Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
78 |
-6 |
26 |
6 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
72 |
-4 |
26 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
26 |
10 |
26 |
16 |
78 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
25 |
9 |
24 |
14 |
72 |
Molecule Parameter
| Number of Atoms (N) |
26 |
| Number of internal coordinates |
72 |
| Number of independant internal coordinates |
25 |
| Number of vibrational modes |
72 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
25 |
9 |
24 |
14 |
63 / 9 |
| Quadratic (Raman) |
25 |
9 |
24 |
14 |
72 / 0 |
| IR + Raman |
25 |
- |
24 |
14 |
63 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
72 |
-4 |
26 |
6 |
| quadratic |
2 |
2.628 |
44 |
374 |
54 |
| cubic |
3 |
64.824 |
-156 |
3.874 |
254 |
| quartic |
4 |
1.215.450 |
970 |
32.100 |
1.380 |
| quintic |
5 |
18.474.840 |
-3.116 |
225.030 |
5.466 |
| sextic |
6 |
237.093.780 |
14.364 |
1.381.730 |
22.946 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
25 |
9 |
24 |
14 |
| quadratic |
2 |
775 |
561 |
726 |
566 |
| cubic |
3 |
17.199 |
15.135 |
17.150 |
15.340 |
| quartic |
4 |
312.475 |
295.735 |
311.300 |
295.940 |
| quintic |
5 |
4.675.555 |
4.560.307 |
4.674.380 |
4.564.598 |
| sextic |
6 |
59.628.205 |
58.925.867 |
59.609.550 |
58.930.158 |
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