Reduction formula for point group D3
Characters for molecular motions
Motion |
E |
2C3 (z) |
3C'2 |
Cartesian 3N |
324 |
0 |
0 |
Translation (x,y,z) |
3 |
0 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
Vibration |
318 |
0 |
2 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
E |
Total |
Cartesian 3N |
54 |
54 |
108 |
216 |
Translation (x,y,z) |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
Vibration |
54 |
52 |
106 |
212 |
Molecule Parameter
Number of Atoms (N) |
108 |
Number of internal coordinates |
318 |
Number of independant internal coordinates |
54 |
Number of vibrational modes |
212 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
E |
Total |
Linear (IR) |
54 |
52 |
106 |
158 / 54 |
Quadratic (Raman) |
54 |
52 |
106 |
160 / 52 |
IR + Raman |
- |
- |
106 |
106 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3C'2 |
linear |
1 |
318 |
0 |
2 |
quadratic |
2 |
50.721 |
0 |
161 |
cubic |
3 |
5.410.240 |
106 |
320 |
quartic |
4 |
434.171.760 |
0 |
13.040 |
quintic |
5 |
27.960.661.344 |
0 |
25.760 |
sextic |
6 |
1.505.215.602.352 |
5.671 |
708.400 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
E |
linear |
1 |
54 |
52 |
106 |
quadratic |
2 |
8.534 |
8.373 |
16.907 |
cubic |
3 |
901.902 |
901.582 |
1.803.378 |
quartic |
4 |
72.368.480 |
72.355.440 |
144.723.920 |
quintic |
5 |
4.660.123.104 |
4.660.097.344 |
9.320.220.448 |
sextic |
6 |
250.869.623.149 |
250.868.914.749 |
501.738.532.227 |
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