Reduction formula for point group T
Characters for molecular motions
| Motion |
E |
4C3 |
4(C3)2 |
3C2 |
| Cartesian 3N |
78 |
0 |
0 |
-2 |
| Translation (x,y,z) |
3 |
0 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
-1 |
| Vibration |
72 |
0 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A |
E |
T |
Total |
| Cartesian 3N |
6 |
6 |
20 |
32 |
| Translation (x,y,z) |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
1 |
1 |
| Vibration |
6 |
6 |
18 |
30 |
Molecule Parameter
| Number of Atoms (N) |
26 |
| Number of internal coordinates |
72 |
| Number of independant internal coordinates |
6 |
| Number of vibrational modes |
30 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
T |
Total |
| Linear (IR) |
6 |
6 |
18 |
18 / 12 |
| Quadratic (Raman) |
6 |
6 |
18 |
30 / 0 |
| IR + Raman |
- |
- |
18 |
18 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
4C3 |
4(C3)2 |
3C2 |
| linear |
1 |
72 |
0 |
0 |
0 |
| quadratic |
2 |
2.628 |
0 |
0 |
36 |
| cubic |
3 |
64.824 |
24 |
24 |
0 |
| quartic |
4 |
1.215.450 |
0 |
0 |
666 |
| quintic |
5 |
18.474.840 |
0 |
0 |
0 |
| sextic |
6 |
237.093.780 |
300 |
300 |
8.436 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
T |
| linear |
1 |
6 |
6 |
18 |
| quadratic |
2 |
228 |
228 |
648 |
| cubic |
3 |
5.418 |
5.394 |
16.206 |
| quartic |
4 |
101.454 |
101.454 |
303.696 |
| quintic |
5 |
1.539.570 |
1.539.570 |
4.618.710 |
| sextic |
6 |
19.760.124 |
19.759.824 |
59.271.336 |
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