Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
78 |
8 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
72 |
8 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
43 |
35 |
78 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
40 |
32 |
72 |
Molecule Parameter
| Number of Atoms (N) |
26 |
| Number of internal coordinates |
72 |
| Number of independant internal coordinates |
40 |
| Number of vibrational modes |
72 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
40 |
32 |
72 / 0 |
| Quadratic (Raman) |
40 |
32 |
72 / 0 |
| IR + Raman |
40 |
32 |
72 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
72 |
8 |
| quadratic |
2 |
2.628 |
68 |
| cubic |
3 |
64.824 |
376 |
| quartic |
4 |
1.215.450 |
2.010 |
| quintic |
5 |
18.474.840 |
8.856 |
| sextic |
6 |
237.093.780 |
37.268 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
40 |
32 |
| quadratic |
2 |
1.348 |
1.280 |
| cubic |
3 |
32.600 |
32.224 |
| quartic |
4 |
608.730 |
606.720 |
| quintic |
5 |
9.241.848 |
9.232.992 |
| sextic |
6 |
118.565.524 |
118.528.256 |
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