Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
42 |
10 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
36 |
10 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
26 |
16 |
42 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
23 |
13 |
36 |
Molecule Parameter
Number of Atoms (N) |
14 |
Number of internal coordinates |
36 |
Number of independant internal coordinates |
23 |
Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
23 |
13 |
36 / 0 |
Quadratic (Raman) |
23 |
13 |
36 / 0 |
IR + Raman |
23 |
13 |
36 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
36 |
10 |
quadratic |
2 |
666 |
68 |
cubic |
3 |
8.436 |
350 |
quartic |
4 |
82.251 |
1.521 |
quintic |
5 |
658.008 |
5.772 |
sextic |
6 |
4.496.388 |
19.760 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
23 |
13 |
quadratic |
2 |
367 |
299 |
cubic |
3 |
4.393 |
4.043 |
quartic |
4 |
41.886 |
40.365 |
quintic |
5 |
331.890 |
326.118 |
sextic |
6 |
2.258.074 |
2.238.314 |
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