Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
102 |
0 |
0 |
14 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
96 |
2 |
0 |
14 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
29 |
22 |
22 |
29 |
102 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
28 |
21 |
20 |
27 |
96 |
Molecule Parameter
| Number of Atoms (N) |
34 |
| Number of internal coordinates |
96 |
| Number of independant internal coordinates |
28 |
| Number of vibrational modes |
96 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
28 |
21 |
20 |
27 |
75 / 21 |
| Quadratic (Raman) |
28 |
21 |
20 |
27 |
96 / 0 |
| IR + Raman |
28 |
- |
20 |
27 |
75 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
96 |
2 |
0 |
14 |
| quadratic |
2 |
4.656 |
50 |
48 |
146 |
| cubic |
3 |
152.096 |
98 |
0 |
1.134 |
| quartic |
4 |
3.764.376 |
1.274 |
1.176 |
7.546 |
| quintic |
5 |
75.287.520 |
2.450 |
0 |
43.582 |
| sextic |
6 |
1.267.339.920 |
22.050 |
19.600 |
227.458 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
28 |
21 |
20 |
27 |
| quadratic |
2 |
1.225 |
1.128 |
1.127 |
1.176 |
| cubic |
3 |
38.332 |
37.765 |
37.716 |
38.283 |
| quartic |
4 |
943.593 |
939.232 |
939.183 |
942.368 |
| quintic |
5 |
18.833.388 |
18.811.597 |
18.810.372 |
18.832.163 |
| sextic |
6 |
316.902.257 |
316.778.728 |
316.777.503 |
316.881.432 |
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