Reduction formula for point group D3h
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3C'2 |
 h (xy) |
2S3 |
3v |
| Cartesian 3N |
216 |
0 |
-8 |
72 |
0 |
8 |
| Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
| Vibration |
210 |
0 |
-6 |
72 |
0 |
8 |
Decomposition into Irreducible representations
| Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Cartesian 3N |
24 |
24 |
48 |
8 |
16 |
24 |
144 |
| Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
| Vibration |
24 |
23 |
47 |
8 |
15 |
23 |
140 |
Molecule Parameter
| Number of Atoms (N) |
72 |
| Number of internal coordinates |
210 |
| Number of independant internal coordinates |
24 |
| Number of vibrational modes |
140 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Linear (IR) |
24 |
23 |
47 |
8 |
15 |
23 |
62 / 78 |
| Quadratic (Raman) |
24 |
23 |
47 |
8 |
15 |
23 |
94 / 46 |
| IR + Raman |
- |
23 |
47 |
8 |
- |
- |
47 / 31 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
| linear |
1 |
210 |
0 |
-6 |
72 |
0 |
8 |
| quadratic |
2 |
22.155 |
0 |
123 |
2.697 |
0 |
137 |
| cubic |
3 |
1.565.620 |
70 |
-668 |
69.792 |
24 |
928 |
| quartic |
4 |
83.369.265 |
0 |
7.521 |
1.399.197 |
0 |
9.117 |
| quintic |
5 |
3.568.204.542 |
0 |
-37.482 |
23.121.576 |
0 |
54.120 |
| sextic |
6 |
127.860.662.755 |
2.485 |
305.731 |
327.363.605 |
323 |
397.333 |
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 |
24 |
23 |
47 |
8 |
15 |
23 |
| quadratic |
2 |
2.136 |
2.006 |
4.142 |
1.618 |
1.625 |
3.243 |
| cubic |
3 |
136.365 |
136.235 |
272.553 |
124.261 |
125.059 |
249.297 |
| quartic |
4 |
7.068.198 |
7.059.879 |
14.128.077 |
6.830.440 |
6.831.238 |
13.661.678 |
| quintic |
5 |
299.281.336 |
299.273.017 |
598.554.353 |
295.400.680 |
295.446.481 |
590.847.161 |
| sextic |
6 |
10.682.511.764 |
10.682.160.232 |
21.364.670.592 |
10.627.752.389 |
10.627.798.190 |
21.255.549.498 |
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