Reduction formula for point group D3h
Characters for molecular motions
Motion |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
Cartesian 3N |
33 |
0 |
-3 |
7 |
-2 |
7 |
Translation (x,y,z) |
3 |
0 |
-1 |
1 |
-2 |
1 |
Rotation (Rx,Ry,Rz) |
3 |
0 |
-1 |
-1 |
2 |
-1 |
Vibration |
27 |
0 |
-1 |
7 |
-2 |
7 |
Decomposition into Irreducible representations
Motion |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
Cartesian 3N |
4 |
2 |
7 |
0 |
5 |
4 |
22 |
Translation (x,y,z) |
0 |
0 |
1 |
0 |
1 |
0 |
2 |
Rotation (Rx,Ry,Rz) |
0 |
1 |
0 |
0 |
0 |
1 |
2 |
Vibration |
4 |
1 |
6 |
0 |
4 |
3 |
18 |
Molecule Parameter
Number of Atoms (N) |
11 |
Number of internal coordinates |
27 |
Number of independant internal coordinates |
4 |
Number of vibrational modes |
18 |
Force field analysis
Allowed / forbidden vibronational transitions
Operator |
A'1 |
A'2 |
E' |
A''1 |
A''2 |
E'' |
Total |
Linear (IR) |
4 |
1 |
6 |
0 |
4 |
3 |
10 / 8 |
Quadratic (Raman) |
4 |
1 |
6 |
0 |
4 |
3 |
13 / 5 |
IR + Raman |
- |
1 |
6 |
0 |
- |
- |
6 / 1 |
Characters of symmetric powers for vibration representation
Force field |
Tensor Order |
E |
2C3 (z) |
3C'2 |
h (xy) |
2S3 |
3v |
linear |
1 |
27 |
0 |
-1 |
7 |
-2 |
7 |
quadratic |
2 |
378 |
0 |
14 |
38 |
2 |
38 |
cubic |
3 |
3.654 |
9 |
-14 |
154 |
1 |
154 |
quartic |
4 |
27.405 |
0 |
105 |
545 |
-4 |
545 |
quintic |
5 |
169.911 |
0 |
-105 |
1.687 |
4 |
1.687 |
sextic |
6 |
906.192 |
45 |
560 |
4.784 |
5 |
4.784 |
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 |
4 |
1 |
6 |
0 |
4 |
3 |
quadratic |
2 |
48 |
22 |
69 |
22 |
34 |
57 |
cubic |
3 |
354 |
284 |
633 |
251 |
335 |
582 |
quartic |
4 |
2.491 |
2.166 |
4.659 |
2.129 |
2.349 |
4.476 |
quintic |
5 |
14.696 |
13.905 |
28.599 |
13.570 |
14.466 |
28.038 |
sextic |
6 |
77.259 |
74.587 |
151.821 |
74.068 |
76.180 |
150.228 |
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