Reduction formula for point group C3
Characters for molecular motions
Motion |
E |
C3 |
(C3)2 |
Cartesian 3N |
21 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
0 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
Vibration |
15 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A |
E |
Total |
Cartesian 3N |
7 |
7 |
14 |
Translation (x,y,z) |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
1 |
1 |
2 |
Vibration |
5 |
5 |
10 |
Molecule Parameter
Number of Atoms (N) |
7 |
Number of internal coordinates |
15 |
Number of independant internal coordinates |
5 |
Number of vibrational modes |
10 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A |
E |
Total |
Linear (IR) |
5 |
5 |
10 / 0 |
Quadratic (Raman) |
5 |
5 |
10 / 0 |
IR + Raman |
5 |
5 |
10 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
C3 |
(C3)2 |
linear |
1 |
15 |
0 |
0 |
quadratic |
2 |
120 |
0 |
0 |
cubic |
3 |
680 |
5 |
5 |
quartic |
4 |
3.060 |
0 |
0 |
quintic |
5 |
11.628 |
0 |
0 |
sextic |
6 |
38.760 |
15 |
15 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A |
E |
linear |
1 |
5 |
5 |
quadratic |
2 |
40 |
40 |
cubic |
3 |
230 |
225 |
quartic |
4 |
1.020 |
1.020 |
quintic |
5 |
3.876 |
3.876 |
sextic |
6 |
12.930 |
12.915 |
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