Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
60 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
54 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
14 |
6 |
20 |
40 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
13 |
5 |
18 |
36 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
13 |
| Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
13 |
5 |
18 |
31 / 5 |
| Quadratic (Raman) |
13 |
5 |
18 |
31 / 5 |
| IR + Raman |
13 |
5 |
18 |
31 / 5 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
54 |
0 |
8 |
| quadratic |
2 |
1.485 |
0 |
59 |
| cubic |
3 |
27.720 |
18 |
304 |
| quartic |
4 |
395.010 |
0 |
1.434 |
| quintic |
5 |
4.582.116 |
0 |
5.760 |
| sextic |
6 |
45.057.474 |
171 |
21.542 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
13 |
5 |
18 |
| quadratic |
2 |
277 |
218 |
495 |
| cubic |
3 |
4.778 |
4.474 |
9.234 |
| quartic |
4 |
66.552 |
65.118 |
131.670 |
| quintic |
5 |
766.566 |
760.806 |
1.527.372 |
| sextic |
6 |
7.520.407 |
7.498.865 |
15.019.101 |
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