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 |
156 |
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 |
150 |
0 |
0 |
2 |
0 |
0 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
Total |
| Cartesian 3N |
7 |
7 |
19 |
6 |
6 |
20 |
65 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
| Vibration |
7 |
7 |
18 |
6 |
6 |
19 |
63 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
7 |
| Number of vibrational modes |
63 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
Total |
| Linear (IR) |
7 |
7 |
18 |
6 |
6 |
19 |
19 / 44 |
| Quadratic (Raman) |
7 |
7 |
18 |
6 |
6 |
19 |
32 / 31 |
| IR + Raman |
- |
- |
- |
6 |
6 |
- |
0* / 12 |
* 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 |
150 |
0 |
0 |
2 |
0 |
0 |
0 |
4 |
| quadratic |
2 |
11.325 |
0 |
0 |
77 |
75 |
0 |
0 |
83 |
| cubic |
3 |
573.800 |
50 |
50 |
152 |
0 |
0 |
0 |
312 |
| quartic |
4 |
21.947.850 |
0 |
0 |
3.002 |
2.850 |
0 |
0 |
3.466 |
| quintic |
5 |
675.993.780 |
0 |
0 |
5.852 |
0 |
0 |
0 |
12.320 |
| sextic |
6 |
17.463.172.650 |
1.275 |
1.275 |
79.002 |
73.150 |
25 |
25 |
97.174 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
Ag |
Eg |
Tg |
Au |
Eu |
Tu |
| linear |
1 |
7 |
7 |
18 |
6 |
6 |
19 |
| quadratic |
2 |
495 |
495 |
1.405 |
468 |
468 |
1.407 |
| cubic |
3 |
23.983 |
23.958 |
71.667 |
23.905 |
23.880 |
71.745 |
| quartic |
4 |
915.421 |
915.421 |
2.743.029 |
914.317 |
914.317 |
2.743.183 |
| quintic |
5 |
28.168.679 |
28.168.679 |
84.496.951 |
28.165.599 |
28.165.599 |
84.500.031 |
| sextic |
6 |
727.657.697 |
727.657.047 |
2.182.883.703 |
727.627.291 |
727.626.666 |
2.182.889.709 |
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