Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
48 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
42 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
12 |
4 |
16 |
32 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
11 |
3 |
14 |
28 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
28 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
11 |
3 |
14 |
25 / 3 |
| Quadratic (Raman) |
11 |
3 |
14 |
25 / 3 |
| IR + Raman |
11 |
3 |
14 |
25 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
42 |
0 |
8 |
| quadratic |
2 |
903 |
0 |
53 |
| cubic |
3 |
13.244 |
14 |
256 |
| quartic |
4 |
148.995 |
0 |
1.095 |
| quintic |
5 |
1.370.754 |
0 |
4.056 |
| sextic |
6 |
10.737.573 |
105 |
13.803 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
11 |
3 |
14 |
| quadratic |
2 |
177 |
124 |
301 |
| cubic |
3 |
2.340 |
2.084 |
4.410 |
| quartic |
4 |
25.380 |
24.285 |
49.665 |
| quintic |
5 |
230.487 |
226.431 |
456.918 |
| sextic |
6 |
1.796.532 |
1.782.729 |
3.579.156 |
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