Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
156 |
14 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
150 |
14 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
85 |
71 |
156 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
82 |
68 |
150 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
82 |
| Number of vibrational modes |
150 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
82 |
68 |
150 / 0 |
| Quadratic (Raman) |
82 |
68 |
150 / 0 |
| IR + Raman |
82 |
68 |
150 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
150 |
14 |
| quadratic |
2 |
11.325 |
173 |
| cubic |
3 |
573.800 |
1.512 |
| quartic |
4 |
21.947.850 |
11.866 |
| quintic |
5 |
675.993.780 |
79.492 |
| sextic |
6 |
17.463.172.650 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
82 |
68 |
| quadratic |
2 |
5.749 |
5.576 |
| cubic |
3 |
287.656 |
286.144 |
| quartic |
4 |
10.979.858 |
10.967.992 |
| quintic |
5 |
338.036.636 |
337.957.144 |
| sextic |
6 |
8.731.831.346 |
8.731.341.304 |
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