Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
75 |
5 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
69 |
5 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
40 |
35 |
75 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
37 |
32 |
69 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
37 |
| Number of vibrational modes |
69 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
37 |
32 |
69 / 0 |
| Quadratic (Raman) |
37 |
32 |
69 / 0 |
| IR + Raman |
37 |
32 |
69 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
69 |
5 |
| quadratic |
2 |
2.415 |
47 |
| cubic |
3 |
57.155 |
195 |
| quartic |
4 |
1.028.790 |
1.078 |
| quintic |
5 |
15.020.334 |
3.886 |
| sextic |
6 |
185.250.786 |
16.354 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
37 |
32 |
| quadratic |
2 |
1.231 |
1.184 |
| cubic |
3 |
28.675 |
28.480 |
| quartic |
4 |
514.934 |
513.856 |
| quintic |
5 |
7.512.110 |
7.508.224 |
| sextic |
6 |
92.633.570 |
92.617.216 |
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