Reduction formula for point group Th
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
i |
4(S6)5 |
4S6 |
3 h |
| Cartesian 3N |
180 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
-3 |
0 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
3 |
0 |
0 |
-1 |
| Vibration |
174 |
0 |
0 |
2 |
0 |
0 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
Total |
| Cartesian 3N |
8 |
8 |
22 |
7 |
7 |
23 |
75 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
| Vibration |
8 |
8 |
21 |
7 |
7 |
22 |
73 |
Molecule Parameter
| Number of Atoms (N) |
60 |
| Number of internal coordinates |
174 |
| Number of independant internal coordinates |
8 |
| Number of vibrational modes |
73 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
Total |
| Linear (IR) |
8 |
8 |
21 |
7 |
7 |
22 |
22 / 51 |
| Quadratic (Raman) |
8 |
8 |
21 |
7 |
7 |
22 |
37 / 36 |
| IR + Raman |
- |
- |
- |
7 |
7 |
- |
0* / 14 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
i |
4(S6)5 |
4S6 |
3h |
| linear |
1 |
174 |
0 |
0 |
2 |
0 |
0 |
0 |
4 |
| quadratic |
2 |
15.225 |
0 |
0 |
89 |
87 |
0 |
0 |
95 |
| cubic |
3 |
893.200 |
58 |
58 |
176 |
0 |
0 |
0 |
360 |
| quartic |
4 |
39.524.100 |
0 |
0 |
4.004 |
3.828 |
0 |
0 |
4.540 |
| quintic |
5 |
1.407.057.960 |
0 |
0 |
7.832 |
0 |
0 |
0 |
16.376 |
| sextic |
6 |
41.977.229.140 |
1.711 |
1.711 |
121.396 |
113.564 |
29 |
29 |
145.604 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
| linear |
1 |
8 |
8 |
21 |
7 |
7 |
22 |
| quadratic |
2 |
661 |
661 |
1.891 |
630 |
630 |
1.893 |
| cubic |
3 |
37.303 |
37.274 |
111.583 |
37.213 |
37.184 |
111.673 |
| quartic |
4 |
1.648.065 |
1.648.065 |
4.939.923 |
1.646.611 |
1.646.611 |
4.940.101 |
| quintic |
5 |
58.630.441 |
58.630.441 |
175.879.219 |
58.626.347 |
58.626.347 |
175.883.313 |
| sextic |
6 |
1.749.089.901 |
1.749.089.031 |
5.247.134.463 |
1.749.044.017 |
1.749.043.176 |
5.247.142.473 |
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