Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
180 |
0 |
4 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
174 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
32 |
28 |
60 |
120 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
31 |
27 |
58 |
116 |
Molecule Parameter
| Number of Atoms (N) |
60 |
| Number of internal coordinates |
174 |
| Number of independant internal coordinates |
31 |
| Number of vibrational modes |
116 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
31 |
27 |
58 |
89 / 27 |
| Quadratic (Raman) |
31 |
27 |
58 |
89 / 27 |
| IR + Raman |
31 |
27 |
58 |
89 / 27 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
174 |
0 |
4 |
| quadratic |
2 |
15.225 |
0 |
95 |
| cubic |
3 |
893.200 |
58 |
360 |
| quartic |
4 |
39.524.100 |
0 |
4.540 |
| quintic |
5 |
1.407.057.960 |
0 |
16.376 |
| sextic |
6 |
41.977.229.140 |
1.711 |
145.604 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
31 |
27 |
58 |
| quadratic |
2 |
2.585 |
2.490 |
5.075 |
| cubic |
3 |
149.066 |
148.706 |
297.714 |
| quartic |
4 |
6.589.620 |
6.585.080 |
13.174.700 |
| quintic |
5 |
234.517.848 |
234.501.472 |
469.019.320 |
| sextic |
6 |
6.996.278.229 |
6.996.132.625 |
13.992.409.143 |
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