Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
36 |
0 |
0 |
4 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
30 |
2 |
0 |
4 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
10 |
8 |
8 |
10 |
36 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
9 |
7 |
6 |
8 |
30 |
Molecule Parameter
Number of Atoms (N) |
12 |
Number of internal coordinates |
30 |
Number of independant internal coordinates |
9 |
Number of vibrational modes |
30 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
9 |
7 |
6 |
8 |
23 / 7 |
Quadratic (Raman) |
9 |
7 |
6 |
8 |
30 / 0 |
IR + Raman |
9 |
- |
6 |
8 |
23 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
30 |
2 |
0 |
4 |
quadratic |
2 |
465 |
17 |
15 |
23 |
cubic |
3 |
4.960 |
32 |
0 |
72 |
quartic |
4 |
40.920 |
152 |
120 |
256 |
quintic |
5 |
278.256 |
272 |
0 |
680 |
sextic |
6 |
1.623.160 |
952 |
680 |
1.904 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
9 |
7 |
6 |
8 |
quadratic |
2 |
130 |
111 |
110 |
114 |
cubic |
3 |
1.266 |
1.230 |
1.214 |
1.250 |
quartic |
4 |
10.362 |
10.174 |
10.158 |
10.226 |
quintic |
5 |
69.802 |
69.462 |
69.326 |
69.666 |
sextic |
6 |
406.674 |
405.382 |
405.246 |
405.858 |
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