Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
90 |
6 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
84 |
6 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
48 |
42 |
90 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
45 |
39 |
84 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
45 |
| Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
45 |
39 |
84 / 0 |
| Quadratic (Raman) |
45 |
39 |
84 / 0 |
| IR + Raman |
45 |
39 |
84 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
84 |
6 |
| quadratic |
2 |
3.570 |
60 |
| cubic |
3 |
102.340 |
290 |
| quartic |
4 |
2.225.895 |
1.725 |
| quintic |
5 |
39.175.752 |
7.116 |
| sextic |
6 |
581.106.988 |
32.416 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
45 |
39 |
| quadratic |
2 |
1.815 |
1.755 |
| cubic |
3 |
51.315 |
51.025 |
| quartic |
4 |
1.113.810 |
1.112.085 |
| quintic |
5 |
19.591.434 |
19.584.318 |
| sextic |
6 |
290.569.702 |
290.537.286 |
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