Reduction formula for point group S4
Characters for molecular motions
| Motion |
E |
S4 |
C2 |
(S4)3 |
| Cartesian 3N |
27 |
-1 |
-1 |
-1 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
| Vibration |
21 |
-1 |
1 |
-1 |
Decomposition into Irreducible representations
| Motion |
A |
B |
E |
Total |
| Cartesian 3N |
6 |
7 |
7 |
20 |
| Translation (x,y,z) |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
| Vibration |
5 |
6 |
5 |
16 |
Molecule Parameter
| Number of Atoms (N) |
9 |
| Number of internal coordinates |
21 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
16 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
E |
Total |
| Linear (IR) |
5 |
6 |
5 |
11 / 5 |
| Quadratic (Raman) |
5 |
6 |
5 |
16 / 0 |
| IR + Raman |
- |
6 |
5 |
11 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
S4 |
C2 |
(S4)3 |
| linear |
1 |
21 |
-1 |
1 |
-1 |
| quadratic |
2 |
231 |
1 |
11 |
1 |
| cubic |
3 |
1.771 |
-1 |
11 |
-1 |
| quartic |
4 |
10.626 |
6 |
66 |
6 |
| quintic |
5 |
53.130 |
-6 |
66 |
-6 |
| sextic |
6 |
230.230 |
6 |
286 |
6 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
E |
| linear |
1 |
5 |
6 |
5 |
| quadratic |
2 |
61 |
60 |
55 |
| cubic |
3 |
445 |
446 |
440 |
| quartic |
4 |
2.676 |
2.670 |
2.640 |
| quintic |
5 |
13.296 |
13.302 |
13.266 |
| sextic |
6 |
57.632 |
57.626 |
57.486 |
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