Reduction formula for point group T
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
| Cartesian 3N |
66 |
0 |
0 |
-2 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
| Vibration |
60 |
0 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A |
E |
T |
Total |
| Cartesian 3N |
5 |
5 |
17 |
27 |
| Translation (x,y,z) |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
| Vibration |
5 |
5 |
15 |
25 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
25 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
T |
Total |
| Linear (IR) |
5 |
5 |
15 |
15 / 10 |
| Quadratic (Raman) |
5 |
5 |
15 |
25 / 0 |
| IR + Raman |
- |
- |
15 |
15 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
| linear |
1 |
60 |
0 |
0 |
0 |
| quadratic |
2 |
1.830 |
0 |
0 |
30 |
| cubic |
3 |
37.820 |
20 |
20 |
0 |
| quartic |
4 |
595.665 |
0 |
0 |
465 |
| quintic |
5 |
7.624.512 |
0 |
0 |
0 |
| sextic |
6 |
82.598.880 |
210 |
210 |
4.960 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
T |
| linear |
1 |
5 |
5 |
15 |
| quadratic |
2 |
160 |
160 |
450 |
| cubic |
3 |
3.165 |
3.145 |
9.455 |
| quartic |
4 |
49.755 |
49.755 |
148.800 |
| quintic |
5 |
635.376 |
635.376 |
1.906.128 |
| sextic |
6 |
6.884.620 |
6.884.410 |
20.648.480 |
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