Reduction formula for point group Cs
Characters for molecular motions
| Motion |
E |
 h |
| Cartesian 3N |
93 |
9 |
| Translation (x,y,z) |
3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
87 |
9 |
Decomposition into Irreducible representations
| Motion |
A' |
A'' |
Total |
| Cartesian 3N |
51 |
42 |
93 |
| Translation (x,y,z) |
2 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
48 |
39 |
87 |
Molecule Parameter
| Number of Atoms (N) |
31 |
| Number of internal coordinates |
87 |
| Number of independant internal coordinates |
48 |
| Number of vibrational modes |
87 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A' |
A'' |
Total |
| Linear (IR) |
48 |
39 |
87 / 0 |
| Quadratic (Raman) |
48 |
39 |
87 / 0 |
| IR + Raman |
48 |
39 |
87 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
h |
| linear |
1 |
87 |
9 |
| quadratic |
2 |
3.828 |
84 |
| cubic |
3 |
113.564 |
516 |
| quartic |
4 |
2.555.190 |
3.030 |
| quintic |
5 |
46.504.458 |
14.742 |
| sextic |
6 |
713.068.356 |
68.068 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A' |
A'' |
| linear |
1 |
48 |
39 |
| quadratic |
2 |
1.956 |
1.872 |
| cubic |
3 |
57.040 |
56.524 |
| quartic |
4 |
1.279.110 |
1.276.080 |
| quintic |
5 |
23.259.600 |
23.244.858 |
| sextic |
6 |
356.568.212 |
356.500.144 |
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