Reduction formula for point group C2h
Characters for molecular motions
| Motion |
E |
C2 (z) |
i |
 h |
| Cartesian 3N |
99 |
-1 |
-3 |
1 |
| Translation (x,y,z) |
3 |
-1 |
-3 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
3 |
-1 |
| Vibration |
93 |
1 |
-3 |
1 |
Decomposition into Irreducible representations
| Motion |
Ag |
Bg |
Au |
Bu |
Total |
| Cartesian 3N |
24 |
24 |
25 |
26 |
99 |
| Translation (x,y,z) |
0 |
0 |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
0 |
0 |
3 |
| Vibration |
23 |
22 |
24 |
24 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Bg |
Au |
Bu |
Total |
| Linear (IR) |
23 |
22 |
24 |
24 |
48 / 45 |
| Quadratic (Raman) |
23 |
22 |
24 |
24 |
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 |
1 |
| quadratic |
2 |
4.371 |
47 |
51 |
47 |
| cubic |
3 |
138.415 |
47 |
-145 |
47 |
| quartic |
4 |
3.321.960 |
1.128 |
1.320 |
1.128 |
| quintic |
5 |
64.446.024 |
1.128 |
-3.576 |
1.128 |
| sextic |
6 |
1.052.618.392 |
18.424 |
23.128 |
18.424 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Bg |
Au |
Bu |
| linear |
1 |
23 |
22 |
24 |
24 |
| quadratic |
2 |
1.129 |
1.082 |
1.080 |
1.080 |
| cubic |
3 |
34.591 |
34.544 |
34.640 |
34.640 |
| quartic |
4 |
831.384 |
830.256 |
830.160 |
830.160 |
| quintic |
5 |
16.111.176 |
16.110.048 |
16.112.400 |
16.112.400 |
| sextic |
6 |
263.169.592 |
263.151.168 |
263.148.816 |
263.148.816 |
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