Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
99 |
-1 |
-3 |
9 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
93 |
1 |
-3 |
9 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
26 |
22 |
23 |
28 |
99 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
25 |
20 |
22 |
26 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
25 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
25 |
20 |
22 |
26 |
48 / 45 |
| Quadratic (Raman) |
25 |
20 |
22 |
26 |
45 / 48 |
| 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 |
93 |
1 |
-3 |
9 |
| quadratic |
2 |
4.371 |
47 |
51 |
87 |
| cubic |
3 |
138.415 |
47 |
-145 |
543 |
| quartic |
4 |
3.321.960 |
1.128 |
1.320 |
3.288 |
| quintic |
5 |
64.446.024 |
1.128 |
-3.576 |
16.344 |
| sextic |
6 |
1.052.618.392 |
18.424 |
23.128 |
77.672 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
25 |
20 |
22 |
26 |
| quadratic |
2 |
1.139 |
1.072 |
1.070 |
1.090 |
| cubic |
3 |
34.715 |
34.420 |
34.516 |
34.764 |
| quartic |
4 |
831.924 |
829.716 |
829.620 |
830.700 |
| quintic |
5 |
16.114.980 |
16.106.244 |
16.108.596 |
16.116.204 |
| sextic |
6 |
263.184.404 |
263.136.356 |
263.134.004 |
263.163.628 |
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