Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
216 |
72 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
210 |
72 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
144 |
72 |
216 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
141 |
69 |
210 |
Molecule Parameter
Number of Atoms (N) |
72 |
Number of internal coordinates |
210 |
Number of independant internal coordinates |
141 |
Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
141 |
69 |
210 / 0 |
Quadratic (Raman) |
141 |
69 |
210 / 0 |
IR + Raman |
141 |
69 |
210 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
210 |
72 |
quadratic |
2 |
22.155 |
2.697 |
cubic |
3 |
1.565.620 |
69.792 |
quartic |
4 |
83.369.265 |
1.399.197 |
quintic |
5 |
3.568.204.542 |
23.121.576 |
sextic |
6 |
127.860.662.755 |
327.363.605 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
141 |
69 |
quadratic |
2 |
12.426 |
9.729 |
cubic |
3 |
817.706 |
747.914 |
quartic |
4 |
42.384.231 |
40.985.034 |
quintic |
5 |
1.795.663.059 |
1.772.541.483 |
sextic |
6 |
64.094.013.180 |
63.766.649.575 |
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