Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
216 |
0 |
72 |
0 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
210 |
2 |
72 |
0 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
72 |
36 |
72 |
36 |
216 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
71 |
35 |
70 |
34 |
210 |
Molecule Parameter
| Number of Atoms (N) |
72 |
| Number of internal coordinates |
210 |
| Number of independant internal coordinates |
71 |
| Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
71 |
35 |
70 |
34 |
175 / 35 |
| Quadratic (Raman) |
71 |
35 |
70 |
34 |
210 / 0 |
| IR + Raman |
71 |
- |
70 |
34 |
175 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
210 |
2 |
72 |
0 |
| quadratic |
2 |
22.155 |
107 |
2.697 |
105 |
| cubic |
3 |
1.565.620 |
212 |
69.792 |
0 |
| quartic |
4 |
83.369.265 |
5.777 |
1.399.197 |
5.565 |
| quintic |
5 |
3.568.204.542 |
11.342 |
23.121.576 |
0 |
| sextic |
6 |
127.860.662.755 |
209.827 |
327.363.605 |
198.485 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
71 |
35 |
70 |
34 |
| quadratic |
2 |
6.266 |
4.865 |
6.160 |
4.864 |
| cubic |
3 |
408.906 |
374.010 |
408.800 |
373.904 |
| quartic |
4 |
21.194.951 |
20.492.570 |
21.189.280 |
20.492.464 |
| quintic |
5 |
897.834.365 |
886.273.577 |
897.828.694 |
886.267.906 |
| sextic |
6 |
32.047.108.668 |
31.883.327.623 |
32.046.904.512 |
31.883.321.952 |
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