Reduction formula for point group C2
Characters for molecular motions
| Motion |
E |
C2 |
| Cartesian 3N |
54 |
-4 |
| Translation (x,y,z) |
3 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
| Vibration |
48 |
-2 |
Decomposition into Irreducible representations
| Motion |
A |
B |
Total |
| Cartesian 3N |
25 |
29 |
54 |
| Translation (x,y,z) |
1 |
2 |
3 |
| Rotation (Rx,Ry,Rz) |
1 |
2 |
3 |
| Vibration |
23 |
25 |
48 |
Molecule Parameter
| Number of Atoms (N) |
18 |
| Number of internal coordinates |
48 |
| Number of independant internal coordinates |
23 |
| Number of vibrational modes |
48 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
Total |
| Linear (IR) |
23 |
25 |
48 / 0 |
| Quadratic (Raman) |
23 |
25 |
48 / 0 |
| IR + Raman |
23 |
25 |
48 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 |
| linear |
1 |
48 |
-2 |
| quadratic |
2 |
1.176 |
26 |
| cubic |
3 |
19.600 |
-50 |
| quartic |
4 |
249.900 |
350 |
| quintic |
5 |
2.598.960 |
-650 |
| sextic |
6 |
22.957.480 |
3.250 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
| linear |
1 |
23 |
25 |
| quadratic |
2 |
601 |
575 |
| cubic |
3 |
9.775 |
9.825 |
| quartic |
4 |
125.125 |
124.775 |
| quintic |
5 |
1.299.155 |
1.299.805 |
| sextic |
6 |
11.480.365 |
11.477.115 |
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