Calculation of the Vibrational
Frequency of CO on Ni(111)
The vibrational frequency calculation is run
using the Calculate keyword frequency.
The input file will have the following appearance:
#Calculate optimize
#Calculate
energy
#Calculate
optimize_frequency
#Calculate
ts_search
Calculate frequency
#Calculate
gradient
#Calculate Molecular_Dynamics
#Calculate Simulated_Annealing
The numerical elements of the second derivative
(Hessian) matrix are written to the .hesswk
file. This job is sufficiently large
(even using effective core potentials
#Vibration_steps
2 0.01
Vibration_steps 1 0.01
Vibration_Project on
Vibration_restart on
Once the job is completed you will find the
calculated frequencies in the outmol file. Since we fixed the Ni atoms the lower
frequencies are meaningless (i.e. the Ni atoms were not properly optimized and
so the forces between them are not accurate).
However, the two CO frequencies (and perhaps the two Ni-CO stretching
frequencies) are meaningful. The
frequencies obtained in a trial run are shown below.
vibrational frequencies
mode au_amu cm-1 meV THz
1
-0.013756 -70.7 -8.77 -2.120
2
-0.006381 -32.8 -4.07 -0.983
3
0.015628 80.3 9.96 2.408
4
0.016125 82.9 10.28 2.485
5
0.018901 97.2 12.05 2.913
6
0.022171 114.0 14.13 3.417
…..
63
0.078266 402.3 49.88 12.061
64
0.078588 404.0 50.09 12.111
65
0.357898 1839.8 228.10 55.155
66
0.366515 1884.1 233.60 56.483
Note that there are 3N degrees of freedom where
N is the number of atoms. In this case
N=22 so there are 66 degrees of freedom.
In gas phase or liquid phase there are 3 rotations and 3 translations so
that 6 degrees of freedom are not actual vibrations (there 3N-6 vibrations for
a non-linear polyatomic molecule).
However, for the solid there are no rotations or translations and all 66
degrees of freedom are included. Note
that the calculation suggests that there are two normal modes that involve the
C-O stretch these are 1840 cm-1 and 1884 cm-1. You will want to compare these to the
calculated value for free CO. To make
this comparison you will want to create a diatomic CO in a car file and run a
geometry optimization and frequency calculation. The value you obtain
will approximately 2159 cm-1.
This can be compared to the experimental frequency of 2143 cm-1.
You can examine the form of the normal modes by
reading the car and outmol files into insightII. Use the Molecule/Get
command to read in the ni_111_co_vib.car file.
Create appropriate rendering and then use the left spiral icon to call
the DMol3 submenu. In this menu use the Analyze/Normal_Mode command.
Click on the XXX menu box and select the ni_111_co_vib.outmol file. When the InsightII program reads in the outmol file it will automatically generate a list of frequencies
in the Frequencies1 menu and a graph of the normal modes. For solids the graph is meaningless since the
intensities are not calculated. You will
need to move the graph or “blank” it using the Object/Blank command with the
selection Graph1.
To continue with plotting you will need to reopen the Analyze/Normal_Mode menu and then click on the Select
Vector option.
Then click on the following selections Arrow_Style,
A_scale
Scroll
down the menu Frequencies1 until the desired mode is reached (e.g. 1839.8) and
click on it. The normal mode has the
appearance shown in the Figure below.
Note that this is one eigenvector of matrix used to diagonalize.
Figure 1. Normal mode for the
1839 cm-1 vibration.
Several
other normal modes are shown below as well.
These can be generated simply by clicking on the appropriate frequency
in the Frequencies1 menu (provided the Normal_Mode
menu is still open).
Figure 2. Normal mode for the
1884 cm-1 vibration.
Figure 3. Normal mode for the
402 cm-1 vibration.
Figure 4. Normal mode for the
404 cm-1 vibration.