Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
144 |
8 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
138 |
8 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
76 |
68 |
144 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
73 |
65 |
138 |
Molecule Parameter
| Number of Atoms (N) |
48 |
| Number of internal coordinates |
138 |
| Number of independant internal coordinates |
73 |
| Number of vibrational modes |
138 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
73 |
65 |
138 / 0 |
| Quadratic (Raman) |
73 |
65 |
138 / 0 |
| IR + Raman |
73 |
65 |
138 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
138 |
8 |
| quadratic |
2 |
9.591 |
101 |
| cubic |
3 |
447.580 |
640 |
| quartic |
4 |
15.777.195 |
4.815 |
| quintic |
5 |
448.072.338 |
25.752 |
| sextic |
6 |
10.679.057.389 |
148.291 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
73 |
65 |
| quadratic |
2 |
4.846 |
4.745 |
| cubic |
3 |
224.110 |
223.470 |
| quartic |
4 |
7.891.005 |
7.886.190 |
| quintic |
5 |
224.049.045 |
224.023.293 |
| sextic |
6 |
5.339.602.840 |
5.339.454.549 |
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