Reduction formula for point group D3
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3C'2 |
| Cartesian 3N |
90 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
-1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
| Vibration |
84 |
0 |
2 |
Decomposition into Irreducible representations
| Motion |
A1 |
A2 |
E |
Total |
| Cartesian 3N |
15 |
15 |
30 |
60 |
| Translation (x,y,z) |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
2 |
| Vibration |
15 |
13 |
28 |
56 |
Molecule Parameter
| Number of Atoms (N) |
30 |
| Number of internal coordinates |
84 |
| Number of independant internal coordinates |
15 |
| Number of vibrational modes |
56 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1 |
A2 |
E |
Total |
| Linear (IR) |
15 |
13 |
28 |
41 / 15 |
| Quadratic (Raman) |
15 |
13 |
28 |
43 / 13 |
| IR + Raman |
- |
- |
28 |
28 / 0 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3C'2 |
| linear |
1 |
84 |
0 |
2 |
| quadratic |
2 |
3.570 |
0 |
44 |
| cubic |
3 |
102.340 |
28 |
86 |
| quartic |
4 |
2.225.895 |
0 |
989 |
| quintic |
5 |
39.175.752 |
0 |
1.892 |
| sextic |
6 |
581.106.988 |
406 |
15.136 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1 |
A2 |
E |
| linear |
1 |
15 |
13 |
28 |
| quadratic |
2 |
617 |
573 |
1.190 |
| cubic |
3 |
17.109 |
17.023 |
34.104 |
| quartic |
4 |
371.477 |
370.488 |
741.965 |
| quintic |
5 |
6.530.238 |
6.528.346 |
13.058.584 |
| sextic |
6 |
96.858.868 |
96.843.732 |
193.702.194 |
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