Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
75 |
0 |
9 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
69 |
0 |
9 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
17 |
8 |
25 |
50 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
16 |
7 |
23 |
46 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
46 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
16 |
7 |
23 |
39 / 7 |
| Quadratic (Raman) |
16 |
7 |
23 |
39 / 7 |
| IR + Raman |
16 |
7 |
23 |
39 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
69 |
0 |
9 |
| quadratic |
2 |
2.415 |
0 |
75 |
| cubic |
3 |
57.155 |
23 |
435 |
| quartic |
4 |
1.028.790 |
0 |
2.310 |
| quintic |
5 |
15.020.334 |
0 |
10.422 |
| sextic |
6 |
185.250.786 |
276 |
43.738 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
16 |
7 |
23 |
| quadratic |
2 |
440 |
365 |
805 |
| cubic |
3 |
9.751 |
9.316 |
19.044 |
| quartic |
4 |
172.620 |
170.310 |
342.930 |
| quintic |
5 |
2.508.600 |
2.498.178 |
5.006.778 |
| sextic |
6 |
30.897.092 |
30.853.354 |
61.750.170 |
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