Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
42 |
-2 |
14 |
2 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
36 |
0 |
14 |
2 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
14 |
6 |
14 |
8 |
42 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
13 |
5 |
12 |
6 |
36 |
Molecule Parameter
| Number of Atoms (N) |
14 |
| Number of internal coordinates |
36 |
| Number of independant internal coordinates |
13 |
| Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
13 |
5 |
12 |
6 |
31 / 5 |
| Quadratic (Raman) |
13 |
5 |
12 |
6 |
36 / 0 |
| IR + Raman |
13 |
- |
12 |
6 |
31 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
36 |
0 |
14 |
2 |
| quadratic |
2 |
666 |
18 |
116 |
20 |
| cubic |
3 |
8.436 |
0 |
714 |
38 |
| quartic |
4 |
82.251 |
171 |
3.601 |
209 |
| quintic |
5 |
658.008 |
0 |
15.652 |
380 |
| sextic |
6 |
4.496.388 |
1.140 |
60.528 |
1.520 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
13 |
5 |
12 |
6 |
| quadratic |
2 |
205 |
137 |
186 |
138 |
| cubic |
3 |
2.297 |
1.921 |
2.278 |
1.940 |
| quartic |
4 |
21.558 |
19.653 |
21.368 |
19.672 |
| quintic |
5 |
168.510 |
160.494 |
168.320 |
160.684 |
| sextic |
6 |
1.139.894 |
1.108.870 |
1.138.564 |
1.109.060 |
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