Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
90 |
30 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
84 |
30 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
60 |
30 |
90 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
57 |
27 |
84 |
Molecule Parameter
Number of Atoms (N) |
30 |
Number of internal coordinates |
84 |
Number of independant internal coordinates |
57 |
Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
57 |
27 |
84 / 0 |
Quadratic (Raman) |
57 |
27 |
84 / 0 |
IR + Raman |
57 |
27 |
84 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
84 |
30 |
quadratic |
2 |
3.570 |
492 |
cubic |
3 |
102.340 |
5.770 |
quartic |
4 |
2.225.895 |
53.853 |
quintic |
5 |
39.175.752 |
423.516 |
sextic |
6 |
581.106.988 |
2.907.424 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
57 |
27 |
quadratic |
2 |
2.031 |
1.539 |
cubic |
3 |
54.055 |
48.285 |
quartic |
4 |
1.139.874 |
1.086.021 |
quintic |
5 |
19.799.634 |
19.376.118 |
sextic |
6 |
292.007.206 |
289.099.782 |
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