Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
90 |
0 |
2 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
84 |
2 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
23 |
22 |
23 |
22 |
90 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
22 |
21 |
21 |
20 |
84 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
22 |
| Number of vibrational modes |
84 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
22 |
21 |
21 |
20 |
63 / 21 |
| Quadratic (Raman) |
22 |
21 |
21 |
20 |
84 / 0 |
| IR + Raman |
22 |
- |
21 |
20 |
63 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
84 |
2 |
2 |
0 |
| quadratic |
2 |
3.570 |
44 |
44 |
42 |
| cubic |
3 |
102.340 |
86 |
86 |
0 |
| quartic |
4 |
2.225.895 |
989 |
989 |
903 |
| quintic |
5 |
39.175.752 |
1.892 |
1.892 |
0 |
| sextic |
6 |
581.106.988 |
15.136 |
15.136 |
13.244 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
22 |
21 |
21 |
20 |
| quadratic |
2 |
925 |
882 |
882 |
881 |
| cubic |
3 |
25.628 |
25.585 |
25.585 |
25.542 |
| quartic |
4 |
557.194 |
556.248 |
556.248 |
556.205 |
| quintic |
5 |
9.794.884 |
9.793.938 |
9.793.938 |
9.792.992 |
| sextic |
6 |
145.287.626 |
145.273.436 |
145.273.436 |
145.272.490 |
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