Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
66 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
60 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
14 |
8 |
22 |
44 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
13 |
7 |
20 |
40 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
13 |
| Number of vibrational modes |
40 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
13 |
7 |
20 |
33 / 7 |
| Quadratic (Raman) |
13 |
7 |
20 |
33 / 7 |
| IR + Raman |
13 |
7 |
20 |
33 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
60 |
0 |
6 |
| quadratic |
2 |
1.830 |
0 |
48 |
| cubic |
3 |
37.820 |
20 |
218 |
| quartic |
4 |
595.665 |
0 |
1.071 |
| quintic |
5 |
7.624.512 |
0 |
4.032 |
| sextic |
6 |
82.598.880 |
210 |
15.456 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
13 |
7 |
20 |
| quadratic |
2 |
329 |
281 |
610 |
| cubic |
3 |
6.419 |
6.201 |
12.600 |
| quartic |
4 |
99.813 |
98.742 |
198.555 |
| quintic |
5 |
1.272.768 |
1.268.736 |
2.541.504 |
| sextic |
6 |
13.774.278 |
13.758.822 |
27.532.890 |
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