Reduction formula for point group D2
Characters for molecular motions
| Motion |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| Cartesian 3N |
288 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
-1 |
-1 |
-1 |
| Vibration |
282 |
2 |
2 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
B1 |
B2 |
B3 |
Total |
| Cartesian 3N |
72 |
72 |
72 |
72 |
288 |
| Translation (x,y,z) |
0 |
1 |
1 |
1 |
3 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
1 |
3 |
| Vibration |
72 |
70 |
70 |
70 |
282 |
Molecule Parameter
| Number of Atoms (N) |
96 |
| Number of internal coordinates |
282 |
| Number of independant internal coordinates |
72 |
| Number of vibrational modes |
282 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B1 |
B2 |
B3 |
Total |
| Linear (IR) |
72 |
70 |
70 |
70 |
210 / 72 |
| Quadratic (Raman) |
72 |
70 |
70 |
70 |
282 / 0 |
| IR + Raman |
- |
70 |
70 |
70 |
210 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C2 (z) |
C2 (y) |
C2 (x) |
| linear |
1 |
282 |
2 |
2 |
2 |
| quadratic |
2 |
39.903 |
143 |
143 |
143 |
| cubic |
3 |
3.777.484 |
284 |
284 |
284 |
| quartic |
4 |
269.145.735 |
10.295 |
10.295 |
10.295 |
| quintic |
5 |
15.395.136.042 |
20.306 |
20.306 |
20.306 |
| sextic |
6 |
736.400.674.009 |
497.497 |
497.497 |
497.497 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B1 |
B2 |
B3 |
| linear |
1 |
72 |
70 |
70 |
70 |
| quadratic |
2 |
10.083 |
9.940 |
9.940 |
9.940 |
| cubic |
3 |
944.584 |
944.300 |
944.300 |
944.300 |
| quartic |
4 |
67.294.155 |
67.283.860 |
67.283.860 |
67.283.860 |
| quintic |
5 |
3.848.799.240 |
3.848.778.934 |
3.848.778.934 |
3.848.778.934 |
| sextic |
6 |
184.100.541.625 |
184.100.044.128 |
184.100.044.128 |
184.100.044.128 |
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