Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
21 |
-1 |
5 |
3 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
15 |
1 |
5 |
3 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
7 |
3 |
6 |
5 |
21 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
6 |
2 |
4 |
3 |
15 |
Molecule Parameter
| Number of Atoms (N) |
7 |
| Number of internal coordinates |
15 |
| Number of independant internal coordinates |
6 |
| Number of vibrational modes |
15 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
6 |
2 |
4 |
3 |
13 / 2 |
| Quadratic (Raman) |
6 |
2 |
4 |
3 |
15 / 0 |
| IR + Raman |
6 |
- |
4 |
3 |
13 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
15 |
1 |
5 |
3 |
| quadratic |
2 |
120 |
8 |
20 |
12 |
| cubic |
3 |
680 |
8 |
60 |
28 |
| quartic |
4 |
3.060 |
36 |
160 |
72 |
| quintic |
5 |
11.628 |
36 |
376 |
144 |
| sextic |
6 |
38.760 |
120 |
820 |
300 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
6 |
2 |
4 |
3 |
| quadratic |
2 |
40 |
24 |
30 |
26 |
| cubic |
3 |
194 |
150 |
176 |
160 |
| quartic |
4 |
832 |
716 |
778 |
734 |
| quintic |
5 |
3.046 |
2.786 |
2.956 |
2.840 |
| sextic |
6 |
10.000 |
9.440 |
9.790 |
9.530 |
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