Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
42 |
-2 |
4 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
36 |
0 |
4 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
12 |
8 |
11 |
11 |
42 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
11 |
7 |
9 |
9 |
36 |
Molecule Parameter
| Number of Atoms (N) |
14 |
| Number of internal coordinates |
36 |
| Number of independant internal coordinates |
11 |
| Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
11 |
7 |
9 |
9 |
29 / 7 |
| Quadratic (Raman) |
11 |
7 |
9 |
9 |
36 / 0 |
| IR + Raman |
11 |
- |
9 |
9 |
29 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
36 |
0 |
4 |
4 |
| quadratic |
2 |
666 |
18 |
26 |
26 |
| cubic |
3 |
8.436 |
0 |
84 |
84 |
| quartic |
4 |
82.251 |
171 |
331 |
331 |
| quintic |
5 |
658.008 |
0 |
920 |
920 |
| sextic |
6 |
4.496.388 |
1.140 |
2.820 |
2.820 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
11 |
7 |
9 |
9 |
| quadratic |
2 |
184 |
158 |
162 |
162 |
| cubic |
3 |
2.151 |
2.067 |
2.109 |
2.109 |
| quartic |
4 |
20.771 |
20.440 |
20.520 |
20.520 |
| quintic |
5 |
164.962 |
164.042 |
164.502 |
164.502 |
| sextic |
6 |
1.125.792 |
1.122.972 |
1.123.812 |
1.123.812 |
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