Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
60 |
0 |
12 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
54 |
2 |
12 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
18 |
12 |
18 |
12 |
60 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
17 |
11 |
16 |
10 |
54 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
17 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
17 |
11 |
16 |
10 |
43 / 11 |
| Quadratic (Raman) |
17 |
11 |
16 |
10 |
54 / 0 |
| IR + Raman |
17 |
- |
16 |
10 |
43 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
54 |
2 |
12 |
0 |
| quadratic |
2 |
1.485 |
29 |
99 |
27 |
| cubic |
3 |
27.720 |
56 |
616 |
0 |
| quartic |
4 |
395.010 |
434 |
3.234 |
378 |
| quintic |
5 |
4.582.116 |
812 |
14.784 |
0 |
| sextic |
6 |
45.057.474 |
4.466 |
60.830 |
3.654 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
17 |
11 |
16 |
10 |
| quadratic |
2 |
410 |
347 |
382 |
346 |
| cubic |
3 |
7.098 |
6.790 |
7.070 |
6.762 |
| quartic |
4 |
99.764 |
97.958 |
99.358 |
97.930 |
| quintic |
5 |
1.149.428 |
1.142.036 |
1.149.022 |
1.141.630 |
| sextic |
6 |
11.281.606 |
11.249.364 |
11.277.546 |
11.248.958 |
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