Example: Numerical Frequencies: NH3¶
- 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 BeckeGrid quality good End 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 BeckeGrid quality good End 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 overridden 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 BeckeGrid quality good End end input eor