Reduction formula for point group C3
Characters for molecular motions
| Motion |
E |
C3 |
(C3)2 |
| Cartesian 3N |
252 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
0 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
0 |
| Vibration |
246 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A |
E |
Total |
| Cartesian 3N |
84 |
84 |
168 |
| Translation (x,y,z) |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
1 |
1 |
2 |
| Vibration |
82 |
82 |
164 |
Molecule Parameter
| Number of Atoms (N) |
84 |
| Number of internal coordinates |
246 |
| Number of independant internal coordinates |
82 |
| Number of vibrational modes |
164 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A |
E |
Total |
| Linear (IR) |
82 |
82 |
164 / 0 |
| Quadratic (Raman) |
82 |
82 |
164 / 0 |
| IR + Raman |
82 |
82 |
164 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
C3 |
(C3)2 |
| linear |
1 |
246 |
0 |
0 |
| quadratic |
2 |
30.381 |
0 |
0 |
| cubic |
3 |
2.511.496 |
82 |
82 |
| quartic |
4 |
156.340.626 |
0 |
0 |
| quintic |
5 |
7.817.031.300 |
0 |
0 |
| sextic |
6 |
327.012.476.050 |
3.403 |
3.403 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A |
E |
| linear |
1 |
82 |
82 |
| quadratic |
2 |
10.127 |
10.127 |
| cubic |
3 |
837.220 |
837.138 |
| quartic |
4 |
52.113.542 |
52.113.542 |
| quintic |
5 |
2.605.677.100 |
2.605.677.100 |
| sextic |
6 |
109.004.160.952 |
109.004.157.549 |
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