Reduction formula for point group C2v
Characters for molecular motions
Motion |
E |
C2 (z) |
v(xz) |
v(yz) |
Cartesian 3N |
63 |
-1 |
1 |
5 |
Translation (x,y,z) |
3 |
-1 |
1 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
Vibration |
57 |
1 |
1 |
5 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
B1 |
B2 |
Total |
Cartesian 3N |
17 |
14 |
15 |
17 |
63 |
Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
Vibration |
16 |
13 |
13 |
15 |
57 |
Molecule Parameter
Number of Atoms (N) |
21 |
Number of internal coordinates |
57 |
Number of independant internal coordinates |
16 |
Number of vibrational modes |
57 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
B1 |
B2 |
Total |
Linear (IR) |
16 |
13 |
13 |
15 |
44 / 13 |
Quadratic (Raman) |
16 |
13 |
13 |
15 |
57 / 0 |
IR + Raman |
16 |
- |
13 |
15 |
44 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
linear |
1 |
57 |
1 |
1 |
5 |
quadratic |
2 |
1.653 |
29 |
29 |
41 |
cubic |
3 |
32.509 |
29 |
29 |
165 |
quartic |
4 |
487.635 |
435 |
435 |
811 |
quintic |
5 |
5.949.147 |
435 |
435 |
2.791 |
sextic |
6 |
61.474.519 |
4.495 |
4.495 |
10.571 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
B1 |
B2 |
linear |
1 |
16 |
13 |
13 |
15 |
quadratic |
2 |
438 |
403 |
403 |
409 |
cubic |
3 |
8.183 |
8.086 |
8.086 |
8.154 |
quartic |
4 |
122.329 |
121.706 |
121.706 |
121.894 |
quintic |
5 |
1.488.202 |
1.486.589 |
1.486.589 |
1.487.767 |
sextic |
6 |
15.373.520 |
15.365.987 |
15.365.987 |
15.369.025 |
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