Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
54 |
-4 |
18 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
48 |
-2 |
18 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
18 |
7 |
18 |
11 |
54 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
17 |
6 |
16 |
9 |
48 |
Molecule Parameter
| Number of Atoms (N) |
18 |
| Number of internal coordinates |
48 |
| Number of independant internal coordinates |
17 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
17 |
6 |
16 |
9 |
42 / 6 |
| Quadratic (Raman) |
17 |
6 |
16 |
9 |
48 / 0 |
| IR + Raman |
17 |
- |
16 |
9 |
42 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
48 |
-2 |
18 |
4 |
| quadratic |
2 |
1.176 |
26 |
186 |
32 |
| cubic |
3 |
19.600 |
-50 |
1.410 |
108 |
| quartic |
4 |
249.900 |
350 |
8.670 |
508 |
| quintic |
5 |
2.598.960 |
-650 |
45.594 |
1.508 |
| sextic |
6 |
22.957.480 |
3.250 |
211.922 |
5.408 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
17 |
6 |
16 |
9 |
| quadratic |
2 |
355 |
246 |
326 |
249 |
| cubic |
3 |
5.267 |
4.508 |
5.238 |
4.587 |
| quartic |
4 |
64.857 |
60.268 |
64.428 |
60.347 |
| quintic |
5 |
661.353 |
637.802 |
660.924 |
638.881 |
| sextic |
6 |
5.794.515 |
5.685.850 |
5.790.186 |
5.686.929 |
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