Reduction formula for point group Cs
Characters for molecular motions
Motion |
E |
h |
Cartesian 3N |
78 |
26 |
Translation (x,y,z) |
3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
Vibration |
72 |
26 |
Decomposition into Irreducible representations
Motion |
A' |
A'' |
Total |
Cartesian 3N |
52 |
26 |
78 |
Translation (x,y,z) |
2 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
Vibration |
49 |
23 |
72 |
Molecule Parameter
Number of Atoms (N) |
26 |
Number of internal coordinates |
72 |
Number of independant internal coordinates |
49 |
Number of vibrational modes |
72 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A' |
A'' |
Total |
Linear (IR) |
49 |
23 |
72 / 0 |
Quadratic (Raman) |
49 |
23 |
72 / 0 |
IR + Raman |
49 |
23 |
72 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
h |
linear |
1 |
72 |
26 |
quadratic |
2 |
2.628 |
374 |
cubic |
3 |
64.824 |
3.874 |
quartic |
4 |
1.215.450 |
32.100 |
quintic |
5 |
18.474.840 |
225.030 |
sextic |
6 |
237.093.780 |
1.381.730 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A' |
A'' |
linear |
1 |
49 |
23 |
quadratic |
2 |
1.501 |
1.127 |
cubic |
3 |
34.349 |
30.475 |
quartic |
4 |
623.775 |
591.675 |
quintic |
5 |
9.349.935 |
9.124.905 |
sextic |
6 |
119.237.755 |
117.856.025 |
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