Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
84 |
0 |
6 |
6 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
78 |
2 |
6 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
24 |
18 |
21 |
21 |
84 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
23 |
17 |
19 |
19 |
78 |
Molecule Parameter
| Number of Atoms (N) |
28 |
| Number of internal coordinates |
78 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
78 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
23 |
17 |
19 |
19 |
61 / 17 |
| Quadratic (Raman) |
23 |
17 |
19 |
19 |
78 / 0 |
| IR + Raman |
23 |
- |
19 |
19 |
61 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
78 |
2 |
6 |
6 |
| quadratic |
2 |
3.081 |
41 |
57 |
57 |
| cubic |
3 |
82.160 |
80 |
272 |
272 |
| quartic |
4 |
1.663.740 |
860 |
1.548 |
1.548 |
| quintic |
5 |
27.285.336 |
1.640 |
6.264 |
6.264 |
| sextic |
6 |
377.447.148 |
12.300 |
27.420 |
27.420 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
23 |
17 |
19 |
19 |
| quadratic |
2 |
809 |
752 |
760 |
760 |
| cubic |
3 |
20.696 |
20.424 |
20.520 |
20.520 |
| quartic |
4 |
416.924 |
415.376 |
415.720 |
415.720 |
| quintic |
5 |
6.824.876 |
6.818.612 |
6.820.924 |
6.820.924 |
| sextic |
6 |
94.378.572 |
94.351.152 |
94.358.712 |
94.358.712 |
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