Reduction formula for point group S4
Characters for molecular motions
| Motion |
E |
S4 |
C2 |
(S4)3 |
| Cartesian 3N |
75 |
-1 |
-1 |
-1 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
| Vibration |
69 |
-1 |
1 |
-1 |
Decomposition into Irreducible representations
| Motion |
A |
B |
E |
Total |
| Cartesian 3N |
18 |
19 |
19 |
56 |
| Translation (x,y,z) |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
| Vibration |
17 |
18 |
17 |
52 |
Molecule Parameter
| Number of Atoms (N) |
25 |
| Number of internal coordinates |
69 |
| Number of independant internal coordinates |
17 |
| Number of vibrational modes |
52 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
E |
Total |
| Linear (IR) |
17 |
18 |
17 |
35 / 17 |
| Quadratic (Raman) |
17 |
18 |
17 |
52 / 0 |
| IR + Raman |
- |
18 |
17 |
35 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
S4 |
C2 |
(S4)3 |
| linear |
1 |
69 |
-1 |
1 |
-1 |
| quadratic |
2 |
2.415 |
1 |
35 |
1 |
| cubic |
3 |
57.155 |
-1 |
35 |
-1 |
| quartic |
4 |
1.028.790 |
18 |
630 |
18 |
| quintic |
5 |
15.020.334 |
-18 |
630 |
-18 |
| sextic |
6 |
185.250.786 |
18 |
7.770 |
18 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
E |
| linear |
1 |
17 |
18 |
17 |
| quadratic |
2 |
613 |
612 |
595 |
| cubic |
3 |
14.297 |
14.298 |
14.280 |
| quartic |
4 |
257.364 |
257.346 |
257.040 |
| quintic |
5 |
3.755.232 |
3.755.250 |
3.754.926 |
| sextic |
6 |
46.314.648 |
46.314.630 |
46.310.754 |
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