Reduction formula for point group C2
Characters for molecular motions
| Motion |
E |
C2 |
| Cartesian 3N |
240 |
0 |
| Translation (x,y,z) |
3 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
234 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
B |
Total |
| Cartesian 3N |
120 |
120 |
240 |
| Translation (x,y,z) |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
118 |
116 |
234 |
Molecule Parameter
| Number of Atoms (N) |
80 |
| Number of internal coordinates |
234 |
| Number of independant internal coordinates |
118 |
| Number of vibrational modes |
234 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
Total |
| Linear (IR) |
118 |
116 |
234 / 0 |
| Quadratic (Raman) |
118 |
116 |
234 / 0 |
| IR + Raman |
118 |
116 |
234 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 |
| linear |
1 |
234 |
2 |
| quadratic |
2 |
27.495 |
119 |
| cubic |
3 |
2.162.940 |
236 |
| quartic |
4 |
128.154.195 |
7.139 |
| quintic |
5 |
6.100.139.682 |
14.042 |
| sextic |
6 |
242.988.897.333 |
287.861 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
| linear |
1 |
118 |
116 |
| quadratic |
2 |
13.807 |
13.688 |
| cubic |
3 |
1.081.588 |
1.081.352 |
| quartic |
4 |
64.080.667 |
64.073.528 |
| quintic |
5 |
3.050.076.862 |
3.050.062.820 |
| sextic |
6 |
121.494.592.597 |
121.494.304.736 |
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