Reduction formula for point group C2h
Characters for molecular motions
Motion |
E |
C2 (z) |
i |
h |
Cartesian 3N |
48 |
0 |
0 |
16 |
Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
Vibration |
42 |
2 |
0 |
16 |
Decomposition into Irreducible representations
Motion |
Ag |
Bg |
Au |
Bu |
Total |
Cartesian 3N |
16 |
8 |
8 |
16 |
48 |
Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
Vibration |
15 |
6 |
7 |
14 |
42 |
Molecule Parameter
Number of Atoms (N) |
16 |
Number of internal coordinates |
42 |
Number of independant internal coordinates |
15 |
Number of vibrational modes |
42 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Bg |
Au |
Bu |
Total |
Linear (IR) |
15 |
6 |
7 |
14 |
21 / 21 |
Quadratic (Raman) |
15 |
6 |
7 |
14 |
21 / 21 |
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 |
42 |
2 |
0 |
16 |
quadratic |
2 |
903 |
23 |
21 |
149 |
cubic |
3 |
13.244 |
44 |
0 |
1.024 |
quartic |
4 |
148.995 |
275 |
231 |
5.735 |
quintic |
5 |
1.370.754 |
506 |
0 |
27.568 |
sextic |
6 |
10.737.573 |
2.277 |
1.771 |
117.483 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Bg |
Au |
Bu |
linear |
1 |
15 |
6 |
7 |
14 |
quadratic |
2 |
274 |
188 |
189 |
252 |
cubic |
3 |
3.578 |
3.044 |
3.066 |
3.556 |
quartic |
4 |
38.809 |
35.804 |
35.826 |
38.556 |
quintic |
5 |
349.707 |
335.670 |
335.923 |
349.454 |
sextic |
6 |
2.714.776 |
2.654.896 |
2.655.149 |
2.712.752 |
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