Reduction formula for point group D3h
Characters for molecular motions
| Motion |
E |
2C3 (z) |
3C'2 |
 h (xy) |
2S3 |
3v |
| Cartesian 3N |
102 |
0 |
0 |
0 |
0 |
14 |
| Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
| Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
| Vibration |
96 |
0 |
2 |
0 |
0 |
14 |
Decomposition into Irreducible representations
| Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Cartesian 3N |
12 |
5 |
17 |
5 |
12 |
17 |
68 |
| Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
| Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
| Vibration |
12 |
4 |
16 |
5 |
11 |
16 |
64 |
Molecule Parameter
| Number of Atoms (N) |
34 |
| Number of internal coordinates |
96 |
| Number of independant internal coordinates |
12 |
| Number of vibrational modes |
64 |
Force field analysis
Allowed / forbidden vibronational transitions
| Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
| Linear (IR) |
12 |
4 |
16 |
5 |
11 |
16 |
27 / 37 |
| Quadratic (Raman) |
12 |
4 |
16 |
5 |
11 |
16 |
44 / 20 |
| IR + Raman |
- |
4 |
16 |
5 |
- |
- |
16 / 9 |
Characters of symmetric powers for vibration representation
| Force field |
Tensor
Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
| linear |
1 |
96 |
0 |
2 |
0 |
0 |
14 |
| quadratic |
2 |
4.656 |
0 |
50 |
48 |
0 |
146 |
| cubic |
3 |
152.096 |
32 |
98 |
0 |
0 |
1.134 |
| quartic |
4 |
3.764.376 |
0 |
1.274 |
1.176 |
0 |
7.546 |
| quintic |
5 |
75.287.520 |
0 |
2.450 |
0 |
0 |
43.582 |
| sextic |
6 |
1.267.339.920 |
528 |
22.050 |
19.600 |
16 |
227.458 |
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 |
4 |
16 |
5 |
11 |
16 |
| quadratic |
2 |
441 |
343 |
784 |
360 |
408 |
768 |
| cubic |
3 |
12.988 |
12.372 |
25.344 |
12.421 |
12.939 |
25.344 |
| quartic |
4 |
316.001 |
311.591 |
627.592 |
312.032 |
315.168 |
627.200 |
| quintic |
5 |
6.285.468 |
6.262.452 |
12.547.920 |
6.263.677 |
6.284.243 |
12.547.920 |
| sextic |
6 |
105.675.761 |
105.551.007 |
211.226.496 |
105.558.760 |
105.661.464 |
211.219.968 |
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