Reduction formula for point group D2
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| Cartesian 3N |
144 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
138 |
2 |
2 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
B1 |
B2 |
B3 |
Total |
| Cartesian 3N |
36 |
36 |
36 |
36 |
144 |
| Translation (x,y,z) |
0 |
1 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
36 |
34 |
34 |
34 |
138 |
Molecule Parameter
| Number of Atoms (N) |
48 |
| Number of internal coordinates |
138 |
| Number of independant internal coordinates |
36 |
| Number of vibrational modes |
138 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B1 |
B2 |
B3 |
Total |
| Linear (IR) |
36 |
34 |
34 |
34 |
102 / 36 |
| Quadratic (Raman) |
36 |
34 |
34 |
34 |
138 / 0 |
| IR + Raman |
- |
34 |
34 |
34 |
102 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| linear |
1 |
138 |
2 |
2 |
2 |
| quadratic |
2 |
9.591 |
71 |
71 |
71 |
| cubic |
3 |
447.580 |
140 |
140 |
140 |
| quartic |
4 |
15.777.195 |
2.555 |
2.555 |
2.555 |
| quintic |
5 |
448.072.338 |
4.970 |
4.970 |
4.970 |
| sextic |
6 |
10.679.057.389 |
62.125 |
62.125 |
62.125 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B1 |
B2 |
B3 |
| linear |
1 |
36 |
34 |
34 |
34 |
| quadratic |
2 |
2.451 |
2.380 |
2.380 |
2.380 |
| cubic |
3 |
112.000 |
111.860 |
111.860 |
111.860 |
| quartic |
4 |
3.946.215 |
3.943.660 |
3.943.660 |
3.943.660 |
| quintic |
5 |
112.021.812 |
112.016.842 |
112.016.842 |
112.016.842 |
| sextic |
6 |
2.669.810.941 |
2.669.748.816 |
2.669.748.816 |
2.669.748.816 |
Literature
- J.K.G. Watson, J. Mol. Spec. 41 229 (1972)
The Numbers of Structural Parameters and Potential Constants of Molecules
- X.F. Zhou, P. Pulay. J. Comp. Chem. 10 No. 7, 935-938 (1989)
Characters for Symmetric and Antisymmetric Higher Powers of Representations:
Application to the Number of Anharmonic Force Constants in Symmetrical Molecules
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement