Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
15 |
5 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry)* |
2 |
0 |
Vibration |
10 |
4 |
* Linear molecule
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
10 |
5 |
15 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry)* |
1 |
1 |
2 |
Vibration |
7 |
3 |
10 |
* Linear molecule
Molecule Parameter
Number of Atoms (N) |
5 |
Number of internal coordinates |
10 |
Number of independant internal coordinates |
7 |
Number of vibrational modes |
10 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
7 |
3 |
10 / 0 |
Quadratic (Raman) |
7 |
3 |
10 / 0 |
IR + Raman |
7 |
3 |
10 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
10 |
4 |
quadratic |
2 |
55 |
13 |
cubic |
3 |
220 |
32 |
quartic |
4 |
715 |
71 |
quintic |
5 |
2.002 |
140 |
sextic |
6 |
5.005 |
259 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
7 |
3 |
quadratic |
2 |
34 |
21 |
cubic |
3 |
126 |
94 |
quartic |
4 |
393 |
322 |
quintic |
5 |
1.071 |
931 |
sextic |
6 |
2.632 |
2.373 |
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