Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
18 |
-2 |
6 |
2 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
12 |
0 |
6 |
2 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
6 |
2 |
6 |
4 |
18 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
5 |
1 |
4 |
2 |
12 |
Molecule Parameter
Number of Atoms (N) |
6 |
Number of internal coordinates |
12 |
Number of independant internal coordinates |
5 |
Number of vibrational modes |
12 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
5 |
1 |
4 |
2 |
11 / 1 |
Quadratic (Raman) |
5 |
1 |
4 |
2 |
12 / 0 |
IR + Raman |
5 |
- |
4 |
2 |
11 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
12 |
0 |
6 |
2 |
quadratic |
2 |
78 |
6 |
24 |
8 |
cubic |
3 |
364 |
0 |
74 |
14 |
quartic |
4 |
1.365 |
21 |
195 |
35 |
quintic |
5 |
4.368 |
0 |
456 |
56 |
sextic |
6 |
12.376 |
56 |
976 |
112 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
5 |
1 |
4 |
2 |
quadratic |
2 |
29 |
13 |
22 |
14 |
cubic |
3 |
113 |
69 |
106 |
76 |
quartic |
4 |
404 |
289 |
376 |
296 |
quintic |
5 |
1.220 |
964 |
1.192 |
992 |
sextic |
6 |
3.380 |
2.836 |
3.296 |
2.864 |
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