Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
54 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
48 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
12 |
6 |
18 |
36 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
11 |
5 |
16 |
32 |
Molecule Parameter
| Number of Atoms (N) |
18 |
| Number of internal coordinates |
48 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
32 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
11 |
5 |
16 |
27 / 5 |
| Quadratic (Raman) |
11 |
5 |
16 |
27 / 5 |
| IR + Raman |
11 |
5 |
16 |
27 / 5 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
48 |
0 |
6 |
| quadratic |
2 |
1.176 |
0 |
42 |
| cubic |
3 |
19.600 |
16 |
182 |
| quartic |
4 |
249.900 |
0 |
798 |
| quintic |
5 |
2.598.960 |
0 |
2.814 |
| sextic |
6 |
22.957.480 |
136 |
9.730 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
11 |
5 |
16 |
| quadratic |
2 |
217 |
175 |
392 |
| cubic |
3 |
3.363 |
3.181 |
6.528 |
| quartic |
4 |
42.049 |
41.251 |
83.300 |
| quintic |
5 |
434.567 |
431.753 |
866.320 |
| sextic |
6 |
3.831.157 |
3.821.427 |
7.652.448 |
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