Reduction formula for point group D3
Characters for molecular motions
Motion |
E |
2C3 (z) |
3C'2 |
Cartesian 3N |
60 |
0 |
-2 |
Translation (x,y,z) |
3 |
0 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
Vibration |
54 |
0 |
0 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
E |
Total |
Cartesian 3N |
9 |
11 |
20 |
40 |
Translation (x,y,z) |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
Vibration |
9 |
9 |
18 |
36 |
Molecule Parameter
Number of Atoms (N) |
20 |
Number of internal coordinates |
54 |
Number of independant internal coordinates |
9 |
Number of vibrational modes |
36 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
E |
Total |
Linear (IR) |
9 |
9 |
18 |
27 / 9 |
Quadratic (Raman) |
9 |
9 |
18 |
27 / 9 |
IR + Raman |
- |
- |
18 |
18 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3C'2 |
linear |
1 |
54 |
0 |
0 |
quadratic |
2 |
1.485 |
0 |
27 |
cubic |
3 |
27.720 |
18 |
0 |
quartic |
4 |
395.010 |
0 |
378 |
quintic |
5 |
4.582.116 |
0 |
0 |
sextic |
6 |
45.057.474 |
171 |
3.654 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
E |
linear |
1 |
9 |
9 |
18 |
quadratic |
2 |
261 |
234 |
495 |
cubic |
3 |
4.626 |
4.626 |
9.234 |
quartic |
4 |
66.024 |
65.646 |
131.670 |
quintic |
5 |
763.686 |
763.686 |
1.527.372 |
sextic |
6 |
7.511.463 |
7.507.809 |
15.019.101 |
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