Reduction formula for point group D3d
Characters for molecular motions
| Motion |
E |
2C3 |
3C'2 |
i |
2S6 |
3 d |
| Cartesian 3N |
156 |
0 |
-2 |
0 |
0 |
14 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
3 |
0 |
-1 |
| Vibration |
150 |
0 |
0 |
0 |
0 |
14 |
Decomposition into Irreducible representations
| Motion |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Cartesian 3N |
16 |
10 |
26 |
9 |
17 |
26 |
104 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
16 |
9 |
25 |
9 |
16 |
25 |
100 |
Molecule Parameter
| Number of Atoms (N) |
52 |
| Number of internal coordinates |
150 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
100 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Linear (IR) |
16 |
9 |
25 |
9 |
16 |
25 |
41 / 59 |
| Quadratic (Raman) |
16 |
9 |
25 |
9 |
16 |
25 |
41 / 59 |
| IR + Raman |
- |
9 |
- |
9 |
- |
- |
0* / 18 |
* Center of inversion: Mutual Exclusion Principle
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 |
3C'2 |
i |
2S6 |
3d |
| linear |
1 |
150 |
0 |
0 |
0 |
0 |
14 |
| quadratic |
2 |
11.325 |
0 |
75 |
75 |
0 |
173 |
| cubic |
3 |
573.800 |
50 |
0 |
0 |
0 |
1.512 |
| quartic |
4 |
21.947.850 |
0 |
2.850 |
2.850 |
0 |
11.866 |
| quintic |
5 |
675.993.780 |
0 |
0 |
0 |
0 |
79.492 |
| sextic |
6 |
17.463.172.650 |
1.275 |
73.150 |
73.150 |
25 |
490.042 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
| linear |
1 |
16 |
9 |
25 |
9 |
16 |
25 |
| quadratic |
2 |
1.012 |
888 |
1.900 |
913 |
962 |
1.875 |
| cubic |
3 |
48.203 |
47.447 |
95.625 |
47.447 |
48.203 |
95.625 |
| quartic |
4 |
1.832.904 |
1.825.546 |
3.658.450 |
1.826.496 |
1.831.004 |
3.657.500 |
| quintic |
5 |
56.352.688 |
56.312.942 |
112.665.630 |
56.312.942 |
56.352.688 |
112.665.630 |
| sextic |
6 |
1.455.411.498 |
1.455.129.902 |
2.910.540.750 |
1.455.154.277 |
1.455.362.723 |
2.910.516.375 |
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