Reduction formula for point group Td
Characters for molecular motions
| Motion |
E |
8C3 |
3C2 |
6S4 |
6 d |
| Cartesian 3N |
84 |
0 |
0 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
1 |
-1 |
| Vibration |
78 |
0 |
2 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Cartesian 3N |
5 |
2 |
7 |
9 |
12 |
35 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
0 |
1 |
0 |
1 |
| Vibration |
5 |
2 |
7 |
8 |
11 |
33 |
Molecule Parameter
| Number of Atoms (N) |
28 |
| Number of internal coordinates |
78 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
33 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Linear (IR) |
5 |
2 |
7 |
8 |
11 |
11 / 22 |
| Quadratic (Raman) |
5 |
2 |
7 |
8 |
11 |
23 / 10 |
| IR + Raman |
- |
2 |
- |
8 |
11 |
11 / 10 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
8C3 |
3C2 |
6S4 |
6d |
| linear |
1 |
78 |
0 |
2 |
0 |
6 |
| quadratic |
2 |
3.081 |
0 |
41 |
1 |
57 |
| cubic |
3 |
82.160 |
26 |
80 |
0 |
272 |
| quartic |
4 |
1.663.740 |
0 |
860 |
20 |
1.548 |
| quintic |
5 |
27.285.336 |
0 |
1.640 |
0 |
6.264 |
| sextic |
6 |
377.447.148 |
351 |
12.300 |
20 |
27.420 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
T1 |
T2 |
| linear |
1 |
5 |
2 |
7 |
8 |
11 |
| quadratic |
2 |
148 |
119 |
267 |
366 |
394 |
| cubic |
3 |
3.510 |
3.374 |
6.858 |
10.192 |
10.328 |
| quartic |
4 |
69.822 |
69.038 |
138.860 |
207.478 |
208.242 |
| quintic |
5 |
1.138.660 |
1.135.528 |
2.274.188 |
3.408.896 |
3.412.028 |
| sextic |
6 |
15.735.479 |
15.721.759 |
31.456.887 |
47.172.506 |
47.186.206 |
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