Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
102 |
14 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
96 |
14 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
58 |
44 |
102 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
55 |
41 |
96 |
Molecule Parameter
Number of Atoms (N) |
34 |
Number of internal coordinates |
96 |
Number of independant internal coordinates |
55 |
Number of vibrational modes |
96 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
55 |
41 |
96 / 0 |
Quadratic (Raman) |
55 |
41 |
96 / 0 |
IR + Raman |
55 |
41 |
96 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
96 |
14 |
quadratic |
2 |
4.656 |
146 |
cubic |
3 |
152.096 |
1.134 |
quartic |
4 |
3.764.376 |
7.546 |
quintic |
5 |
75.287.520 |
43.582 |
sextic |
6 |
1.267.339.920 |
227.458 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
55 |
41 |
quadratic |
2 |
2.401 |
2.255 |
cubic |
3 |
76.615 |
75.481 |
quartic |
4 |
1.885.961 |
1.878.415 |
quintic |
5 |
37.665.551 |
37.621.969 |
sextic |
6 |
633.783.689 |
633.556.231 |
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