Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
33 |
0 |
7 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
27 |
0 |
7 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
9 |
2 |
11 |
22 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
8 |
1 |
9 |
18 |
Molecule Parameter
| Number of Atoms (N) |
11 |
| Number of internal coordinates |
27 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
8 |
1 |
9 |
17 / 1 |
| Quadratic (Raman) |
8 |
1 |
9 |
17 / 1 |
| IR + Raman |
8 |
1 |
9 |
17 / 1 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
27 |
0 |
7 |
| quadratic |
2 |
378 |
0 |
38 |
| cubic |
3 |
3.654 |
9 |
154 |
| quartic |
4 |
27.405 |
0 |
545 |
| quintic |
5 |
169.911 |
0 |
1.687 |
| sextic |
6 |
906.192 |
45 |
4.784 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
8 |
1 |
9 |
| quadratic |
2 |
82 |
44 |
126 |
| cubic |
3 |
689 |
535 |
1.215 |
| quartic |
4 |
4.840 |
4.295 |
9.135 |
| quintic |
5 |
29.162 |
27.475 |
56.637 |
| sextic |
6 |
153.439 |
148.655 |
302.049 |
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