Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
60 |
6 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
54 |
6 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
33 |
27 |
60 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
30 |
24 |
54 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
30 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
30 |
24 |
54 / 0 |
| Quadratic (Raman) |
30 |
24 |
54 / 0 |
| IR + Raman |
30 |
24 |
54 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
54 |
6 |
| quadratic |
2 |
1.485 |
45 |
| cubic |
3 |
27.720 |
200 |
| quartic |
4 |
395.010 |
930 |
| quintic |
5 |
4.582.116 |
3.396 |
| sextic |
6 |
45.057.474 |
12.386 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
30 |
24 |
| quadratic |
2 |
765 |
720 |
| cubic |
3 |
13.960 |
13.760 |
| quartic |
4 |
197.970 |
197.040 |
| quintic |
5 |
2.292.756 |
2.289.360 |
| sextic |
6 |
22.534.930 |
22.522.544 |
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