Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
75 |
-1 |
-3 |
9 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
69 |
1 |
-3 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
20 |
16 |
17 |
22 |
75 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
19 |
14 |
16 |
20 |
69 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
69 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
19 |
14 |
16 |
20 |
36 / 33 |
| Quadratic (Raman) |
19 |
14 |
16 |
20 |
33 / 36 |
| 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 |
69 |
1 |
-3 |
9 |
| quadratic |
2 |
2.415 |
35 |
39 |
75 |
| cubic |
3 |
57.155 |
35 |
-109 |
435 |
| quartic |
4 |
1.028.790 |
630 |
774 |
2.310 |
| quintic |
5 |
15.020.334 |
630 |
-2.034 |
10.422 |
| sextic |
6 |
185.250.786 |
7.770 |
10.434 |
43.738 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
19 |
14 |
16 |
20 |
| quadratic |
2 |
641 |
586 |
584 |
604 |
| cubic |
3 |
14.379 |
14.144 |
14.216 |
14.416 |
| quartic |
4 |
258.126 |
256.656 |
256.584 |
257.424 |
| quintic |
5 |
3.757.338 |
3.751.812 |
3.753.144 |
3.758.040 |
| sextic |
6 |
46.328.182 |
46.302.428 |
46.301.096 |
46.319.080 |
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