Reduction formula for point group D3
Characters for molecular motions
Motion |
E |
2C3 (z) |
3C'2 |
Cartesian 3N |
75 |
0 |
-1 |
Translation (x,y,z) |
3 |
0 |
-1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
Vibration |
69 |
0 |
1 |
Decomposition into Irreducible representations
Motion |
A1 |
A2 |
E |
Total |
Cartesian 3N |
12 |
13 |
25 |
50 |
Translation (x,y,z) |
0 |
1 |
1 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
Vibration |
12 |
11 |
23 |
46 |
Molecule Parameter
Number of Atoms (N) |
25 |
Number of internal coordinates |
69 |
Number of independant internal coordinates |
12 |
Number of vibrational modes |
46 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A1 |
A2 |
E |
Total |
Linear (IR) |
12 |
11 |
23 |
34 / 12 |
Quadratic (Raman) |
12 |
11 |
23 |
35 / 11 |
IR + Raman |
- |
- |
23 |
23 / 0 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3C'2 |
linear |
1 |
69 |
0 |
1 |
quadratic |
2 |
2.415 |
0 |
35 |
cubic |
3 |
57.155 |
23 |
35 |
quartic |
4 |
1.028.790 |
0 |
630 |
quintic |
5 |
15.020.334 |
0 |
630 |
sextic |
6 |
185.250.786 |
276 |
7.770 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field |
Tensor Order |
A1 |
A2 |
E |
linear |
1 |
12 |
11 |
23 |
quadratic |
2 |
420 |
385 |
805 |
cubic |
3 |
9.551 |
9.516 |
19.044 |
quartic |
4 |
171.780 |
171.150 |
342.930 |
quintic |
5 |
2.503.704 |
2.503.074 |
5.006.778 |
sextic |
6 |
30.879.108 |
30.871.338 |
61.750.170 |
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