Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
78 |
0 |
6 |
0 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
72 |
2 |
6 |
0 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
21 |
18 |
21 |
18 |
78 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
20 |
17 |
19 |
16 |
72 |
Molecule Parameter
Number of Atoms (N) |
26 |
Number of internal coordinates |
72 |
Number of independant internal coordinates |
20 |
Number of vibrational modes |
72 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
20 |
17 |
19 |
16 |
55 / 17 |
Quadratic (Raman) |
20 |
17 |
19 |
16 |
72 / 0 |
IR + Raman |
20 |
- |
19 |
16 |
55 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
72 |
2 |
6 |
0 |
quadratic |
2 |
2.628 |
38 |
54 |
36 |
cubic |
3 |
64.824 |
74 |
254 |
0 |
quartic |
4 |
1.215.450 |
740 |
1.380 |
666 |
quintic |
5 |
18.474.840 |
1.406 |
5.466 |
0 |
sextic |
6 |
237.093.780 |
9.842 |
22.946 |
8.436 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
20 |
17 |
19 |
16 |
quadratic |
2 |
689 |
644 |
652 |
643 |
cubic |
3 |
16.288 |
16.161 |
16.251 |
16.124 |
quartic |
4 |
304.559 |
303.536 |
303.856 |
303.499 |
quintic |
5 |
4.620.428 |
4.617.695 |
4.619.725 |
4.616.992 |
sextic |
6 |
59.283.751 |
59.268.060 |
59.274.612 |
59.267.357 |
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