Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
75 |
-1 |
1 |
9 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
69 |
1 |
1 |
9 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
21 |
16 |
17 |
21 |
75 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
20 |
15 |
15 |
19 |
69 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
20 |
| Number of vibrational modes |
69 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
20 |
15 |
15 |
19 |
54 / 15 |
| Quadratic (Raman) |
20 |
15 |
15 |
19 |
69 / 0 |
| IR + Raman |
20 |
- |
15 |
19 |
54 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
69 |
1 |
1 |
9 |
| quadratic |
2 |
2.415 |
35 |
35 |
75 |
| cubic |
3 |
57.155 |
35 |
35 |
435 |
| quartic |
4 |
1.028.790 |
630 |
630 |
2.310 |
| quintic |
5 |
15.020.334 |
630 |
630 |
10.422 |
| sextic |
6 |
185.250.786 |
7.770 |
7.770 |
43.738 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
20 |
15 |
15 |
19 |
| quadratic |
2 |
640 |
585 |
585 |
605 |
| cubic |
3 |
14.415 |
14.180 |
14.180 |
14.380 |
| quartic |
4 |
258.090 |
256.620 |
256.620 |
257.460 |
| quintic |
5 |
3.758.004 |
3.752.478 |
3.752.478 |
3.757.374 |
| sextic |
6 |
46.327.516 |
46.301.762 |
46.301.762 |
46.319.746 |
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