Reduction formula for point group Td
Characters for molecular motions
| Motion |
E |
8C3 |
3C2 |
6S4 |
6 d |
| Cartesian 3N |
39 |
0 |
-5 |
-1 |
5 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
1 |
-1 |
| Vibration |
33 |
0 |
-3 |
-1 |
5 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Cartesian 3N |
2 |
0 |
2 |
4 |
7 |
15 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
0 |
1 |
0 |
1 |
| Vibration |
2 |
0 |
2 |
3 |
6 |
13 |
Molecule Parameter
| Number of Atoms (N) |
13 |
| Number of internal coordinates |
33 |
| Number of independant internal coordinates |
2 |
| Number of vibrational modes |
13 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Linear (IR) |
2 |
0 |
2 |
3 |
6 |
6 / 7 |
| Quadratic (Raman) |
2 |
0 |
2 |
3 |
6 |
10 / 3 |
| IR + Raman |
- |
0 |
- |
3 |
6 |
6 / 3 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
8C3 |
3C2 |
6S4 |
6d |
| linear |
1 |
33 |
0 |
-3 |
-1 |
5 |
| quadratic |
2 |
561 |
0 |
21 |
-1 |
29 |
| cubic |
3 |
6.545 |
11 |
-55 |
1 |
105 |
| quartic |
4 |
58.905 |
0 |
225 |
9 |
385 |
| quintic |
5 |
435.897 |
0 |
-531 |
-9 |
1.141 |
| sextic |
6 |
2.760.681 |
66 |
1.653 |
-9 |
3.325 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
T1 |
T2 |
| linear |
1 |
2 |
0 |
2 |
3 |
6 |
| quadratic |
2 |
33 |
19 |
52 |
60 |
75 |
| cubic |
3 |
296 |
243 |
528 |
799 |
851 |
| quartic |
4 |
2.581 |
2.384 |
4.965 |
7.241 |
7.429 |
| quintic |
5 |
18.379 |
17.813 |
36.192 |
54.266 |
54.841 |
| sextic |
6 |
116.086 |
114.428 |
230.448 |
344.045 |
345.712 |
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