Reduction formula for point group Ci
Characters for molecular motions
| Motion |
E |
i |
| Cartesian 3N |
12 |
0 |
| Translation (x,y,z) |
3 |
-3 |
| Rotation (Rx,Ry)* |
2 |
2 |
| Vibration |
7 |
1 |
* Linear molecule
Decomposition into Irreducible representations
| Motion |
Ag |
Au |
Total |
| Cartesian 3N |
6 |
6 |
12 |
| Translation (x,y,z) |
0 |
3 |
3 |
| Rotation (Rx,Ry)* |
2 |
0 |
2 |
| Vibration |
4 |
3 |
7 |
* Linear molecule
Molecule Parameter
| Number of Atoms (N) |
4 |
| Number of internal coordinates |
7 |
| Number of independant internal coordinates |
4 |
| Number of vibrational modes |
7 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Au |
Total |
| Linear (IR) |
4 |
3 |
3 / 4 |
| Quadratic (Raman) |
4 |
3 |
4 / 3 |
| 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 |
7 |
1 |
| quadratic |
2 |
28 |
4 |
| cubic |
3 |
84 |
4 |
| quartic |
4 |
210 |
10 |
| quintic |
5 |
462 |
10 |
| sextic |
6 |
924 |
20 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Au |
| linear |
1 |
4 |
3 |
| quadratic |
2 |
16 |
12 |
| cubic |
3 |
44 |
40 |
| quartic |
4 |
110 |
100 |
| quintic |
5 |
236 |
226 |
| sextic |
6 |
472 |
452 |
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