Reduction formula for point group S6
Characters for molecular motions
Motion |
E |
C3(z) |
(C3)2 |
i |
(S6)5 |
S6 |
Cartesian 3N |
180 |
0 |
0 |
0 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
-3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
3 |
0 |
0 |
Vibration |
174 |
0 |
0 |
0 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
Eg |
Au |
Eu |
Total |
Cartesian 3N |
30 |
30 |
30 |
30 |
120 |
Translation (x,y,z) |
0 |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
0 |
0 |
2 |
Vibration |
29 |
29 |
29 |
29 |
116 |
Molecule Parameter
Number of Atoms (N) |
60 |
Number of internal coordinates |
174 |
Number of independant internal coordinates |
29 |
Number of vibrational modes |
116 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Eg |
Au |
Eu |
Total |
Linear (IR) |
29 |
29 |
29 |
29 |
58 / 58 |
Quadratic (Raman) |
29 |
29 |
29 |
29 |
58 / 58 |
IR + Raman |
- |
- |
- |
- |
0* / 0 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3(z) |
(C3)2 |
i |
(S6)5 |
S6 |
linear |
1 |
174 |
0 |
0 |
0 |
0 |
0 |
quadratic |
2 |
15.225 |
0 |
0 |
87 |
0 |
0 |
cubic |
3 |
893.200 |
58 |
58 |
0 |
0 |
0 |
quartic |
4 |
39.524.100 |
0 |
0 |
3.828 |
0 |
0 |
quintic |
5 |
1.407.057.960 |
0 |
0 |
0 |
0 |
0 |
sextic |
6 |
41.977.229.140 |
1.711 |
1.711 |
113.564 |
29 |
29 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Eg |
Au |
Eu |
linear |
1 |
29 |
29 |
29 |
29 |
quadratic |
2 |
2.552 |
2.552 |
2.523 |
2.523 |
cubic |
3 |
148.886 |
148.857 |
148.886 |
148.857 |
quartic |
4 |
6.587.988 |
6.587.988 |
6.586.712 |
6.586.712 |
quintic |
5 |
234.509.660 |
234.509.660 |
234.509.660 |
234.509.660 |
sextic |
6 |
6.996.224.364 |
6.996.223.494 |
6.996.186.490 |
6.996.185.649 |
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