Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
72 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
66 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
16 |
8 |
24 |
48 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
15 |
7 |
22 |
44 |
Molecule Parameter
| Number of Atoms (N) |
24 |
| Number of internal coordinates |
66 |
| Number of independant internal coordinates |
15 |
| Number of vibrational modes |
44 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
15 |
7 |
22 |
37 / 7 |
| Quadratic (Raman) |
15 |
7 |
22 |
37 / 7 |
| IR + Raman |
15 |
7 |
22 |
37 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
66 |
0 |
8 |
| quadratic |
2 |
2.211 |
0 |
65 |
| cubic |
3 |
50.116 |
22 |
352 |
| quartic |
4 |
864.501 |
0 |
1.809 |
| quintic |
5 |
12.103.014 |
0 |
7.752 |
| sextic |
6 |
143.218.999 |
253 |
31.441 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
15 |
7 |
22 |
| quadratic |
2 |
401 |
336 |
737 |
| cubic |
3 |
8.536 |
8.184 |
16.698 |
| quartic |
4 |
144.988 |
143.179 |
288.167 |
| quintic |
5 |
2.021.045 |
2.013.293 |
4.034.338 |
| sextic |
6 |
23.885.638 |
23.854.197 |
47.739.582 |
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