Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
18 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry)* |
2 |
-1 |
0 |
| Vibration |
13 |
1 |
5 |
* Linear molecule
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
6 |
0 |
6 |
12 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry)* |
0 |
0 |
1 |
1 |
| Vibration |
5 |
0 |
4 |
9 |
* Linear molecule
Molecule Parameter
| Number of Atoms (N) |
6 |
| Number of internal coordinates |
13 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
9 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
5 |
0 |
4 |
9 / 0 |
| Quadratic (Raman) |
5 |
0 |
4 |
9 / 0 |
| IR + Raman |
5 |
0 |
4 |
9 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
13 |
1 |
5 |
| quadratic |
2 |
91 |
1 |
19 |
| cubic |
3 |
455 |
5 |
55 |
| quartic |
4 |
1.820 |
5 |
140 |
| quintic |
5 |
6.188 |
5 |
316 |
| sextic |
6 |
18.564 |
15 |
660 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
5 |
0 |
4 |
| quadratic |
2 |
25 |
6 |
30 |
| cubic |
3 |
105 |
50 |
150 |
| quartic |
4 |
375 |
235 |
605 |
| quintic |
5 |
1.191 |
875 |
2.061 |
| sextic |
6 |
3.429 |
2.769 |
6.183 |
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