Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
99 |
9 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
93 |
9 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
54 |
45 |
99 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
51 |
42 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
51 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
51 |
42 |
93 / 0 |
| Quadratic (Raman) |
51 |
42 |
93 / 0 |
| IR + Raman |
51 |
42 |
93 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
93 |
9 |
| quadratic |
2 |
4.371 |
87 |
| cubic |
3 |
138.415 |
543 |
| quartic |
4 |
3.321.960 |
3.288 |
| quintic |
5 |
64.446.024 |
16.344 |
| sextic |
6 |
1.052.618.392 |
77.672 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
51 |
42 |
| quadratic |
2 |
2.229 |
2.142 |
| cubic |
3 |
69.479 |
68.936 |
| quartic |
4 |
1.662.624 |
1.659.336 |
| quintic |
5 |
32.231.184 |
32.214.840 |
| sextic |
6 |
526.348.032 |
526.270.360 |
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