Reduction formula for point group S4
Characters for molecular motions
Motion |
E |
S4 |
C2 |
(S4)3 |
Cartesian 3N |
51 |
-1 |
-1 |
-1 |
Translation (x,y,z) |
3 |
-1 |
-1 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
1 |
-1 |
1 |
Vibration |
45 |
-1 |
1 |
-1 |
Decomposition into Irreducible representations
Motion |
A |
B |
E |
Total |
Cartesian 3N |
12 |
13 |
13 |
38 |
Translation (x,y,z) |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
0 |
1 |
2 |
Vibration |
11 |
12 |
11 |
34 |
Molecule Parameter
Number of Atoms (N) |
17 |
Number of internal coordinates |
45 |
Number of independant internal coordinates |
11 |
Number of vibrational modes |
34 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
B |
E |
Total |
Linear (IR) |
11 |
12 |
11 |
23 / 11 |
Quadratic (Raman) |
11 |
12 |
11 |
34 / 0 |
IR + Raman |
- |
12 |
11 |
23 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
S4 |
C2 |
(S4)3 |
linear |
1 |
45 |
-1 |
1 |
-1 |
quadratic |
2 |
1.035 |
1 |
23 |
1 |
cubic |
3 |
16.215 |
-1 |
23 |
-1 |
quartic |
4 |
194.580 |
12 |
276 |
12 |
quintic |
5 |
1.906.884 |
-12 |
276 |
-12 |
sextic |
6 |
15.890.700 |
12 |
2.300 |
12 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
B |
E |
linear |
1 |
11 |
12 |
11 |
quadratic |
2 |
265 |
264 |
253 |
cubic |
3 |
4.059 |
4.060 |
4.048 |
quartic |
4 |
48.720 |
48.708 |
48.576 |
quintic |
5 |
476.784 |
476.796 |
476.652 |
sextic |
6 |
3.973.256 |
3.973.244 |
3.972.100 |
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