Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
99 |
5 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
93 |
5 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
52 |
47 |
99 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
49 |
44 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
49 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
49 |
44 |
93 / 0 |
| Quadratic (Raman) |
49 |
44 |
93 / 0 |
| IR + Raman |
49 |
44 |
93 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
93 |
5 |
| quadratic |
2 |
4.371 |
59 |
| cubic |
3 |
138.415 |
255 |
| quartic |
4 |
3.321.960 |
1.720 |
| quintic |
5 |
64.446.024 |
6.616 |
| sextic |
6 |
1.052.618.392 |
33.320 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
49 |
44 |
| quadratic |
2 |
2.215 |
2.156 |
| cubic |
3 |
69.335 |
69.080 |
| quartic |
4 |
1.661.840 |
1.660.120 |
| quintic |
5 |
32.226.320 |
32.219.704 |
| sextic |
6 |
526.325.856 |
526.292.536 |
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