Reduction formula for point group C2
Characters for molecular motions
| Motion |
E |
C2 |
| Cartesian 3N |
135 |
-1 |
| Translation (x,y,z) |
3 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
129 |
1 |
Decomposition into Irreducible representations
| Motion |
A |
B |
Total |
| Cartesian 3N |
67 |
68 |
135 |
| Translation (x,y,z) |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
65 |
64 |
129 |
Molecule Parameter
| Number of Atoms (N) |
45 |
| Number of internal coordinates |
129 |
| Number of independant internal coordinates |
65 |
| Number of vibrational modes |
129 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
Total |
| Linear (IR) |
65 |
64 |
129 / 0 |
| Quadratic (Raman) |
65 |
64 |
129 / 0 |
| IR + Raman |
65 |
64 |
129 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 |
| linear |
1 |
129 |
1 |
| quadratic |
2 |
8.385 |
65 |
| cubic |
3 |
366.145 |
65 |
| quartic |
4 |
12.082.785 |
2.145 |
| quintic |
5 |
321.402.081 |
2.145 |
| sextic |
6 |
7.177.979.809 |
47.905 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
| linear |
1 |
65 |
64 |
| quadratic |
2 |
4.225 |
4.160 |
| cubic |
3 |
183.105 |
183.040 |
| quartic |
4 |
6.042.465 |
6.040.320 |
| quintic |
5 |
160.702.113 |
160.699.968 |
| sextic |
6 |
3.589.013.857 |
3.588.965.952 |
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