Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
324 |
0 |
0 |
24 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
318 |
2 |
0 |
24 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
87 |
75 |
75 |
87 |
324 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
86 |
73 |
74 |
85 |
318 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
86 |
| Number of vibrational modes |
318 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
86 |
73 |
74 |
85 |
159 / 159 |
| Quadratic (Raman) |
86 |
73 |
74 |
85 |
159 / 159 |
| 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 |
318 |
2 |
0 |
24 |
| quadratic |
2 |
50.721 |
161 |
159 |
447 |
| cubic |
3 |
5.410.240 |
320 |
0 |
6.128 |
| quartic |
4 |
434.171.760 |
13.040 |
12.720 |
72.528 |
| quintic |
5 |
27.960.661.344 |
25.760 |
0 |
741.552 |
| sextic |
6 |
1.505.215.602.352 |
708.400 |
682.640 |
6.858.544 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
86 |
73 |
74 |
85 |
| quadratic |
2 |
12.872 |
12.568 |
12.569 |
12.712 |
| cubic |
3 |
1.354.172 |
1.350.948 |
1.351.108 |
1.354.012 |
| quartic |
4 |
108.567.512 |
108.524.728 |
108.524.888 |
108.554.632 |
| quintic |
5 |
6.990.357.164 |
6.989.973.508 |
6.989.986.388 |
6.990.344.284 |
| sextic |
6 |
376.305.962.984 |
376.302.179.512 |
376.302.192.392 |
376.305.267.464 |
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