Reduction formula for point group Td
Characters for molecular motions
| Motion |
E |
8C3 |
3C2 |
6S4 |
6 d |
| Cartesian 3N |
156 |
0 |
0 |
0 |
14 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
1 |
-1 |
| Vibration |
150 |
0 |
2 |
0 |
14 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Cartesian 3N |
10 |
3 |
13 |
16 |
23 |
65 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
0 |
1 |
0 |
1 |
| Vibration |
10 |
3 |
13 |
15 |
22 |
63 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
10 |
| Number of vibrational modes |
63 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Linear (IR) |
10 |
3 |
13 |
15 |
22 |
22 / 41 |
| Quadratic (Raman) |
10 |
3 |
13 |
15 |
22 |
45 / 18 |
| IR + Raman |
- |
3 |
- |
15 |
22 |
22 / 18 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
8C3 |
3C2 |
6S4 |
6d |
| linear |
1 |
150 |
0 |
2 |
0 |
14 |
| quadratic |
2 |
11.325 |
0 |
77 |
1 |
173 |
| cubic |
3 |
573.800 |
50 |
152 |
0 |
1.512 |
| quartic |
4 |
21.947.850 |
0 |
3.002 |
38 |
11.866 |
| quintic |
5 |
675.993.780 |
0 |
5.852 |
0 |
79.492 |
| sextic |
6 |
17.463.172.650 |
1.275 |
79.002 |
38 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
T1 |
T2 |
| linear |
1 |
10 |
3 |
13 |
15 |
22 |
| quadratic |
2 |
525 |
438 |
963 |
1.363 |
1.449 |
| cubic |
3 |
24.322 |
23.566 |
47.838 |
71.328 |
72.084 |
| quartic |
4 |
917.845 |
911.893 |
1.829.738 |
2.740.149 |
2.746.063 |
| quintic |
5 |
28.187.012 |
28.147.266 |
56.334.278 |
84.478.618 |
84.518.364 |
| sextic |
6 |
727.765.014 |
727.519.974 |
1.455.283.713 |
2.182.764.205 |
2.183.009.207 |
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