Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
324 |
0 |
12 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
318 |
0 |
12 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
60 |
48 |
108 |
216 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
59 |
47 |
106 |
212 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
59 |
| Number of vibrational modes |
212 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
59 |
47 |
106 |
165 / 47 |
| Quadratic (Raman) |
59 |
47 |
106 |
165 / 47 |
| IR + Raman |
59 |
47 |
106 |
165 / 47 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
318 |
0 |
12 |
| quadratic |
2 |
50.721 |
0 |
231 |
| cubic |
3 |
5.410.240 |
106 |
2.200 |
| quartic |
4 |
434.171.760 |
0 |
25.080 |
| quintic |
5 |
27.960.661.344 |
0 |
201.432 |
| sextic |
6 |
1.505.215.602.352 |
5.671 |
1.748.824 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
59 |
47 |
106 |
| quadratic |
2 |
8.569 |
8.338 |
16.907 |
| cubic |
3 |
902.842 |
900.642 |
1.803.378 |
| quartic |
4 |
72.374.500 |
72.349.420 |
144.723.920 |
| quintic |
5 |
4.660.210.940 |
4.660.009.508 |
9.320.220.448 |
| sextic |
6 |
250.870.143.361 |
250.868.394.537 |
501.738.532.227 |
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