NH₃: Numerical Frequencies

Sample directory: adf/Freq_NH3/

Summary:

• Frequencies with symmetric displacements
• Frequencies with Cartesian displacements
• Isotope effects in the frequencies

Frequencies with symmetric displacements

Computation of frequencies by symmetric displacements. The assumed equilibrium input structure should be given in Cartesian coordinates.

The symmetry is determined automatically by the program as C(3v), from the input coordinates. During the calculation first symmetric atomic displacements are constructed. The number of such displacements in each irreducible representation corresponds to the number of frequencies with the corresponding symmetry. All displaced geometries within one representation have the same symmetry, which enables us to use it to speed up the computation significantly. Another advantage of having the same symmetry is that the numerical integration data can be reused efficiently (see SMOOTH option) thus reducing the level of numerical noise in gradients and force constant matrix.

$ADFBIN/adf <<eor
title NH3 frequencies in symmetric displacements

atoms
   N               0.0000    0.0000    0.0000
   H               0.4729    0.8190    0.3821
   H              -0.9457    0.0000    0.3821
   H               0.4729   -0.8190    0.3821
end

Basis
 Type TZP
 Core Small
End

geometry
  frequencies Symm
end

thermo  T=300,400

integration  5.0

end input
eor

Frequencies with Cartesian displacements

Computation of frequencies by Cartesian displacements. The assumed equilibrium input structure is given in internal coordinates. A dummy atom is used for a convenient definition of the Z-matrix such that it reflects the pointgroup symmetry C(3v).

$ADFBIN/adf <<eor
title NH3 frequencies

define
  rNH=1.02
  theta=112
  phi=120
end

atoms   Z-matrix
  XX   0 0 0
  N    1 0 0   1.0
  H    2 1 0   rNH   theta
  H    2 1 3   rNH   theta   phi
  H    2 1 4   rNH   theta   phi
end

Basis
 Type TZP
 Core Small
End

geometry
  optim  cartesian
  frequencies
end

thermo  T=300,400

integration  5.0

end input
eor

The symmetry is determined automatically by the program as C(3v), from the input coordinates. In a Frequencies calculation the symmetry (specified on input or computed internally) is used for analysis and in some cases to speed up the calculation.

The equilibrium coordinate values are supplied as identifiers that are associated with values in the define block.

Unlike using the geovar key, applying the define key does not mean anything in the sense that the various coordinates that refer to the same identifier would be forced to remain equal; it is just a way to display (to the human reader) symmetry in the equilibrium values, to avoid typing errors and to allow an easy adjustment of starting coordinates for another calculation.

Since the atomic coordinates are input in Z-matrix format, the program would by default carry out displacements in internal coordinates to scan the energy surface and hence compute force constants and frequencies. This is overriden by specifying in the geometry block optim cartesian: carry out cartesian displacements.

The key thermo addresses the thermodynamical analysis (only available in a Frequencies calculation, otherwise ignored). The specification 'T=300,400' means that the thermodynamic properties are printed for the temperature range 300-400K, in steps of 10K (default) and for a pressure of 1.0 atmosphere (default).

Frequencies calculations suffer easily from numerical inaccuracies. Therefore, the default numerical integration precision in a Frequencies calculation is much higher than in an ordinary single-point or minimization run. Here we specify the INTEGRATION level to be 5.0 (quite high, but the default for Frequencies is even 6.0).

Isotope effects in the frequencies

Rename the TAPE21 result file of the previous calculation so we can restart with other masses. Calculate a different isotope of H, in this case deuterium. It will differ from the original one only in the mass of the nucleus. Repeat the frequency calculation with different fragments. It is important to preserve symmetry at this step so we replace fragment files for ALL H atoms. If you want to replace only one fragment then the original calculation must be performed the same way, with different fragment names.

mv TAPE21 restart.t21

$ADFBIN/adf -n1 <<eor
create H M=2.014101779 $ADFRESOURCES/TZP/H
eor

mv TAPE21 t21.D

$ADFBIN/adf <<eor
title NH3 frequencies

define
  rNH=1.02
  theta=112
  phi=120
end

atoms   Z-matrix
  XX   0 0 0
  N    1 0 0   1.0
  H    2 1 0   rNH   theta          
  H    2 1 3   rNH   theta   phi    
  H    2 1 4   rNH   theta   phi    
end

Fragments
  N t21.N
! The different isotope mass sits in the next line.
  H t21.D
End

geometry
  optim  cartesian
  frequencies
end

! Restart the frequency calculation. 
! In fact ADF should perform only one geometry cycle
restart restart.t21

thermo  T=300,400

integration  5.0

end input
eor