Reduction formula for point group C2h
Characters for molecular motions
Motion |
E |
C2 (z) |
i |
h |
Cartesian 3N |
60 |
0 |
0 |
8 |
Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
Vibration |
54 |
2 |
0 |
8 |
Decomposition into Irreducible representations
Motion |
Ag |
Bg |
Au |
Bu |
Total |
Cartesian 3N |
17 |
13 |
13 |
17 |
60 |
Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
Vibration |
16 |
11 |
12 |
15 |
54 |
Molecule Parameter
Number of Atoms (N) |
20 |
Number of internal coordinates |
54 |
Number of independant internal coordinates |
16 |
Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Bg |
Au |
Bu |
Total |
Linear (IR) |
16 |
11 |
12 |
15 |
27 / 27 |
Quadratic (Raman) |
16 |
11 |
12 |
15 |
27 / 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 |
54 |
2 |
0 |
8 |
quadratic |
2 |
1.485 |
29 |
27 |
59 |
cubic |
3 |
27.720 |
56 |
0 |
304 |
quartic |
4 |
395.010 |
434 |
378 |
1.434 |
quintic |
5 |
4.582.116 |
812 |
0 |
5.760 |
sextic |
6 |
45.057.474 |
4.466 |
3.654 |
21.542 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Bg |
Au |
Bu |
linear |
1 |
16 |
11 |
12 |
15 |
quadratic |
2 |
400 |
356 |
357 |
372 |
cubic |
3 |
7.020 |
6.840 |
6.868 |
6.992 |
quartic |
4 |
99.314 |
98.380 |
98.408 |
98.908 |
quintic |
5 |
1.147.172 |
1.143.886 |
1.144.292 |
1.146.766 |
sextic |
6 |
11.271.784 |
11.258.780 |
11.259.186 |
11.267.724 |
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