Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
48 |
0 |
0 |
8 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
42 |
2 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
14 |
10 |
10 |
14 |
48 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
13 |
9 |
8 |
12 |
42 |
Molecule Parameter
| Number of Atoms (N) |
16 |
| Number of internal coordinates |
42 |
| Number of independant internal coordinates |
13 |
| Number of vibrational modes |
42 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
13 |
9 |
8 |
12 |
33 / 9 |
| Quadratic (Raman) |
13 |
9 |
8 |
12 |
42 / 0 |
| IR + Raman |
13 |
- |
8 |
12 |
33 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
42 |
2 |
0 |
8 |
| quadratic |
2 |
903 |
23 |
21 |
53 |
| cubic |
3 |
13.244 |
44 |
0 |
256 |
| quartic |
4 |
148.995 |
275 |
231 |
1.095 |
| quintic |
5 |
1.370.754 |
506 |
0 |
4.056 |
| sextic |
6 |
10.737.573 |
2.277 |
1.771 |
13.803 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
13 |
9 |
8 |
12 |
| quadratic |
2 |
250 |
213 |
212 |
228 |
| cubic |
3 |
3.386 |
3.258 |
3.236 |
3.364 |
| quartic |
4 |
37.649 |
36.986 |
36.964 |
37.396 |
| quintic |
5 |
343.829 |
341.801 |
341.548 |
343.576 |
| sextic |
6 |
2.688.856 |
2.681.069 |
2.680.816 |
2.686.832 |
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