Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
108 |
-4 |
36 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
102 |
-2 |
36 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
36 |
16 |
36 |
20 |
108 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
35 |
15 |
34 |
18 |
102 |
Molecule Parameter
| Number of Atoms (N) |
36 |
| Number of internal coordinates |
102 |
| Number of independant internal coordinates |
35 |
| Number of vibrational modes |
102 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
35 |
15 |
34 |
18 |
87 / 15 |
| Quadratic (Raman) |
35 |
15 |
34 |
18 |
102 / 0 |
| IR + Raman |
35 |
- |
34 |
18 |
87 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
102 |
-2 |
36 |
4 |
| quadratic |
2 |
5.253 |
53 |
699 |
59 |
| cubic |
3 |
182.104 |
-104 |
9.624 |
216 |
| quartic |
4 |
4.780.230 |
1.430 |
104.790 |
1.750 |
| quintic |
5 |
101.340.876 |
-2.756 |
956.592 |
5.936 |
| sextic |
6 |
1.807.245.622 |
26.182 |
7.590.842 |
34.874 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
35 |
15 |
34 |
18 |
| quadratic |
2 |
1.516 |
1.137 |
1.460 |
1.140 |
| cubic |
3 |
47.960 |
43.040 |
47.904 |
43.200 |
| quartic |
4 |
1.222.050 |
1.168.780 |
1.220.460 |
1.168.940 |
| quintic |
5 |
25.575.162 |
25.093.898 |
25.573.572 |
25.098.244 |
| sextic |
6 |
453.724.380 |
449.911.522 |
453.693.852 |
449.915.868 |
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