Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
39 |
0 |
5 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
33 |
0 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
9 |
4 |
13 |
26 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
8 |
3 |
11 |
22 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
22 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
8 |
3 |
11 |
19 / 3 |
| Quadratic (Raman) |
8 |
3 |
11 |
19 / 3 |
| IR + Raman |
8 |
3 |
11 |
19 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
33 |
0 |
5 |
| quadratic |
2 |
561 |
0 |
29 |
| cubic |
3 |
6.545 |
11 |
105 |
| quartic |
4 |
58.905 |
0 |
385 |
| quintic |
5 |
435.897 |
0 |
1.141 |
| sextic |
6 |
2.760.681 |
66 |
3.325 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
8 |
3 |
11 |
| quadratic |
2 |
108 |
79 |
187 |
| cubic |
3 |
1.147 |
1.042 |
2.178 |
| quartic |
4 |
10.010 |
9.625 |
19.635 |
| quintic |
5 |
73.220 |
72.079 |
145.299 |
| sextic |
6 |
461.798 |
458.473 |
920.205 |
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