Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
66 |
-2 |
6 |
6 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
60 |
0 |
6 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
19 |
13 |
17 |
17 |
66 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
18 |
12 |
15 |
15 |
60 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
18 |
| Number of vibrational modes |
60 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
18 |
12 |
15 |
15 |
48 / 12 |
| Quadratic (Raman) |
18 |
12 |
15 |
15 |
60 / 0 |
| IR + Raman |
18 |
- |
15 |
15 |
48 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
60 |
0 |
6 |
6 |
| quadratic |
2 |
1.830 |
30 |
48 |
48 |
| cubic |
3 |
37.820 |
0 |
218 |
218 |
| quartic |
4 |
595.665 |
465 |
1.071 |
1.071 |
| quintic |
5 |
7.624.512 |
0 |
4.032 |
4.032 |
| sextic |
6 |
82.598.880 |
4.960 |
15.456 |
15.456 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
18 |
12 |
15 |
15 |
| quadratic |
2 |
489 |
441 |
450 |
450 |
| cubic |
3 |
9.564 |
9.346 |
9.455 |
9.455 |
| quartic |
4 |
149.568 |
148.497 |
148.800 |
148.800 |
| quintic |
5 |
1.908.144 |
1.904.112 |
1.906.128 |
1.906.128 |
| sextic |
6 |
20.658.688 |
20.643.232 |
20.648.480 |
20.648.480 |
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