Reduction formula for point group Ci
Characters for molecular motions
Motion |
E |
i |
Cartesian 3N |
144 |
0 |
Translation (x,y,z) |
3 |
-3 |
Rotation (Rx,Ry,Rz) |
3 |
3 |
Vibration |
138 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
Au |
Total |
Cartesian 3N |
72 |
72 |
144 |
Translation (x,y,z) |
0 |
3 |
3 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
3 |
Vibration |
69 |
69 |
138 |
Molecule Parameter
Number of Atoms (N) |
48 |
Number of internal coordinates |
138 |
Number of independant internal coordinates |
69 |
Number of vibrational modes |
138 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Au |
Total |
Linear (IR) |
69 |
69 |
69 / 69 |
Quadratic (Raman) |
69 |
69 |
69 / 69 |
IR + Raman |
- |
- |
0* / 0 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
i |
linear |
1 |
138 |
0 |
quadratic |
2 |
9.591 |
69 |
cubic |
3 |
447.580 |
0 |
quartic |
4 |
15.777.195 |
2.415 |
quintic |
5 |
448.072.338 |
0 |
sextic |
6 |
10.679.057.389 |
57.155 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Au |
linear |
1 |
69 |
69 |
quadratic |
2 |
4.830 |
4.761 |
cubic |
3 |
223.790 |
223.790 |
quartic |
4 |
7.889.805 |
7.887.390 |
quintic |
5 |
224.036.169 |
224.036.169 |
sextic |
6 |
5.339.557.272 |
5.339.500.117 |
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