Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
210 |
0 |
10 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
204 |
2 |
10 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
56 |
49 |
54 |
51 |
210 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
55 |
48 |
52 |
49 |
204 |
Molecule Parameter
| Number of Atoms (N) |
70 |
| Number of internal coordinates |
204 |
| Number of independant internal coordinates |
55 |
| Number of vibrational modes |
204 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
55 |
48 |
52 |
49 |
156 / 48 |
| Quadratic (Raman) |
55 |
48 |
52 |
49 |
204 / 0 |
| IR + Raman |
55 |
- |
52 |
49 |
156 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
204 |
2 |
10 |
4 |
| quadratic |
2 |
20.910 |
104 |
152 |
110 |
| cubic |
3 |
1.435.820 |
206 |
1.190 |
420 |
| quartic |
4 |
74.303.685 |
5.459 |
10.803 |
6.085 |
| quintic |
5 |
3.091.033.296 |
10.712 |
70.872 |
22.256 |
| sextic |
6 |
107.670.993.144 |
192.816 |
492.624 |
225.784 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
55 |
48 |
52 |
49 |
| quadratic |
2 |
5.319 |
5.188 |
5.212 |
5.191 |
| cubic |
3 |
359.409 |
358.604 |
359.096 |
358.711 |
| quartic |
4 |
18.581.508 |
18.573.064 |
18.575.736 |
18.573.377 |
| quintic |
5 |
772.784.284 |
772.737.720 |
772.767.800 |
772.743.492 |
| sextic |
6 |
26.917.976.092 |
26.917.616.888 |
26.917.766.792 |
26.917.633.372 |
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