Biomedical Engineering Reference
In-Depth Information
Full mass-weighted force constant matrix:
Low frequencies--- -0.8888 -0.5279 -0.3445 0.0005 0.0006 0.0012
Low frequencies--- 34.4264 43.3413 60.3827
The first six are essentially zero and are therefore taken to represent the redundant coordin-
ates. The next piece of output gives the normal modes, as discussed in Chapters 3 and 4.
Here is a snapshot.
61
62
63
...(Symmetry)...
A
A
A
Frequencies - -
3722.9962
3800.9366
4108.2863
Red. masses - -
1.0501
1.0942
1.0651
Frc consts - -
8.5758
9.3135
10.5919
IR Inten - -
2.7774
5.3387
106.2867
Raman Activ - -
110.9373
67.9404
72.1007
Depolar (P) - -
0.1335
0.6701
0.2986
Depolar (U) - -
0.2356
0.8025
0.4599
Atom AN
X
Y
Z
X
Y
Z
X
Y
Z
1
7
-0.05 0.02 -0.01
0.02 0.02 -0.08
0.00 0.00 0.00
2
1
0.23 -0.29 0.62
0.24 -0.30 0.58
0.00 0.00 0.00
3
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
4
1
0.48 -0.05 -0.50
-0.51 0.08 0.50
0.00 0.00 0.00
5
1
0.00 0.00 0.01
0.00 0.00 0.01
0.00 0.00 0.00
6
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
7
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
8
8
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
9
1
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
10
1
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
11
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
12
8
0.00 0.00 0.00
0.00 0.00 0.00
0.00 -0.06 0.00
13
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
14
6
0.00 0.00 0.00
0.00 0.00 0.00
0.00 0.00 0.00
15
1
0.00 0.00 0.00
0.00 0.00 0.00
-0.07 1.00 -0.01
Output includes the vibration frequencies, reduced masses, force constants, infrared
intensities, Raman activities and depolarization ratios, together with the normal modes
expressed as linear combinations of the Cartesian coordinates of the atoms. Normal mode
63 for example, which is of A symmetry, comprises almost entirely the
y
component for
atom 15, which is a hydrogen atom.
Most packages will simulate the infrared spectrum (Figure 17.6) and allow for on-screen
animation of the normal modes of vibration. I must stress that geometries have to be
optimized before calculating vibrational frequencies, since these are defined as the second
derivative
calculated at the stationary point
.
I want to illustrate one final point by considering a much smaller molecule, carbon
dioxide. It is a linear molecule and so has four vibrational degrees of freedom. It is also a
very topical greenhouse gas.
Table 17.1 shows the calculated frequencies. The agreement with experiment is not par-
ticularly good. The intensities (not shown) are qualitatively correct; the symmetric stretch
