Reduction formula for point group C2h
Characters for molecular motions
Motion |
E |
C2 (z) |
i |
h |
Cartesian 3N |
156 |
-2 |
0 |
14 |
Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
Vibration |
150 |
0 |
0 |
14 |
Decomposition into Irreducible representations
Motion |
Ag |
Bg |
Au |
Bu |
Total |
Cartesian 3N |
42 |
36 |
35 |
43 |
156 |
Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
Vibration |
41 |
34 |
34 |
41 |
150 |
Molecule Parameter
Number of Atoms (N) |
52 |
Number of internal coordinates |
150 |
Number of independant internal coordinates |
41 |
Number of vibrational modes |
150 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Bg |
Au |
Bu |
Total |
Linear (IR) |
41 |
34 |
34 |
41 |
75 / 75 |
Quadratic (Raman) |
41 |
34 |
34 |
41 |
75 / 75 |
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 |
150 |
0 |
0 |
14 |
quadratic |
2 |
11.325 |
75 |
75 |
173 |
cubic |
3 |
573.800 |
0 |
0 |
1.512 |
quartic |
4 |
21.947.850 |
2.850 |
2.850 |
11.866 |
quintic |
5 |
675.993.780 |
0 |
0 |
79.492 |
sextic |
6 |
17.463.172.650 |
73.150 |
73.150 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Bg |
Au |
Bu |
linear |
1 |
41 |
34 |
34 |
41 |
quadratic |
2 |
2.912 |
2.788 |
2.788 |
2.837 |
cubic |
3 |
143.828 |
143.072 |
143.072 |
143.828 |
quartic |
4 |
5.491.354 |
5.483.996 |
5.483.996 |
5.488.504 |
quintic |
5 |
169.018.318 |
168.978.572 |
168.978.572 |
169.018.318 |
sextic |
6 |
4.365.952.248 |
4.365.670.652 |
4.365.670.652 |
4.365.879.098 |
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