Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
60 |
0 |
12 |
8 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
54 |
2 |
12 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
20 |
10 |
16 |
14 |
60 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
19 |
9 |
14 |
12 |
54 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
19 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
19 |
9 |
14 |
12 |
45 / 9 |
| Quadratic (Raman) |
19 |
9 |
14 |
12 |
54 / 0 |
| IR + Raman |
19 |
- |
14 |
12 |
45 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
54 |
2 |
12 |
8 |
| quadratic |
2 |
1.485 |
29 |
99 |
59 |
| cubic |
3 |
27.720 |
56 |
616 |
304 |
| quartic |
4 |
395.010 |
434 |
3.234 |
1.434 |
| quintic |
5 |
4.582.116 |
812 |
14.784 |
5.760 |
| sextic |
6 |
45.057.474 |
4.466 |
60.830 |
21.542 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
19 |
9 |
14 |
12 |
| quadratic |
2 |
418 |
339 |
374 |
354 |
| cubic |
3 |
7.174 |
6.714 |
6.994 |
6.838 |
| quartic |
4 |
100.028 |
97.694 |
99.094 |
98.194 |
| quintic |
5 |
1.150.868 |
1.140.596 |
1.147.582 |
1.143.070 |
| sextic |
6 |
11.286.078 |
11.244.892 |
11.273.074 |
11.253.430 |
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