Reduction formula for point group C2
Characters for molecular motions
| Motion |
E |
C2 |
| Cartesian 3N |
66 |
-6 |
| Translation (x,y,z) |
3 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
60 |
-4 |
Decomposition into Irreducible representations
| Motion |
A |
B |
Total |
| Cartesian 3N |
30 |
36 |
66 |
| Translation (x,y,z) |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
28 |
32 |
60 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
28 |
| Number of vibrational modes |
60 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
Total |
| Linear (IR) |
28 |
32 |
60 / 0 |
| Quadratic (Raman) |
28 |
32 |
60 / 0 |
| IR + Raman |
28 |
32 |
60 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 |
| linear |
1 |
60 |
-4 |
| quadratic |
2 |
1.830 |
38 |
| cubic |
3 |
37.820 |
-132 |
| quartic |
4 |
595.665 |
721 |
| quintic |
5 |
7.624.512 |
-2.240 |
| sextic |
6 |
82.598.880 |
9.184 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
| linear |
1 |
28 |
32 |
| quadratic |
2 |
934 |
896 |
| cubic |
3 |
18.844 |
18.976 |
| quartic |
4 |
298.193 |
297.472 |
| quintic |
5 |
3.811.136 |
3.813.376 |
| sextic |
6 |
41.304.032 |
41.294.848 |
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