Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
120 |
0 |
0 |
12 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
114 |
2 |
0 |
12 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
33 |
27 |
27 |
33 |
120 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
32 |
25 |
26 |
31 |
114 |
Molecule Parameter
| Number of Atoms (N) |
40 |
| Number of internal coordinates |
114 |
| Number of independant internal coordinates |
32 |
| Number of vibrational modes |
114 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
32 |
25 |
26 |
31 |
57 / 57 |
| Quadratic (Raman) |
32 |
25 |
26 |
31 |
57 / 57 |
| 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 |
114 |
2 |
0 |
12 |
| quadratic |
2 |
6.555 |
59 |
57 |
129 |
| cubic |
3 |
253.460 |
116 |
0 |
976 |
| quartic |
4 |
7.413.705 |
1.769 |
1.653 |
6.669 |
| quintic |
5 |
174.963.438 |
3.422 |
0 |
38.844 |
| sextic |
6 |
3.470.108.187 |
35.931 |
32.509 |
208.845 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
32 |
25 |
26 |
31 |
| quadratic |
2 |
1.700 |
1.606 |
1.607 |
1.642 |
| cubic |
3 |
63.638 |
63.092 |
63.150 |
63.580 |
| quartic |
4 |
1.855.949 |
1.851.730 |
1.851.788 |
1.854.238 |
| quintic |
5 |
43.751.426 |
43.730.293 |
43.732.004 |
43.749.715 |
| sextic |
6 |
867.596.368 |
867.473.980 |
867.475.691 |
867.562.148 |
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