************************************************
   Convergence has been achieved 
 
     Number of q in the star =   12
     List of q in the star:
          1   0.250000000   0.250000000   0.000000000
          2  -0.250000000  -0.250000000   0.000000000
          3  -0.250000000   0.250000000   0.000000000
          4   0.250000000  -0.250000000   0.000000000
          5   0.000000000  -0.250000000   0.250000000
          6   0.000000000  -0.250000000  -0.250000000
          7   0.000000000   0.250000000  -0.250000000
          8   0.000000000   0.250000000   0.250000000
          9  -0.250000000   0.000000000   0.250000000
         10  -0.250000000   0.000000000  -0.250000000
         11   0.250000000   0.000000000  -0.250000000
         12   0.250000000   0.000000000   0.250000000

     Diagonalizing the dynamical matrix

     q = (    0.250000000   0.250000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.686703 [THz] =      56.262716
[cm-1]
     omega( 2) =       2.402942 [THz] =      80.154034
[cm-1]
     omega( 3) =       2.708175 [THz] =      90.335592
[cm-1]
     omega( 4) =       2.732119 [THz] =      91.134290
[cm-1]
     omega( 5) =       3.200703 [THz] =     106.764679
[cm-1]
     omega( 6) =       3.459543 [THz] =     115.398702
[cm-1]
     omega( 7) =       4.523122 [THz] =     150.876101
[cm-1]
     omega( 8) =       6.579514 [THz] =     219.470414
[cm-1]
     omega( 9) =       7.701478 [THz] =     256.895363
[cm-1]
     omega(10) =      20.388755 [THz] =     680.100186
[cm-1]
     omega(11) =      20.415623 [THz] =     680.996404
[cm-1]
     omega(12) =      20.938536 [THz] =     698.439021
[cm-1]

**************************************************************************

**************************************************************************

**************************************************************************
 treated as insolator(semiconductor):

  Convergence has been achieved 
 
     Number of q in the star =    1
     List of q in the star:
          1   0.000000000   0.000000000   0.000000000

          Dielectric constant in cartesian axis 

          (        8.79115        0.00000       
0.00000 )
          (        0.00000        8.79115       
0.00000 )
          (        0.00000        0.00000       
8.79115 )

          Effective charges E-U in cartesian axis 

                    Z_{alpha}{s,beta} 

           Atom     1
          (       -0.86100        0.00000       
0.00000 )
          (        0.00000       -0.86100       
0.00000 )
          (        0.00000        0.00000      
-0.86100 )
           Atom     2
          (        1.07428        0.00000       
0.00000 )
          (        0.00000       -0.03660       
0.00000 )
          (        0.00000        0.00000      
-0.03660 )
           Atom     3
          (       -0.03660        0.00000       
0.00000 )
          (        0.00000        1.07428       
0.00000 )
          (        0.00000        0.00000      
-0.03660 )
           Atom     4
          (       -0.03660        0.00000       
0.00000 )
          (        0.00000       -0.03660       
0.00000 )
          (        0.00000        0.00000       
1.07428 )

     Diagonalizing the dynamical matrix

     q = (    0.000000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       0.559055 [THz] =      18.648185
[cm-1]
     omega( 2) =       0.559055 [THz] =      18.648185
[cm-1]
     omega( 3) =       0.559055 [THz] =      18.648185
[cm-1]
     omega( 4) =       3.019518 [THz] =     100.720945
[cm-1]
     omega( 5) =       3.019518 [THz] =     100.720945
[cm-1]
     omega( 6) =       3.019518 [THz] =     100.720945
[cm-1]
     omega( 7) =       4.783115 [THz] =     159.548617
[cm-1]
     omega( 8) =       4.783115 [THz] =     159.548617
[cm-1]
     omega( 9) =       4.783115 [THz] =     159.548617
[cm-1]
     omega(10) =      21.153921 [THz] =     705.623535
[cm-1]
     omega(11) =      21.153921 [THz] =     705.623535
[cm-1]
     omega(12) =      21.153921 [THz] =     705.623535
[cm-1]

**************************************************************************

  Convergence has been achieved 
 
     Number of q in the star =    6
     List of q in the star:
          1   0.250000000   0.000000000   0.000000000
          2  -0.250000000   0.000000000   0.000000000
          3   0.000000000   0.250000000   0.000000000
          4   0.000000000  -0.250000000   0.000000000
          5   0.000000000   0.000000000   0.250000000
          6   0.000000000   0.000000000  -0.250000000

