Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
15 |
-1 |
3 |
3 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
9 |
1 |
3 |
3 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
5 |
2 |
4 |
4 |
15 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
4 |
1 |
2 |
2 |
9 |
Molecule Parameter
Number of Atoms (N) |
5 |
Number of internal coordinates |
9 |
Number of independant internal coordinates |
4 |
Number of vibrational modes |
9 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
4 |
1 |
2 |
2 |
8 / 1 |
Quadratic (Raman) |
4 |
1 |
2 |
2 |
9 / 0 |
IR + Raman |
4 |
- |
2 |
2 |
8 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
9 |
1 |
3 |
3 |
quadratic |
2 |
45 |
5 |
9 |
9 |
cubic |
3 |
165 |
5 |
19 |
19 |
quartic |
4 |
495 |
15 |
39 |
39 |
quintic |
5 |
1.287 |
15 |
69 |
69 |
sextic |
6 |
3.003 |
35 |
119 |
119 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
4 |
1 |
2 |
2 |
quadratic |
2 |
17 |
8 |
10 |
10 |
cubic |
3 |
52 |
33 |
40 |
40 |
quartic |
4 |
147 |
108 |
120 |
120 |
quintic |
5 |
360 |
291 |
318 |
318 |
sextic |
6 |
819 |
700 |
742 |
742 |
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