Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
54 |
2 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
48 |
2 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
28 |
26 |
54 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
25 |
23 |
48 |
Molecule Parameter
Number of Atoms (N) |
18 |
Number of internal coordinates |
48 |
Number of independant internal coordinates |
25 |
Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
25 |
23 |
48 / 0 |
Quadratic (Raman) |
25 |
23 |
48 / 0 |
IR + Raman |
25 |
23 |
48 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
48 |
2 |
quadratic |
2 |
1.176 |
26 |
cubic |
3 |
19.600 |
50 |
quartic |
4 |
249.900 |
350 |
quintic |
5 |
2.598.960 |
650 |
sextic |
6 |
22.957.480 |
3.250 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
25 |
23 |
quadratic |
2 |
601 |
575 |
cubic |
3 |
9.825 |
9.775 |
quartic |
4 |
125.125 |
124.775 |
quintic |
5 |
1.299.805 |
1.299.155 |
sextic |
6 |
11.480.365 |
11.477.115 |
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