Reduction formula for point group S6
Characters for molecular motions
Motion |
E |
C3(z) |
(C3)2 |
i |
(S6)5 |
S6 |
Cartesian 3N |
39 |
0 |
0 |
-3 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
-3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
3 |
0 |
0 |
Vibration |
33 |
0 |
0 |
-3 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
Ag |
Eg |
Au |
Eu |
Total |
Cartesian 3N |
6 |
6 |
7 |
7 |
26 |
Translation (x,y,z) |
0 |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
0 |
0 |
2 |
Vibration |
5 |
5 |
6 |
6 |
22 |
Molecule Parameter
Number of Atoms (N) |
13 |
Number of internal coordinates |
33 |
Number of independant internal coordinates |
5 |
Number of vibrational modes |
22 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
Ag |
Eg |
Au |
Eu |
Total |
Linear (IR) |
5 |
5 |
6 |
6 |
12 / 10 |
Quadratic (Raman) |
5 |
5 |
6 |
6 |
10 / 12 |
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 |
33 |
0 |
0 |
-3 |
0 |
0 |
quadratic |
2 |
561 |
0 |
0 |
21 |
0 |
0 |
cubic |
3 |
6.545 |
11 |
11 |
-55 |
-1 |
-1 |
quartic |
4 |
58.905 |
0 |
0 |
225 |
0 |
0 |
quintic |
5 |
435.897 |
0 |
0 |
-531 |
0 |
0 |
sextic |
6 |
2.760.681 |
66 |
66 |
1.653 |
6 |
6 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
Ag |
Eg |
Au |
Eu |
linear |
1 |
5 |
5 |
6 |
6 |
quadratic |
2 |
97 |
97 |
90 |
90 |
cubic |
3 |
1.085 |
1.080 |
1.104 |
1.098 |
quartic |
4 |
9.855 |
9.855 |
9.780 |
9.780 |
quintic |
5 |
72.561 |
72.561 |
72.738 |
72.738 |
sextic |
6 |
460.413 |
460.377 |
459.858 |
459.828 |
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