Reduction formula for point group D3d
Characters for molecular motions
| Motion |
E |
2C3 |
3C'2 |
i |
2S6 |
3 d |
| Cartesian 3N |
180 |
0 |
0 |
0 |
0 |
4 |
| Translation (x,y,z) |
3 |
0 |
-1 |
-3 |
0 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
3 |
0 |
-1 |
| Vibration |
174 |
0 |
2 |
0 |
0 |
4 |
Decomposition into Irreducible representations
| Motion |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Cartesian 3N |
16 |
14 |
30 |
14 |
16 |
30 |
120 |
| Translation (x,y,z) |
0 |
0 |
0 |
0 |
1 |
1 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
1 |
0 |
0 |
0 |
2 |
| Vibration |
16 |
13 |
29 |
14 |
15 |
29 |
116 |
Molecule Parameter
| Number of Atoms (N) |
60 |
| Number of internal coordinates |
174 |
| Number of independant internal coordinates |
16 |
| Number of vibrational modes |
116 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
Total |
| Linear (IR) |
16 |
13 |
29 |
14 |
15 |
29 |
44 / 72 |
| Quadratic (Raman) |
16 |
13 |
29 |
14 |
15 |
29 |
45 / 71 |
| IR + Raman |
- |
13 |
- |
14 |
- |
- |
0* / 27 |
* 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 |
174 |
0 |
2 |
0 |
0 |
4 |
| quadratic |
2 |
15.225 |
0 |
89 |
87 |
0 |
95 |
| cubic |
3 |
893.200 |
58 |
176 |
0 |
0 |
360 |
| quartic |
4 |
39.524.100 |
0 |
4.004 |
3.828 |
0 |
4.540 |
| quintic |
5 |
1.407.057.960 |
0 |
7.832 |
0 |
0 |
16.376 |
| sextic |
6 |
41.977.229.140 |
1.711 |
121.396 |
113.564 |
29 |
145.604 |
Decomposition into Irreducible representations
Number of nonvanshing force constants
| Force field |
Tensor
Order |
A1g |
A2g |
Eg |
A1u |
A2u |
Eu |
| linear |
1 |
16 |
13 |
29 |
14 |
15 |
29 |
| quadratic |
2 |
1.322 |
1.230 |
2.552 |
1.260 |
1.263 |
2.523 |
| cubic |
3 |
74.577 |
74.309 |
148.857 |
74.397 |
74.489 |
148.857 |
| quartic |
4 |
3.296.130 |
3.291.858 |
6.587.988 |
3.293.222 |
3.293.490 |
6.586.712 |
| quintic |
5 |
117.260.882 |
117.248.778 |
234.509.660 |
117.252.694 |
117.256.966 |
234.509.660 |
| sextic |
6 |
3.498.178.932 |
3.498.045.432 |
6.996.223.494 |
3.498.087.193 |
3.498.099.297 |
6.996.185.649 |
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