Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
252 |
4 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
246 |
4 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
128 |
124 |
252 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
125 |
121 |
246 |
Molecule Parameter
| Number of Atoms (N) |
84 |
| Number of internal coordinates |
246 |
| Number of independant internal coordinates |
125 |
| Number of vibrational modes |
246 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
125 |
121 |
246 / 0 |
| Quadratic (Raman) |
125 |
121 |
246 / 0 |
| IR + Raman |
125 |
121 |
246 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
246 |
4 |
| quadratic |
2 |
30.381 |
131 |
| cubic |
3 |
2.511.496 |
504 |
| quartic |
4 |
156.340.626 |
8.626 |
| quintic |
5 |
7.817.031.300 |
32.000 |
| sextic |
6 |
327.012.476.050 |
380.750 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
125 |
121 |
| quadratic |
2 |
15.256 |
15.125 |
| cubic |
3 |
1.256.000 |
1.255.496 |
| quartic |
4 |
78.174.626 |
78.166.000 |
| quintic |
5 |
3.908.531.650 |
3.908.499.650 |
| sextic |
6 |
163.506.428.400 |
163.506.047.650 |
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