Reduction formula for point group C3v
Characters for molecular motions
Motion |
E |
2C3 (z) |
3v |
Cartesian 3N |
75 |
0 |
5 |
Translation (x,y,z) |
3 |
0 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
Vibration |
69 |
0 |
5 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
E |
Total |
Cartesian 3N |
15 |
10 |
25 |
50 |
Translation (x,y,z) |
1 |
0 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
Vibration |
14 |
9 |
23 |
46 |
Molecule Parameter
Number of Atoms (N) |
25 |
Number of internal coordinates |
69 |
Number of independant internal coordinates |
14 |
Number of vibrational modes |
46 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
E |
Total |
Linear (IR) |
14 |
9 |
23 |
37 / 9 |
Quadratic (Raman) |
14 |
9 |
23 |
37 / 9 |
IR + Raman |
14 |
9 |
23 |
37 / 9 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3v |
linear |
1 |
69 |
0 |
5 |
quadratic |
2 |
2.415 |
0 |
47 |
cubic |
3 |
57.155 |
23 |
195 |
quartic |
4 |
1.028.790 |
0 |
1.078 |
quintic |
5 |
15.020.334 |
0 |
3.886 |
sextic |
6 |
185.250.786 |
276 |
16.354 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
E |
linear |
1 |
14 |
9 |
23 |
quadratic |
2 |
426 |
379 |
805 |
cubic |
3 |
9.631 |
9.436 |
19.044 |
quartic |
4 |
172.004 |
170.926 |
342.930 |
quintic |
5 |
2.505.332 |
2.501.446 |
5.006.778 |
sextic |
6 |
30.883.400 |
30.867.046 |
61.750.170 |
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