Reduction formula for point group S4
Characters for molecular motions
| Motion |
E |
S4 |
C2 |
(S4)3 |
| Cartesian 3N |
24 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
| Vibration |
18 |
0 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
A |
B |
E |
Total |
| Cartesian 3N |
6 |
6 |
6 |
18 |
| Translation (x,y,z) |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
| Vibration |
5 |
5 |
4 |
14 |
Molecule Parameter
| Number of Atoms (N) |
8 |
| Number of internal coordinates |
18 |
| Number of independant internal coordinates |
5 |
| Number of vibrational modes |
14 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
E |
Total |
| Linear (IR) |
5 |
5 |
4 |
9 / 5 |
| Quadratic (Raman) |
5 |
5 |
4 |
14 / 0 |
| IR + Raman |
- |
5 |
4 |
9 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
S4 |
C2 |
(S4)3 |
| linear |
1 |
18 |
0 |
2 |
0 |
| quadratic |
2 |
171 |
1 |
11 |
1 |
| cubic |
3 |
1.140 |
0 |
20 |
0 |
| quartic |
4 |
5.985 |
5 |
65 |
5 |
| quintic |
5 |
26.334 |
0 |
110 |
0 |
| sextic |
6 |
100.947 |
5 |
275 |
5 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
E |
| linear |
1 |
5 |
5 |
4 |
| quadratic |
2 |
46 |
45 |
40 |
| cubic |
3 |
290 |
290 |
280 |
| quartic |
4 |
1.515 |
1.510 |
1.480 |
| quintic |
5 |
6.611 |
6.611 |
6.556 |
| sextic |
6 |
25.308 |
25.303 |
25.168 |
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