Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
99 |
-1 |
1 |
9 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
93 |
1 |
1 |
9 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
27 |
22 |
23 |
27 |
99 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
26 |
21 |
21 |
25 |
93 |
Molecule Parameter
| Number of Atoms (N) |
33 |
| Number of internal coordinates |
93 |
| Number of independant internal coordinates |
26 |
| Number of vibrational modes |
93 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
26 |
21 |
21 |
25 |
72 / 21 |
| Quadratic (Raman) |
26 |
21 |
21 |
25 |
93 / 0 |
| IR + Raman |
26 |
- |
21 |
25 |
72 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
93 |
1 |
1 |
9 |
| quadratic |
2 |
4.371 |
47 |
47 |
87 |
| cubic |
3 |
138.415 |
47 |
47 |
543 |
| quartic |
4 |
3.321.960 |
1.128 |
1.128 |
3.288 |
| quintic |
5 |
64.446.024 |
1.128 |
1.128 |
16.344 |
| sextic |
6 |
1.052.618.392 |
18.424 |
18.424 |
77.672 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
26 |
21 |
21 |
25 |
| quadratic |
2 |
1.138 |
1.071 |
1.071 |
1.091 |
| cubic |
3 |
34.763 |
34.468 |
34.468 |
34.716 |
| quartic |
4 |
831.876 |
829.668 |
829.668 |
830.748 |
| quintic |
5 |
16.116.156 |
16.107.420 |
16.107.420 |
16.115.028 |
| sextic |
6 |
263.183.228 |
263.135.180 |
263.135.180 |
263.164.804 |
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