Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
90 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
84 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
18 |
12 |
30 |
60 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
17 |
11 |
28 |
56 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
17 |
| Number of vibrational modes |
56 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
17 |
11 |
28 |
45 / 11 |
| Quadratic (Raman) |
17 |
11 |
28 |
45 / 11 |
| IR + Raman |
17 |
11 |
28 |
45 / 11 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
84 |
0 |
6 |
| quadratic |
2 |
3.570 |
0 |
60 |
| cubic |
3 |
102.340 |
28 |
290 |
| quartic |
4 |
2.225.895 |
0 |
1.725 |
| quintic |
5 |
39.175.752 |
0 |
7.116 |
| sextic |
6 |
581.106.988 |
406 |
32.416 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
17 |
11 |
28 |
| quadratic |
2 |
625 |
565 |
1.190 |
| cubic |
3 |
17.211 |
16.921 |
34.104 |
| quartic |
4 |
371.845 |
370.120 |
741.965 |
| quintic |
5 |
6.532.850 |
6.525.734 |
13.058.584 |
| sextic |
6 |
96.867.508 |
96.835.092 |
193.702.194 |
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