Reduction formula for point group C3v
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3 v |
| Cartesian 3N |
108 |
0 |
4 |
| Translation (x,y,z) |
3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
102 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
20 |
16 |
36 |
72 |
| Translation (x,y,z) |
1 |
0 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
19 |
15 |
34 |
68 |
Molecule Parameter
| Number of Atoms (N) |
36 |
| Number of internal coordinates |
102 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
68 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
19 |
15 |
34 |
53 / 15 |
| Quadratic (Raman) |
19 |
15 |
34 |
53 / 15 |
| IR + Raman |
19 |
15 |
34 |
53 / 15 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3v |
| linear |
1 |
102 |
0 |
4 |
| quadratic |
2 |
5.253 |
0 |
59 |
| cubic |
3 |
182.104 |
34 |
216 |
| quartic |
4 |
4.780.230 |
0 |
1.750 |
| quintic |
5 |
101.340.876 |
0 |
5.936 |
| sextic |
6 |
1.807.245.622 |
595 |
34.874 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
19 |
15 |
34 |
| quadratic |
2 |
905 |
846 |
1.751 |
| cubic |
3 |
30.470 |
30.254 |
60.690 |
| quartic |
4 |
797.580 |
795.830 |
1.593.410 |
| quintic |
5 |
16.893.114 |
16.887.178 |
33.780.292 |
| sextic |
6 |
301.225.239 |
301.190.365 |
602.415.009 |
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