Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
144 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
138 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
24 |
24 |
48 |
96 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
23 |
23 |
46 |
92 |
Molecule Parameter
| Number of Atoms (N) |
48 |
| Number of internal coordinates |
138 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
92 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
23 |
23 |
46 |
69 / 23 |
| Quadratic (Raman) |
23 |
23 |
46 |
69 / 23 |
| IR + Raman |
23 |
23 |
46 |
69 / 23 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
138 |
0 |
0 |
| quadratic |
2 |
9.591 |
0 |
69 |
| cubic |
3 |
447.580 |
46 |
0 |
| quartic |
4 |
15.777.195 |
0 |
2.415 |
| quintic |
5 |
448.072.338 |
0 |
0 |
| sextic |
6 |
10.679.057.389 |
1.081 |
57.155 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
23 |
23 |
46 |
| quadratic |
2 |
1.633 |
1.564 |
3.197 |
| cubic |
3 |
74.612 |
74.612 |
149.178 |
| quartic |
4 |
2.630.740 |
2.628.325 |
5.259.065 |
| quintic |
5 |
74.678.723 |
74.678.723 |
149.357.446 |
| sextic |
6 |
1.779.871.836 |
1.779.814.681 |
3.559.685.436 |
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