Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
180 |
0 |
4 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
174 |
2 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
47 |
43 |
45 |
45 |
180 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
46 |
42 |
43 |
43 |
174 |
Molecule Parameter
| Number of Atoms (N) |
60 |
| Number of internal coordinates |
174 |
| Number of independant internal coordinates |
46 |
| Number of vibrational modes |
174 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
46 |
42 |
43 |
43 |
132 / 42 |
| Quadratic (Raman) |
46 |
42 |
43 |
43 |
174 / 0 |
| IR + Raman |
46 |
- |
43 |
43 |
132 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
174 |
2 |
4 |
4 |
| quadratic |
2 |
15.225 |
89 |
95 |
95 |
| cubic |
3 |
893.200 |
176 |
360 |
360 |
| quartic |
4 |
39.524.100 |
4.004 |
4.540 |
4.540 |
| quintic |
5 |
1.407.057.960 |
7.832 |
16.376 |
16.376 |
| sextic |
6 |
41.977.229.140 |
121.396 |
145.604 |
145.604 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
46 |
42 |
43 |
43 |
| quadratic |
2 |
3.876 |
3.781 |
3.784 |
3.784 |
| cubic |
3 |
223.524 |
223.164 |
223.256 |
223.256 |
| quartic |
4 |
9.884.296 |
9.879.756 |
9.880.024 |
9.880.024 |
| quintic |
5 |
351.774.636 |
351.758.260 |
351.762.532 |
351.762.532 |
| sextic |
6 |
10.494.410.436 |
10.494.264.832 |
10.494.276.936 |
10.494.276.936 |
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