Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
57 |
-3 |
-3 |
9 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
51 |
-1 |
-3 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
15 |
12 |
12 |
18 |
57 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
14 |
10 |
11 |
16 |
51 |
Molecule Parameter
| Number of Atoms (N) |
19 |
| Number of internal coordinates |
51 |
| Number of independant internal coordinates |
14 |
| Number of vibrational modes |
51 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
14 |
10 |
11 |
16 |
27 / 24 |
| Quadratic (Raman) |
14 |
10 |
11 |
16 |
24 / 27 |
| 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 |
51 |
-1 |
-3 |
9 |
| quadratic |
2 |
1.326 |
26 |
30 |
66 |
| cubic |
3 |
23.426 |
-26 |
-82 |
354 |
| quartic |
4 |
316.251 |
351 |
459 |
1.671 |
| quintic |
5 |
3.478.761 |
-351 |
-1.161 |
6.831 |
| sextic |
6 |
32.468.436 |
3.276 |
4.788 |
25.564 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
14 |
10 |
11 |
16 |
| quadratic |
2 |
362 |
316 |
314 |
334 |
| cubic |
3 |
5.918 |
5.754 |
5.782 |
5.972 |
| quartic |
4 |
79.683 |
78.672 |
78.618 |
79.278 |
| quintic |
5 |
871.020 |
867.780 |
868.185 |
871.776 |
| sextic |
6 |
8.125.516 |
8.111.096 |
8.110.340 |
8.121.484 |
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