Reduction formula for point group D3h
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3C'2 |
 h (xy) |
2S3 |
3v |
| Cartesian 3N |
108 |
0 |
0 |
36 |
0 |
0 |
| Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
| Vibration |
102 |
0 |
2 |
36 |
0 |
0 |
Decomposition into Irreducible representations
| Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Cartesian 3N |
12 |
12 |
24 |
6 |
6 |
12 |
72 |
| Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
| Vibration |
12 |
11 |
23 |
6 |
5 |
11 |
68 |
Molecule Parameter
| Number of Atoms (N) |
36 |
| Number of internal coordinates |
102 |
| Number of independant internal coordinates |
12 |
| Number of vibrational modes |
68 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Linear (IR) |
12 |
11 |
23 |
6 |
5 |
11 |
28 / 40 |
| Quadratic (Raman) |
12 |
11 |
23 |
6 |
5 |
11 |
46 / 22 |
| IR + Raman |
- |
11 |
23 |
6 |
- |
- |
23 / 17 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
| linear |
1 |
102 |
0 |
2 |
36 |
0 |
0 |
| quadratic |
2 |
5.253 |
0 |
53 |
699 |
0 |
51 |
| cubic |
3 |
182.104 |
34 |
104 |
9.624 |
12 |
0 |
| quartic |
4 |
4.780.230 |
0 |
1.430 |
104.790 |
0 |
1.326 |
| quintic |
5 |
101.340.876 |
0 |
2.756 |
956.592 |
0 |
0 |
| sextic |
6 |
1.807.245.622 |
595 |
26.182 |
7.590.842 |
89 |
23.426 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
| linear |
1 |
12 |
11 |
23 |
6 |
5 |
11 |
| quadratic |
2 |
522 |
470 |
992 |
380 |
379 |
759 |
| cubic |
3 |
16.011 |
15.959 |
31.947 |
14.403 |
14.351 |
28.743 |
| quartic |
4 |
407.774 |
406.396 |
814.170 |
389.646 |
389.594 |
779.240 |
| quintic |
5 |
8.525.478 |
8.524.100 |
17.049.578 |
8.366.046 |
8.364.668 |
16.730.714 |
| sextic |
6 |
151.248.888 |
151.224.084 |
302.472.630 |
149.972.005 |
149.970.627 |
299.942.379 |
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