Reduction formula for point group T
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
| Cartesian 3N |
288 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
| Vibration |
282 |
0 |
0 |
2 |
Decomposition into Irreducible representations
| Motion |
A |
E |
T |
Total |
| Cartesian 3N |
24 |
24 |
72 |
120 |
| Translation (x,y,z) |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
| Vibration |
24 |
24 |
70 |
118 |
Molecule Parameter
| Number of Atoms (N) |
96 |
| Number of internal coordinates |
282 |
| Number of independant internal coordinates |
24 |
| Number of vibrational modes |
118 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
T |
Total |
| Linear (IR) |
24 |
24 |
70 |
70 / 48 |
| Quadratic (Raman) |
24 |
24 |
70 |
118 / 0 |
| IR + Raman |
- |
- |
70 |
70 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
| linear |
1 |
282 |
0 |
0 |
2 |
| quadratic |
2 |
39.903 |
0 |
0 |
143 |
| cubic |
3 |
3.777.484 |
94 |
94 |
284 |
| quartic |
4 |
269.145.735 |
0 |
0 |
10.295 |
| quintic |
5 |
15.395.136.042 |
0 |
0 |
20.306 |
| sextic |
6 |
736.400.674.009 |
4.465 |
4.465 |
497.497 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
T |
| linear |
1 |
24 |
24 |
70 |
| quadratic |
2 |
3.361 |
3.361 |
9.940 |
| cubic |
3 |
314.924 |
314.830 |
944.300 |
| quartic |
4 |
22.431.385 |
22.431.385 |
67.283.860 |
| quintic |
5 |
1.282.933.080 |
1.282.933.080 |
3.848.778.934 |
| sextic |
6 |
61.366.850.185 |
61.366.845.720 |
184.100.044.128 |
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