Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
90 |
0 |
0 |
6 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
84 |
2 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
24 |
21 |
21 |
24 |
90 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
23 |
19 |
20 |
22 |
84 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
23 |
19 |
20 |
22 |
42 / 42 |
| Quadratic (Raman) |
23 |
19 |
20 |
22 |
42 / 42 |
| 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 |
84 |
2 |
0 |
6 |
| quadratic |
2 |
3.570 |
44 |
42 |
60 |
| cubic |
3 |
102.340 |
86 |
0 |
290 |
| quartic |
4 |
2.225.895 |
989 |
903 |
1.725 |
| quintic |
5 |
39.175.752 |
1.892 |
0 |
7.116 |
| sextic |
6 |
581.106.988 |
15.136 |
13.244 |
32.416 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
23 |
19 |
20 |
22 |
| quadratic |
2 |
929 |
877 |
878 |
886 |
| cubic |
3 |
25.679 |
25.491 |
25.534 |
25.636 |
| quartic |
4 |
557.378 |
556.021 |
556.064 |
556.432 |
| quintic |
5 |
9.796.190 |
9.791.686 |
9.792.632 |
9.795.244 |
| sextic |
6 |
145.291.946 |
145.268.170 |
145.269.116 |
145.277.756 |
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