Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
72 |
0 |
24 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
66 |
2 |
24 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
24 |
12 |
24 |
12 |
72 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
23 |
11 |
22 |
10 |
66 |
Molecule Parameter
| Number of Atoms (N) |
24 |
| Number of internal coordinates |
66 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
66 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
23 |
11 |
22 |
10 |
55 / 11 |
| Quadratic (Raman) |
23 |
11 |
22 |
10 |
66 / 0 |
| IR + Raman |
23 |
- |
22 |
10 |
55 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
66 |
2 |
24 |
0 |
| quadratic |
2 |
2.211 |
35 |
321 |
33 |
| cubic |
3 |
50.116 |
68 |
3.104 |
0 |
| quartic |
4 |
864.501 |
629 |
24.081 |
561 |
| quintic |
5 |
12.103.014 |
1.190 |
158.424 |
0 |
| sextic |
6 |
143.218.999 |
7.735 |
914.641 |
6.545 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
23 |
11 |
22 |
10 |
| quadratic |
2 |
650 |
473 |
616 |
472 |
| cubic |
3 |
13.322 |
11.770 |
13.288 |
11.736 |
| quartic |
4 |
222.443 |
210.122 |
221.848 |
210.088 |
| quintic |
5 |
3.065.657 |
2.986.445 |
3.065.062 |
2.985.850 |
| sextic |
6 |
36.036.980 |
35.576.387 |
36.029.840 |
35.575.792 |
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