Reduction formula for point group C2v
Characters of input representation
E |
C2 (z) |
v(xz) |
v(yz) |
18 |
2 |
8 |
0 |
Decomposition into Irreducible representations
A1 |
A2 |
B1 |
B2 |
Total |
7 |
3 |
6 |
2 |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
7 |
3 |
6 |
2 |
15 / 3 |
Quadratic (Raman) |
7 |
3 |
6 |
2 |
18 / 0 |
IR + Raman |
7 |
- |
6 |
2 |
15 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
18 |
2 |
8 |
0 |
quadratic |
2 |
171 |
11 |
41 |
9 |
cubic |
3 |
1.140 |
20 |
160 |
0 |
quartic |
4 |
5.985 |
65 |
525 |
45 |
quintic |
5 |
26.334 |
110 |
1.512 |
0 |
sextic |
6 |
100.947 |
275 |
3.941 |
165 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
7 |
3 |
6 |
2 |
quadratic |
2 |
58 |
33 |
48 |
32 |
cubic |
3 |
330 |
250 |
320 |
240 |
quartic |
4 |
1.655 |
1.370 |
1.600 |
1.360 |
quintic |
5 |
6.989 |
6.233 |
6.934 |
6.178 |
sextic |
6 |
26.332 |
24.279 |
26.112 |
24.224 |
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