Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
63 |
0 |
5 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
57 |
0 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
13 |
8 |
21 |
42 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
12 |
7 |
19 |
38 |
Molecule Parameter
| Number of Atoms (N) |
21 |
| Number of internal coordinates |
57 |
| Number of independant internal coordinates |
12 |
| Number of vibrational modes |
38 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
12 |
7 |
19 |
31 / 7 |
| Quadratic (Raman) |
12 |
7 |
19 |
31 / 7 |
| IR + Raman |
12 |
7 |
19 |
31 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
57 |
0 |
5 |
| quadratic |
2 |
1.653 |
0 |
41 |
| cubic |
3 |
32.509 |
19 |
165 |
| quartic |
4 |
487.635 |
0 |
811 |
| quintic |
5 |
5.949.147 |
0 |
2.791 |
| sextic |
6 |
61.474.519 |
190 |
10.571 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
12 |
7 |
19 |
| quadratic |
2 |
296 |
255 |
551 |
| cubic |
3 |
5.507 |
5.342 |
10.830 |
| quartic |
4 |
81.678 |
80.867 |
162.545 |
| quintic |
5 |
992.920 |
990.129 |
1.983.049 |
| sextic |
6 |
10.251.102 |
10.240.531 |
20.491.443 |
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