Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
156 |
0 |
14 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
150 |
0 |
14 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
33 |
19 |
52 |
104 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
32 |
18 |
50 |
100 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
32 |
| Number of vibrational modes |
100 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
32 |
18 |
50 |
82 / 18 |
| Quadratic (Raman) |
32 |
18 |
50 |
82 / 18 |
| IR + Raman |
32 |
18 |
50 |
82 / 18 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
150 |
0 |
14 |
| quadratic |
2 |
11.325 |
0 |
173 |
| cubic |
3 |
573.800 |
50 |
1.512 |
| quartic |
4 |
21.947.850 |
0 |
11.866 |
| quintic |
5 |
675.993.780 |
0 |
79.492 |
| sextic |
6 |
17.463.172.650 |
1.275 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
32 |
18 |
50 |
| quadratic |
2 |
1.974 |
1.801 |
3.775 |
| cubic |
3 |
96.406 |
94.894 |
191.250 |
| quartic |
4 |
3.663.908 |
3.652.042 |
7.315.950 |
| quintic |
5 |
112.705.376 |
112.625.884 |
225.331.260 |
| sextic |
6 |
2.910.774.221 |
2.910.284.179 |
5.821.057.125 |
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