Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
324 |
12 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
318 |
12 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
168 |
156 |
324 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
165 |
153 |
318 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
165 |
| Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
165 |
153 |
318 / 0 |
| Quadratic (Raman) |
165 |
153 |
318 / 0 |
| IR + Raman |
165 |
153 |
318 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
318 |
12 |
| quadratic |
2 |
50.721 |
231 |
| cubic |
3 |
5.410.240 |
2.200 |
| quartic |
4 |
434.171.760 |
25.080 |
| quintic |
5 |
27.960.661.344 |
201.432 |
| sextic |
6 |
1.505.215.602.352 |
1.748.824 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
165 |
153 |
| quadratic |
2 |
25.476 |
25.245 |
| cubic |
3 |
2.706.220 |
2.704.020 |
| quartic |
4 |
217.098.420 |
217.073.340 |
| quintic |
5 |
13.980.431.388 |
13.980.229.956 |
| sextic |
6 |
752.608.675.588 |
752.606.926.764 |
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