Reduction formula for point group C2v
Characters of input representation
| E |
C2 (z) |
 v(xz) |
v(yz) |
| 6 |
2 |
4 |
0 |
Decomposition into Irreducible representations
| A1 |
A2 |
B1 |
B2 |
Total |
| 3 |
1 |
2 |
0 |
6 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
3 |
1 |
2 |
0 |
5 / 1 |
| Quadratic (Raman) |
3 |
1 |
2 |
0 |
6 / 0 |
| IR + Raman |
3 |
- |
2 |
0 |
5 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
6 |
2 |
4 |
0 |
| quadratic |
2 |
21 |
5 |
11 |
3 |
| cubic |
3 |
56 |
8 |
24 |
0 |
| quartic |
4 |
126 |
14 |
46 |
6 |
| quintic |
5 |
252 |
20 |
80 |
0 |
| sextic |
6 |
462 |
30 |
130 |
10 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
3 |
1 |
2 |
0 |
| quadratic |
2 |
10 |
3 |
6 |
2 |
| cubic |
3 |
22 |
10 |
18 |
6 |
| quartic |
4 |
48 |
22 |
38 |
18 |
| quintic |
5 |
88 |
48 |
78 |
38 |
| sextic |
6 |
158 |
88 |
138 |
78 |
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