Reduction formula for point group C3
Characters for molecular motions
Motion |
E |
C3 |
(C3)2 |
Cartesian 3N |
99 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
Vibration |
93 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A |
E |
Total |
Cartesian 3N |
33 |
33 |
66 |
Translation (x,y,z) |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
2 |
Vibration |
31 |
31 |
62 |
Molecule Parameter
Number of Atoms (N) |
33 |
Number of internal coordinates |
93 |
Number of independant internal coordinates |
31 |
Number of vibrational modes |
62 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
E |
Total |
Linear (IR) |
31 |
31 |
62 / 0 |
Quadratic (Raman) |
31 |
31 |
62 / 0 |
IR + Raman |
31 |
31 |
62 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3 |
(C3)2 |
linear |
1 |
93 |
0 |
0 |
quadratic |
2 |
4.371 |
0 |
0 |
cubic |
3 |
138.415 |
31 |
31 |
quartic |
4 |
3.321.960 |
0 |
0 |
quintic |
5 |
64.446.024 |
0 |
0 |
sextic |
6 |
1.052.618.392 |
496 |
496 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
E |
linear |
1 |
31 |
31 |
quadratic |
2 |
1.457 |
1.457 |
cubic |
3 |
46.159 |
46.128 |
quartic |
4 |
1.107.320 |
1.107.320 |
quintic |
5 |
21.482.008 |
21.482.008 |
sextic |
6 |
350.873.128 |
350.872.632 |
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