Reduction formula for point group S4
Characters for molecular motions
| Motion |
E |
S4 |
C2 |
(S4)3 |
| Cartesian 3N |
156 |
0 |
0 |
0 |
| Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
| Vibration |
150 |
0 |
2 |
0 |
Decomposition into Irreducible representations
| Motion |
A |
B |
E |
Total |
| Cartesian 3N |
39 |
39 |
39 |
117 |
| Translation (x,y,z) |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
| Vibration |
38 |
38 |
37 |
113 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
38 |
| Number of vibrational modes |
113 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
B |
E |
Total |
| Linear (IR) |
38 |
38 |
37 |
75 / 38 |
| Quadratic (Raman) |
38 |
38 |
37 |
113 / 0 |
| IR + Raman |
- |
38 |
37 |
75 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
S4 |
C2 |
(S4)3 |
| linear |
1 |
150 |
0 |
2 |
0 |
| quadratic |
2 |
11.325 |
1 |
77 |
1 |
| cubic |
3 |
573.800 |
0 |
152 |
0 |
| quartic |
4 |
21.947.850 |
38 |
3.002 |
38 |
| quintic |
5 |
675.993.780 |
0 |
5.852 |
0 |
| sextic |
6 |
17.463.172.650 |
38 |
79.002 |
38 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
B |
E |
| linear |
1 |
38 |
38 |
37 |
| quadratic |
2 |
2.851 |
2.850 |
2.812 |
| cubic |
3 |
143.488 |
143.488 |
143.412 |
| quartic |
4 |
5.487.732 |
5.487.694 |
5.486.212 |
| quintic |
5 |
168.999.908 |
168.999.908 |
168.996.982 |
| sextic |
6 |
4.365.812.932 |
4.365.812.894 |
4.365.773.412 |
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