Reduction formula for point group D3h
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3C'2 |
 h (xy) |
2S3 |
3v |
| Cartesian 3N |
324 |
0 |
0 |
24 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
| Vibration |
318 |
0 |
2 |
24 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Cartesian 3N |
31 |
27 |
58 |
23 |
27 |
50 |
216 |
| Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
| Vibration |
31 |
26 |
57 |
23 |
26 |
49 |
212 |
Molecule Parameter
| Number of Atoms (N) |
108 |
| Number of internal coordinates |
318 |
| Number of independant internal coordinates |
31 |
| Number of vibrational modes |
212 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Linear (IR) |
31 |
26 |
57 |
23 |
26 |
49 |
83 / 129 |
| Quadratic (Raman) |
31 |
26 |
57 |
23 |
26 |
49 |
137 / 75 |
| IR + Raman |
- |
26 |
57 |
23 |
- |
- |
57 / 49 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
| linear |
1 |
318 |
0 |
2 |
24 |
0 |
8 |
| quadratic |
2 |
50.721 |
0 |
161 |
447 |
0 |
191 |
| cubic |
3 |
5.410.240 |
106 |
320 |
6.128 |
8 |
1.360 |
| quartic |
4 |
434.171.760 |
0 |
13.040 |
72.528 |
0 |
18.000 |
| quintic |
5 |
27.960.661.344 |
0 |
25.760 |
741.552 |
0 |
116.112 |
| sextic |
6 |
1.505.215.602.352 |
5.671 |
708.400 |
6.858.544 |
85 |
1.120.816 |
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 |
31 |
26 |
57 |
23 |
26 |
49 |
| quadratic |
2 |
4.352 |
4.176 |
8.528 |
4.182 |
4.197 |
8.379 |
| cubic |
3 |
451.803 |
450.963 |
902.709 |
450.099 |
450.619 |
900.669 |
| quartic |
4 |
36.194.784 |
36.179.264 |
72.374.048 |
36.173.696 |
36.176.176 |
72.349.872 |
| quintic |
5 |
2.330.152.376 |
2.330.081.440 |
4.660.233.816 |
2.329.970.728 |
2.330.015.904 |
4.659.986.632 |
| sextic |
6 |
125.435.663.338 |
125.434.748.730 |
250.870.409.190 |
125.433.959.811 |
125.434.166.019 |
250.868.123.037 |
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