Reduction formula for point group T
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
| Cartesian 3N |
60 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
| Vibration |
54 |
0 |
0 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
E |
T |
Total |
| Cartesian 3N |
5 |
5 |
15 |
25 |
| Translation (x,y,z) |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
| Vibration |
5 |
5 |
13 |
23 |
Molecule Parameter
| Number of Atoms (N) |
20 |
| Number of internal coordinates |
54 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
23 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
T |
Total |
| Linear (IR) |
5 |
5 |
13 |
13 / 10 |
| Quadratic (Raman) |
5 |
5 |
13 |
23 / 0 |
| IR + Raman |
- |
- |
13 |
13 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
| linear |
1 |
54 |
0 |
0 |
2 |
| quadratic |
2 |
1.485 |
0 |
0 |
29 |
| cubic |
3 |
27.720 |
18 |
18 |
56 |
| quartic |
4 |
395.010 |
0 |
0 |
434 |
| quintic |
5 |
4.582.116 |
0 |
0 |
812 |
| sextic |
6 |
45.057.474 |
171 |
171 |
4.466 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
T |
| linear |
1 |
5 |
5 |
13 |
| quadratic |
2 |
131 |
131 |
364 |
| cubic |
3 |
2.336 |
2.318 |
6.916 |
| quartic |
4 |
33.026 |
33.026 |
98.644 |
| quintic |
5 |
382.046 |
382.046 |
1.145.326 |
| sextic |
6 |
3.756.020 |
3.755.849 |
11.263.252 |
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