Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
42 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
36 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
10 |
4 |
14 |
28 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
9 |
3 |
12 |
24 |
Molecule Parameter
| Number of Atoms (N) |
14 |
| Number of internal coordinates |
36 |
| Number of independant internal coordinates |
9 |
| Number of vibrational modes |
24 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
9 |
3 |
12 |
21 / 3 |
| Quadratic (Raman) |
9 |
3 |
12 |
21 / 3 |
| IR + Raman |
9 |
3 |
12 |
21 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
36 |
0 |
6 |
| quadratic |
2 |
666 |
0 |
36 |
| cubic |
3 |
8.436 |
12 |
146 |
| quartic |
4 |
82.251 |
0 |
561 |
| quintic |
5 |
658.008 |
0 |
1.812 |
| sextic |
6 |
4.496.388 |
78 |
5.552 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
9 |
3 |
12 |
| quadratic |
2 |
129 |
93 |
222 |
| cubic |
3 |
1.483 |
1.337 |
2.808 |
| quartic |
4 |
13.989 |
13.428 |
27.417 |
| quintic |
5 |
110.574 |
108.762 |
219.336 |
| sextic |
6 |
752.200 |
746.648 |
1.498.770 |
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