Reduction formula for point group C3
Characters for molecular motions
Motion |
E |
C3 |
(C3)2 |
Cartesian 3N |
240 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
Vibration |
234 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A |
E |
Total |
Cartesian 3N |
80 |
80 |
160 |
Translation (x,y,z) |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
2 |
Vibration |
78 |
78 |
156 |
Molecule Parameter
Number of Atoms (N) |
80 |
Number of internal coordinates |
234 |
Number of independant internal coordinates |
78 |
Number of vibrational modes |
156 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
E |
Total |
Linear (IR) |
78 |
78 |
156 / 0 |
Quadratic (Raman) |
78 |
78 |
156 / 0 |
IR + Raman |
78 |
78 |
156 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3 |
(C3)2 |
linear |
1 |
234 |
0 |
0 |
quadratic |
2 |
27.495 |
0 |
0 |
cubic |
3 |
2.162.940 |
78 |
78 |
quartic |
4 |
128.154.195 |
0 |
0 |
quintic |
5 |
6.100.139.682 |
0 |
0 |
sextic |
6 |
242.988.897.333 |
3.081 |
3.081 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
E |
linear |
1 |
78 |
78 |
quadratic |
2 |
9.165 |
9.165 |
cubic |
3 |
721.032 |
720.954 |
quartic |
4 |
42.718.065 |
42.718.065 |
quintic |
5 |
2.033.379.894 |
2.033.379.894 |
sextic |
6 |
80.996.301.165 |
80.996.298.084 |
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