     Diagonalizing the dynamical matrix

     q = (    0.250000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.256465 [THz] =      41.911424
[cm-1]
     omega( 2) =       1.256465 [THz] =      41.911424
[cm-1]
     omega( 3) =       2.750305 [THz] =      91.740894
[cm-1]
     omega( 4) =       2.804905 [THz] =      93.562186
[cm-1]
     omega( 5) =       3.114438 [THz] =     103.887152
[cm-1]
     omega( 6) =       3.114438 [THz] =     103.887152
[cm-1]
     omega( 7) =       4.678704 [THz] =     156.065816
[cm-1]
     omega( 8) =       4.678704 [THz] =     156.065816
[cm-1]
     omega( 9) =       7.214252 [THz] =     240.643148
[cm-1]
     omega(10) =      20.712523 [THz] =     690.900005
[cm-1]
     omega(11) =      21.075562 [THz] =     703.009755
[cm-1]
     omega(12) =      21.075562 [THz] =     703.009755
[cm-1]

**************************************************************************

  Convergence has been achieved 
 
     Number of q in the star =    3
     List of q in the star:
          1   0.500000000   0.000000000   0.000000000
          2   0.000000000   0.500000000   0.000000000
          3   0.000000000   0.000000000   0.500000000

     Diagonalizing the dynamical matrix

     q = (    0.500000000   0.000000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.719289 [THz] =      57.349695
[cm-1]
     omega( 2) =       1.719289 [THz] =      57.349695
[cm-1]
     omega( 3) =       2.518665 [THz] =      84.014176
[cm-1]
     omega( 4) =       3.048277 [THz] =     101.680259
[cm-1]
     omega( 5) =       3.437370 [THz] =     114.659100
[cm-1]
     omega( 6) =       3.437370 [THz] =     114.659100
[cm-1]
     omega( 7) =       4.435697 [THz] =     147.959901
[cm-1]
     omega( 8) =       4.435697 [THz] =     147.959901
[cm-1]
     omega( 9) =       9.721777 [THz] =     324.285722
[cm-1]
     omega(10) =      19.953888 [THz] =     665.594483
[cm-1]
     omega(11) =      20.912939 [THz] =     697.585200
[cm-1]
     omega(12) =      20.912939 [THz] =     697.585200
[cm-1]

**************************************************************************
 Convergence has been achieved 
 
     Number of q in the star =   12
     List of q in the star:
          1   0.250000000   0.250000000   0.000000000
          2  -0.250000000  -0.250000000   0.000000000
          3  -0.250000000   0.250000000   0.000000000
          4   0.250000000  -0.250000000   0.000000000
          5   0.000000000  -0.250000000   0.250000000
          6   0.000000000  -0.250000000  -0.250000000
          7   0.000000000   0.250000000  -0.250000000
          8   0.000000000   0.250000000   0.250000000
          9  -0.250000000   0.000000000   0.250000000
         10  -0.250000000   0.000000000  -0.250000000
         11   0.250000000   0.000000000  -0.250000000
         12   0.250000000   0.000000000   0.250000000

     Diagonalizing the dynamical matrix

     q = (    0.250000000   0.250000000   0.000000000
) 


**************************************************************************
     omega( 1) =       1.694087 [THz] =      56.509035
[cm-1]
     omega( 2) =       2.422894 [THz] =      80.819587
[cm-1]
     omega( 3) =       2.775360 [THz] =      92.576676
[cm-1]
     omega( 4) =       2.793209 [THz] =      93.172038
[cm-1]
     omega( 5) =       3.205310 [THz] =     106.918352
[cm-1]
     omega( 6) =       3.687580 [THz] =     123.005251
[cm-1]
     omega( 7) =       4.522735 [THz] =     150.863198
[cm-1]
     omega( 8) =       6.581124 [THz] =     219.524142
[cm-1]
     omega( 9) =       7.713332 [THz] =     257.290770
[cm-1]
     omega(10) =      20.460174 [THz] =     682.482471
[cm-1]
     omega(11) =      20.598516 [THz] =     687.097091
[cm-1]
     omega(12) =      20.925678 [THz] =     698.010110
[cm-1]

**************************************************************************









		
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