Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
30 |
-2 |
10 |
2 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
24 |
0 |
10 |
2 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
10 |
4 |
10 |
6 |
30 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
9 |
3 |
8 |
4 |
24 |
Molecule Parameter
| Number of Atoms (N) |
10 |
| Number of internal coordinates |
24 |
| Number of independant internal coordinates |
9 |
| Number of vibrational modes |
24 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
9 |
3 |
8 |
4 |
21 / 3 |
| Quadratic (Raman) |
9 |
3 |
8 |
4 |
24 / 0 |
| IR + Raman |
9 |
- |
8 |
4 |
21 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
24 |
0 |
10 |
2 |
| quadratic |
2 |
300 |
12 |
62 |
14 |
| cubic |
3 |
2.600 |
0 |
290 |
26 |
| quartic |
4 |
17.550 |
78 |
1.128 |
104 |
| quintic |
5 |
98.280 |
0 |
3.822 |
182 |
| sextic |
6 |
475.020 |
364 |
11.634 |
546 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
9 |
3 |
8 |
4 |
| quadratic |
2 |
97 |
59 |
84 |
60 |
| cubic |
3 |
729 |
571 |
716 |
584 |
| quartic |
4 |
4.715 |
4.099 |
4.624 |
4.112 |
| quintic |
5 |
25.571 |
23.569 |
25.480 |
23.660 |
| sextic |
6 |
121.891 |
115.801 |
121.436 |
115.892 |
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