Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
78 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
72 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
17 |
9 |
26 |
52 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
16 |
8 |
24 |
48 |
Molecule Parameter
| Number of Atoms (N) |
26 |
| Number of internal coordinates |
72 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
16 |
8 |
24 |
40 / 8 |
| Quadratic (Raman) |
16 |
8 |
24 |
40 / 8 |
| IR + Raman |
16 |
8 |
24 |
40 / 8 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
72 |
0 |
8 |
| quadratic |
2 |
2.628 |
0 |
68 |
| cubic |
3 |
64.824 |
24 |
376 |
| quartic |
4 |
1.215.450 |
0 |
2.010 |
| quintic |
5 |
18.474.840 |
0 |
8.856 |
| sextic |
6 |
237.093.780 |
300 |
37.268 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
16 |
8 |
24 |
| quadratic |
2 |
472 |
404 |
876 |
| cubic |
3 |
11.000 |
10.624 |
21.600 |
| quartic |
4 |
203.580 |
201.570 |
405.150 |
| quintic |
5 |
3.083.568 |
3.074.712 |
6.158.280 |
| sextic |
6 |
39.534.364 |
39.497.096 |
79.031.160 |
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