Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
75 |
9 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
69 |
9 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
42 |
33 |
75 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
39 |
30 |
69 |
Molecule Parameter
Number of Atoms (N) |
25 |
Number of internal coordinates |
69 |
Number of independant internal coordinates |
39 |
Number of vibrational modes |
69 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
39 |
30 |
69 / 0 |
Quadratic (Raman) |
39 |
30 |
69 / 0 |
IR + Raman |
39 |
30 |
69 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
69 |
9 |
quadratic |
2 |
2.415 |
75 |
cubic |
3 |
57.155 |
435 |
quartic |
4 |
1.028.790 |
2.310 |
quintic |
5 |
15.020.334 |
10.422 |
sextic |
6 |
185.250.786 |
43.738 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
39 |
30 |
quadratic |
2 |
1.245 |
1.170 |
cubic |
3 |
28.795 |
28.360 |
quartic |
4 |
515.550 |
513.240 |
quintic |
5 |
7.515.378 |
7.504.956 |
sextic |
6 |
92.647.262 |
92.603.524 |
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