Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
54 |
0 |
6 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
48 |
2 |
6 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
15 |
12 |
15 |
12 |
54 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
14 |
11 |
13 |
10 |
48 |
Molecule Parameter
| Number of Atoms (N) |
18 |
| Number of internal coordinates |
48 |
| Number of independant internal coordinates |
14 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
14 |
11 |
13 |
10 |
37 / 11 |
| Quadratic (Raman) |
14 |
11 |
13 |
10 |
48 / 0 |
| IR + Raman |
14 |
- |
13 |
10 |
37 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
48 |
2 |
6 |
0 |
| quadratic |
2 |
1.176 |
26 |
42 |
24 |
| cubic |
3 |
19.600 |
50 |
182 |
0 |
| quartic |
4 |
249.900 |
350 |
798 |
300 |
| quintic |
5 |
2.598.960 |
650 |
2.814 |
0 |
| sextic |
6 |
22.957.480 |
3.250 |
9.730 |
2.600 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
14 |
11 |
13 |
10 |
| quadratic |
2 |
317 |
284 |
292 |
283 |
| cubic |
3 |
4.958 |
4.867 |
4.933 |
4.842 |
| quartic |
4 |
62.837 |
62.288 |
62.512 |
62.263 |
| quintic |
5 |
650.606 |
649.199 |
650.281 |
648.874 |
| sextic |
6 |
5.743.265 |
5.737.100 |
5.740.340 |
5.736.775 |
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