Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
210 |
10 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
204 |
10 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
110 |
100 |
210 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
107 |
97 |
204 |
Molecule Parameter
| Number of Atoms (N) |
70 |
| Number of internal coordinates |
204 |
| Number of independant internal coordinates |
107 |
| Number of vibrational modes |
204 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
107 |
97 |
204 / 0 |
| Quadratic (Raman) |
107 |
97 |
204 / 0 |
| IR + Raman |
107 |
97 |
204 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
204 |
10 |
| quadratic |
2 |
20.910 |
152 |
| cubic |
3 |
1.435.820 |
1.190 |
| quartic |
4 |
74.303.685 |
10.803 |
| quintic |
5 |
3.091.033.296 |
70.872 |
| sextic |
6 |
107.670.993.144 |
492.624 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
107 |
97 |
| quadratic |
2 |
10.531 |
10.379 |
| cubic |
3 |
718.505 |
717.315 |
| quartic |
4 |
37.157.244 |
37.146.441 |
| quintic |
5 |
1.545.552.084 |
1.545.481.212 |
| sextic |
6 |
53.835.742.884 |
53.835.250.260 |
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