Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
60 |
-2 |
6 |
8 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
54 |
0 |
6 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
18 |
11 |
15 |
16 |
60 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
17 |
10 |
13 |
14 |
54 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
17 |
| Number of vibrational modes |
54 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
17 |
10 |
13 |
14 |
44 / 10 |
| Quadratic (Raman) |
17 |
10 |
13 |
14 |
54 / 0 |
| IR + Raman |
17 |
- |
13 |
14 |
44 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
54 |
0 |
6 |
8 |
| quadratic |
2 |
1.485 |
27 |
45 |
59 |
| cubic |
3 |
27.720 |
0 |
200 |
304 |
| quartic |
4 |
395.010 |
378 |
930 |
1.434 |
| quintic |
5 |
4.582.116 |
0 |
3.396 |
5.760 |
| sextic |
6 |
45.057.474 |
3.654 |
12.386 |
21.542 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
17 |
10 |
13 |
14 |
| quadratic |
2 |
404 |
352 |
361 |
368 |
| cubic |
3 |
7.056 |
6.804 |
6.904 |
6.956 |
| quartic |
4 |
99.438 |
98.256 |
98.532 |
98.784 |
| quintic |
5 |
1.147.818 |
1.143.240 |
1.144.938 |
1.146.120 |
| sextic |
6 |
11.273.764 |
11.256.800 |
11.261.166 |
11.265.744 |
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