Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
87 |
9 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
81 |
9 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
48 |
39 |
87 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
45 |
36 |
81 |
Molecule Parameter
Number of Atoms (N) |
29 |
Number of internal coordinates |
81 |
Number of independant internal coordinates |
45 |
Number of vibrational modes |
81 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
45 |
36 |
81 / 0 |
Quadratic (Raman) |
45 |
36 |
81 / 0 |
IR + Raman |
45 |
36 |
81 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
81 |
9 |
quadratic |
2 |
3.321 |
81 |
cubic |
3 |
91.881 |
489 |
quartic |
4 |
1.929.501 |
2.781 |
quintic |
5 |
32.801.517 |
13.221 |
sextic |
6 |
470.155.077 |
59.229 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
45 |
36 |
quadratic |
2 |
1.701 |
1.620 |
cubic |
3 |
46.185 |
45.696 |
quartic |
4 |
966.141 |
963.360 |
quintic |
5 |
16.407.369 |
16.394.148 |
sextic |
6 |
235.107.153 |
235.047.924 |
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