Reduction formula for point group Td
Characters for molecular motions
| Motion |
E |
8C3 |
3C2 |
6S4 |
6 d |
| Cartesian 3N |
66 |
0 |
-2 |
0 |
6 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-1 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
1 |
-1 |
| Vibration |
60 |
0 |
0 |
0 |
6 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Cartesian 3N |
4 |
1 |
5 |
7 |
10 |
27 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
| Rotation (Rx,Ry,Rz) |
0 |
0 |
0 |
1 |
0 |
1 |
| Vibration |
4 |
1 |
5 |
6 |
9 |
25 |
Molecule Parameter
| Number of Atoms (N) |
22 |
| Number of internal coordinates |
60 |
| Number of independant internal coordinates |
4 |
| Number of vibrational modes |
25 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
T1 |
T2 |
Total |
| Linear (IR) |
4 |
1 |
5 |
6 |
9 |
9 / 16 |
| Quadratic (Raman) |
4 |
1 |
5 |
6 |
9 |
18 / 7 |
| IR + Raman |
- |
1 |
- |
6 |
9 |
9 / 7 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
8C3 |
3C2 |
6S4 |
6d |
| linear |
1 |
60 |
0 |
0 |
0 |
6 |
| quadratic |
2 |
1.830 |
0 |
30 |
0 |
48 |
| cubic |
3 |
37.820 |
20 |
0 |
0 |
218 |
| quartic |
4 |
595.665 |
0 |
465 |
15 |
1.071 |
| quintic |
5 |
7.624.512 |
0 |
0 |
0 |
4.032 |
| sextic |
6 |
82.598.880 |
210 |
4.960 |
0 |
15.456 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
T1 |
T2 |
| linear |
1 |
4 |
1 |
5 |
6 |
9 |
| quadratic |
2 |
92 |
68 |
160 |
213 |
237 |
| cubic |
3 |
1.637 |
1.528 |
3.145 |
4.673 |
4.782 |
| quartic |
4 |
25.149 |
24.606 |
49.755 |
74.136 |
74.664 |
| quintic |
5 |
318.696 |
316.680 |
635.376 |
952.056 |
954.072 |
| sextic |
6 |
3.446.174 |
3.438.446 |
6.884.410 |
10.320.376 |
10.328.104 |
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