Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
120 |
8 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
114 |
8 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
64 |
56 |
120 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
61 |
53 |
114 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
61 |
| Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
61 |
53 |
114 / 0 |
| Quadratic (Raman) |
61 |
53 |
114 / 0 |
| IR + Raman |
61 |
53 |
114 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
114 |
8 |
| quadratic |
2 |
6.555 |
89 |
| cubic |
3 |
253.460 |
544 |
| quartic |
4 |
7.413.705 |
3.669 |
| quintic |
5 |
174.963.438 |
18.600 |
| sextic |
6 |
3.470.108.187 |
96.957 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
61 |
53 |
| quadratic |
2 |
3.322 |
3.233 |
| cubic |
3 |
127.002 |
126.458 |
| quartic |
4 |
3.708.687 |
3.705.018 |
| quintic |
5 |
87.491.019 |
87.472.419 |
| sextic |
6 |
1.735.102.572 |
1.735.005.615 |
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