Reduction formula for point group C2v
Characters for molecular motions
| Motion |
E |
C2 (z) |
 v(xz) |
v(yz) |
| Cartesian 3N |
216 |
0 |
0 |
8 |
| Translation (x,y,z) |
3 |
-1 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
210 |
2 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
B1 |
B2 |
Total |
| Cartesian 3N |
56 |
52 |
52 |
56 |
216 |
| Translation (x,y,z) |
1 |
0 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
55 |
51 |
50 |
54 |
210 |
Molecule Parameter
| Number of Atoms (N) |
72 |
| Number of internal coordinates |
210 |
| Number of independant internal coordinates |
55 |
| Number of vibrational modes |
210 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
B1 |
B2 |
Total |
| Linear (IR) |
55 |
51 |
50 |
54 |
159 / 51 |
| Quadratic (Raman) |
55 |
51 |
50 |
54 |
210 / 0 |
| IR + Raman |
55 |
- |
50 |
54 |
159 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
v(xz) |
v(yz) |
| linear |
1 |
210 |
2 |
0 |
8 |
| quadratic |
2 |
22.155 |
107 |
105 |
137 |
| cubic |
3 |
1.565.620 |
212 |
0 |
928 |
| quartic |
4 |
83.369.265 |
5.777 |
5.565 |
9.117 |
| quintic |
5 |
3.568.204.542 |
11.342 |
0 |
54.120 |
| sextic |
6 |
127.860.662.755 |
209.827 |
198.485 |
397.333 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
B1 |
B2 |
| linear |
1 |
55 |
51 |
50 |
54 |
| quadratic |
2 |
5.626 |
5.505 |
5.504 |
5.520 |
| cubic |
3 |
391.690 |
391.226 |
391.120 |
391.584 |
| quartic |
4 |
20.847.431 |
20.840.090 |
20.839.984 |
20.841.760 |
| quintic |
5 |
892.067.501 |
892.040.441 |
892.034.770 |
892.061.830 |
| sextic |
6 |
31.965.367.100 |
31.965.069.191 |
31.965.063.520 |
31.965.162.944 |
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