Reduction formula for point group C3
Characters for molecular motions
Motion |
E |
C3 |
(C3)2 |
Cartesian 3N |
33 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
Vibration |
27 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A |
E |
Total |
Cartesian 3N |
11 |
11 |
22 |
Translation (x,y,z) |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
2 |
Vibration |
9 |
9 |
18 |
Molecule Parameter
Number of Atoms (N) |
11 |
Number of internal coordinates |
27 |
Number of independant internal coordinates |
9 |
Number of vibrational modes |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
E |
Total |
Linear (IR) |
9 |
9 |
18 / 0 |
Quadratic (Raman) |
9 |
9 |
18 / 0 |
IR + Raman |
9 |
9 |
18 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3 |
(C3)2 |
linear |
1 |
27 |
0 |
0 |
quadratic |
2 |
378 |
0 |
0 |
cubic |
3 |
3.654 |
9 |
9 |
quartic |
4 |
27.405 |
0 |
0 |
quintic |
5 |
169.911 |
0 |
0 |
sextic |
6 |
906.192 |
45 |
45 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
E |
linear |
1 |
9 |
9 |
quadratic |
2 |
126 |
126 |
cubic |
3 |
1.224 |
1.215 |
quartic |
4 |
9.135 |
9.135 |
quintic |
5 |
56.637 |
56.637 |
sextic |
6 |
302.094 |
302.049 |
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