Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
63 |
-1 |
-3 |
5 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
57 |
1 |
-3 |
5 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
16 |
14 |
15 |
18 |
63 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
15 |
12 |
14 |
16 |
57 |
Molecule Parameter
| Number of Atoms (N) |
21 |
| Number of internal coordinates |
57 |
| Number of independant internal coordinates |
15 |
| Number of vibrational modes |
57 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
15 |
12 |
14 |
16 |
30 / 27 |
| Quadratic (Raman) |
15 |
12 |
14 |
16 |
27 / 30 |
| IR + Raman |
- |
- |
- |
- |
0* / 0 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
i |
h |
| linear |
1 |
57 |
1 |
-3 |
5 |
| quadratic |
2 |
1.653 |
29 |
33 |
41 |
| cubic |
3 |
32.509 |
29 |
-91 |
165 |
| quartic |
4 |
487.635 |
435 |
555 |
811 |
| quintic |
5 |
5.949.147 |
435 |
-1.425 |
2.791 |
| sextic |
6 |
61.474.519 |
4.495 |
6.355 |
10.571 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
15 |
12 |
14 |
16 |
| quadratic |
2 |
439 |
404 |
402 |
408 |
| cubic |
3 |
8.153 |
8.056 |
8.116 |
8.184 |
| quartic |
4 |
122.359 |
121.736 |
121.676 |
121.864 |
| quintic |
5 |
1.487.737 |
1.486.124 |
1.487.054 |
1.488.232 |
| sextic |
6 |
15.373.985 |
15.366.452 |
15.365.522 |
15.368.560 |
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