Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
39 |
-5 |
9 |
9 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
33 |
-3 |
9 |
9 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
13 |
4 |
11 |
11 |
39 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
12 |
3 |
9 |
9 |
33 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
12 |
| Number of vibrational modes |
33 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
12 |
3 |
9 |
9 |
30 / 3 |
| Quadratic (Raman) |
12 |
3 |
9 |
9 |
33 / 0 |
| IR + Raman |
12 |
- |
9 |
9 |
30 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
33 |
-3 |
9 |
9 |
| quadratic |
2 |
561 |
21 |
57 |
57 |
| cubic |
3 |
6.545 |
-55 |
273 |
273 |
| quartic |
4 |
58.905 |
225 |
1.113 |
1.113 |
| quintic |
5 |
435.897 |
-531 |
3.969 |
3.969 |
| sextic |
6 |
2.760.681 |
1.653 |
12.817 |
12.817 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
12 |
3 |
9 |
9 |
| quadratic |
2 |
174 |
117 |
135 |
135 |
| cubic |
3 |
1.759 |
1.486 |
1.650 |
1.650 |
| quartic |
4 |
15.339 |
14.226 |
14.670 |
14.670 |
| quintic |
5 |
110.826 |
106.857 |
109.107 |
109.107 |
| sextic |
6 |
696.992 |
684.175 |
689.757 |
689.757 |
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