Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
156 |
-2 |
4 |
14 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
150 |
0 |
4 |
14 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
43 |
34 |
37 |
42 |
156 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
42 |
33 |
35 |
40 |
150 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
42 |
| Number of vibrational modes |
150 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
42 |
33 |
35 |
40 |
117 / 33 |
| Quadratic (Raman) |
42 |
33 |
35 |
40 |
150 / 0 |
| IR + Raman |
42 |
- |
35 |
40 |
117 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
150 |
0 |
4 |
14 |
| quadratic |
2 |
11.325 |
75 |
83 |
173 |
| cubic |
3 |
573.800 |
0 |
312 |
1.512 |
| quartic |
4 |
21.947.850 |
2.850 |
3.466 |
11.866 |
| quintic |
5 |
675.993.780 |
0 |
12.320 |
79.492 |
| sextic |
6 |
17.463.172.650 |
73.150 |
97.174 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
42 |
33 |
35 |
40 |
| quadratic |
2 |
2.914 |
2.786 |
2.790 |
2.835 |
| cubic |
3 |
143.906 |
142.994 |
143.150 |
143.750 |
| quartic |
4 |
5.491.508 |
5.483.842 |
5.484.150 |
5.488.350 |
| quintic |
5 |
169.021.398 |
168.975.492 |
168.981.652 |
169.015.238 |
| sextic |
6 |
4.365.958.254 |
4.365.664.646 |
4.365.676.658 |
4.365.873.092 |
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