Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
48 |
8 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
42 |
8 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
28 |
20 |
48 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
25 |
17 |
42 |
Molecule Parameter
Number of Atoms (N) |
16 |
Number of internal coordinates |
42 |
Number of independant internal coordinates |
25 |
Number of vibrational modes |
42 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
25 |
17 |
42 / 0 |
Quadratic (Raman) |
25 |
17 |
42 / 0 |
IR + Raman |
25 |
17 |
42 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
42 |
8 |
quadratic |
2 |
903 |
53 |
cubic |
3 |
13.244 |
256 |
quartic |
4 |
148.995 |
1.095 |
quintic |
5 |
1.370.754 |
4.056 |
sextic |
6 |
10.737.573 |
13.803 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
25 |
17 |
quadratic |
2 |
478 |
425 |
cubic |
3 |
6.750 |
6.494 |
quartic |
4 |
75.045 |
73.950 |
quintic |
5 |
687.405 |
683.349 |
sextic |
6 |
5.375.688 |
5.361.885 |
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