Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
252 |
0 |
4 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
246 |
2 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
65 |
61 |
63 |
63 |
252 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
64 |
60 |
61 |
61 |
246 |
Molecule Parameter
| Number of Atoms (N) |
84 |
| Number of internal coordinates |
246 |
| Number of independant internal coordinates |
64 |
| Number of vibrational modes |
246 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
64 |
60 |
61 |
61 |
186 / 60 |
| Quadratic (Raman) |
64 |
60 |
61 |
61 |
246 / 0 |
| IR + Raman |
64 |
- |
61 |
61 |
186 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
246 |
2 |
4 |
4 |
| quadratic |
2 |
30.381 |
125 |
131 |
131 |
| cubic |
3 |
2.511.496 |
248 |
504 |
504 |
| quartic |
4 |
156.340.626 |
7.874 |
8.626 |
8.626 |
| quintic |
5 |
7.817.031.300 |
15.500 |
32.000 |
32.000 |
| sextic |
6 |
327.012.476.050 |
333.250 |
380.750 |
380.750 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
64 |
60 |
61 |
61 |
| quadratic |
2 |
7.692 |
7.561 |
7.564 |
7.564 |
| cubic |
3 |
628.188 |
627.684 |
627.812 |
627.812 |
| quartic |
4 |
39.091.438 |
39.082.812 |
39.083.188 |
39.083.188 |
| quintic |
5 |
1.954.277.700 |
1.954.245.700 |
1.954.253.950 |
1.954.253.950 |
| sextic |
6 |
81.753.392.700 |
81.753.011.950 |
81.753.035.700 |
81.753.035.700 |
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