Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
108 |
0 |
0 |
4 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
102 |
2 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
28 |
26 |
26 |
28 |
108 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
27 |
25 |
24 |
26 |
102 |
Molecule Parameter
| Number of Atoms (N) |
36 |
| Number of internal coordinates |
102 |
| Number of independant internal coordinates |
27 |
| Number of vibrational modes |
102 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
27 |
25 |
24 |
26 |
77 / 25 |
| Quadratic (Raman) |
27 |
25 |
24 |
26 |
102 / 0 |
| IR + Raman |
27 |
- |
24 |
26 |
77 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
102 |
2 |
0 |
4 |
| quadratic |
2 |
5.253 |
53 |
51 |
59 |
| cubic |
3 |
182.104 |
104 |
0 |
216 |
| quartic |
4 |
4.780.230 |
1.430 |
1.326 |
1.750 |
| quintic |
5 |
101.340.876 |
2.756 |
0 |
5.936 |
| sextic |
6 |
1.807.245.622 |
26.182 |
23.426 |
34.874 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
27 |
25 |
24 |
26 |
| quadratic |
2 |
1.354 |
1.299 |
1.298 |
1.302 |
| cubic |
3 |
45.606 |
45.498 |
45.446 |
45.554 |
| quartic |
4 |
1.196.184 |
1.194.646 |
1.194.594 |
1.194.806 |
| quintic |
5 |
25.337.392 |
25.334.424 |
25.333.046 |
25.336.014 |
| sextic |
6 |
451.832.526 |
451.803.376 |
451.801.998 |
451.807.722 |
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