Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
15 |
-3 |
5 |
3 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
9 |
-1 |
5 |
3 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
5 |
1 |
5 |
4 |
15 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
4 |
0 |
3 |
2 |
9 |
Molecule Parameter
| Number of Atoms (N) |
5 |
| Number of internal coordinates |
9 |
| Number of independant internal coordinates |
4 |
| Number of vibrational modes |
9 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
4 |
0 |
3 |
2 |
9 / 0 |
| Quadratic (Raman) |
4 |
0 |
3 |
2 |
9 / 0 |
| IR + Raman |
4 |
- |
3 |
2 |
9 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
9 |
-1 |
5 |
3 |
| quadratic |
2 |
45 |
5 |
17 |
9 |
| cubic |
3 |
165 |
-5 |
45 |
19 |
| quartic |
4 |
495 |
15 |
103 |
39 |
| quintic |
5 |
1.287 |
-15 |
211 |
69 |
| sextic |
6 |
3.003 |
35 |
399 |
119 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
4 |
0 |
3 |
2 |
| quadratic |
2 |
19 |
6 |
12 |
8 |
| cubic |
3 |
56 |
24 |
49 |
36 |
| quartic |
4 |
163 |
92 |
136 |
104 |
| quintic |
5 |
388 |
248 |
361 |
290 |
| sextic |
6 |
889 |
630 |
812 |
672 |
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