Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
27 |
3 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
21 |
3 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
15 |
12 |
27 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
12 |
9 |
21 |
Molecule Parameter
Number of Atoms (N) |
9 |
Number of internal coordinates |
21 |
Number of independant internal coordinates |
12 |
Number of vibrational modes |
21 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
12 |
9 |
21 / 0 |
Quadratic (Raman) |
12 |
9 |
21 / 0 |
IR + Raman |
12 |
9 |
21 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
21 |
3 |
quadratic |
2 |
231 |
15 |
cubic |
3 |
1.771 |
37 |
quartic |
4 |
10.626 |
114 |
quintic |
5 |
53.130 |
246 |
sextic |
6 |
230.230 |
598 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
12 |
9 |
quadratic |
2 |
123 |
108 |
cubic |
3 |
904 |
867 |
quartic |
4 |
5.370 |
5.256 |
quintic |
5 |
26.688 |
26.442 |
sextic |
6 |
115.414 |
114.816 |
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