Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
42 |
0 |
0 |
6 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
36 |
2 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
12 |
9 |
9 |
12 |
42 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
11 |
7 |
8 |
10 |
36 |
Molecule Parameter
| Number of Atoms (N) |
14 |
| Number of internal coordinates |
36 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
11 |
7 |
8 |
10 |
18 / 18 |
| Quadratic (Raman) |
11 |
7 |
8 |
10 |
18 / 18 |
| 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 |
36 |
2 |
0 |
6 |
| quadratic |
2 |
666 |
20 |
18 |
36 |
| cubic |
3 |
8.436 |
38 |
0 |
146 |
| quartic |
4 |
82.251 |
209 |
171 |
561 |
| quintic |
5 |
658.008 |
380 |
0 |
1.812 |
| sextic |
6 |
4.496.388 |
1.520 |
1.140 |
5.552 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
11 |
7 |
8 |
10 |
| quadratic |
2 |
185 |
157 |
158 |
166 |
| cubic |
3 |
2.155 |
2.063 |
2.082 |
2.136 |
| quartic |
4 |
20.798 |
20.413 |
20.432 |
20.608 |
| quintic |
5 |
165.050 |
163.954 |
164.144 |
164.860 |
| sextic |
6 |
1.126.150 |
1.122.614 |
1.122.804 |
1.124.820 |
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