Reduction formula for point group S6
Characters for molecular motions
Motion |
E |
C3(z) |
(C3)2 |
i |
(S6)5 |
S6 |
Cartesian 3N |
252 |
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 |
246 |
0 |
0 |
0 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
Eg |
Au |
Eu |
Total |
Cartesian 3N |
42 |
42 |
42 |
42 |
168 |
Translation (x,y,z) |
0 |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
0 |
0 |
2 |
Vibration |
41 |
41 |
41 |
41 |
164 |
Molecule Parameter
Number of Atoms (N) |
84 |
Number of internal coordinates |
246 |
Number of independant internal coordinates |
41 |
Number of vibrational modes |
164 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Eg |
Au |
Eu |
Total |
Linear (IR) |
41 |
41 |
41 |
41 |
82 / 82 |
Quadratic (Raman) |
41 |
41 |
41 |
41 |
82 / 82 |
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 |
246 |
0 |
0 |
0 |
0 |
0 |
quadratic |
2 |
30.381 |
0 |
0 |
123 |
0 |
0 |
cubic |
3 |
2.511.496 |
82 |
82 |
0 |
0 |
0 |
quartic |
4 |
156.340.626 |
0 |
0 |
7.626 |
0 |
0 |
quintic |
5 |
7.817.031.300 |
0 |
0 |
0 |
0 |
0 |
sextic |
6 |
327.012.476.050 |
3.403 |
3.403 |
317.750 |
41 |
41 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Eg |
Au |
Eu |
linear |
1 |
41 |
41 |
41 |
41 |
quadratic |
2 |
5.084 |
5.084 |
5.043 |
5.043 |
cubic |
3 |
418.610 |
418.569 |
418.610 |
418.569 |
quartic |
4 |
26.058.042 |
26.058.042 |
26.055.500 |
26.055.500 |
quintic |
5 |
1.302.838.550 |
1.302.838.550 |
1.302.838.550 |
1.302.838.550 |
sextic |
6 |
54.502.133.448 |
54.502.131.726 |
54.502.027.504 |
54.502.025.823 |
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